calculus early transcendentals fifth edition

Transcription

Mathematics 2014–2015 Catalog
Mathematics
2014–2015 Catalog
CLA DEC 2013
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Contents
Mathematics
Calculus�� 2
Developmental Mathematics��57
Discrete Mathematics�� 62
Finite Mathematics / Applied Calculus��66
Liberal Arts Mathematics��125
Mathematics��140
Mathematics for Education�� 148
Post-Calculus��159
Precalculus��182
Combined Author/Title Index�� 252
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Mathematics
Calculus
teaching tips on how one might use the Capstone
Exercises in class.
• Exercises – revised on actual usage: New exercises
abound in the fifth edition of CALCULUS: EARLY
TRANSCENDENTAL FUNCTIONS, International
Edition. Based on analyses of actual student usage
data, the exercise sets have been overhauled to
improve student understanding. Many exercises were
added, some were revised, and some were removed.
The results are exercise sets that effectively address
student learning needs.
CONTENTS
CALCULUS, 5E
Early Transcendental Functions, International Edition
Ron Larson, The Pennsylvania State University, The Behrend College;
Bruce H. Edwards, University of Florida
Designed for the three-semester engineering calculus
course, CALCULUS: EARLY TRANSCENDENTAL
FUNCTIONS, 5e, International Edition continues to
offer instructors and students innovative teaching
and learning resources. The Larson team always has
two main objectives for text revisions: to develop
precise, readable materials for students that clearly
define and demonstrate concepts and rules of calculus;
and to design comprehensive teaching resources for
instructors that employ proven pedagogical techniques
and save time. The Larson/ Edwards Calculus program
offers a solution to address the needs of any calculus
course and any level of calculus student. Every edition
from the first to the fifth of CALCULUS: EARLY
TRANSCENDENTAL FUNCTIONS, 5e, International
Edition has made the mastery of traditional calculus
skills a priority, while embracing the best features
of new technology and, when appropriate, calculus
reform ideas.
NEW TO THIS EDITION
• New! Capstone Exercises: The Capstone is a new type
of exercise that appears in every section. The exercise
synthesizes the main concepts of the section and
presents them in one exercise. They often contain
computational and non-computational parts. These
exercises are excellent to work through in class to
present a topic for the first time or in class homework
review. The Instructor’s Resource Manual offers
1. PREPARATION FOR CALCULUS. Graphs and Models.
Linear Models and Rates of Change. Functions and
Their Graphs. Fitting Models to Data. Inverse Functions.
Exponential and Logarithmic Functions. 2. LIMITS
AND THEIR PROPERTIES. A Preview of Calculus.
Finding Limits Graphically and Numerically. Evaluating
Limits Analytically. Continuity and One-Sided Limits.
Infinite Limits. Section Project: Graphs and Limits
of Trigonometric Functions. 3. DIFFERENTIATION.
The Derivative and the Tangent Line Problem. Basic
Differentiation Rules and Rates of Change. Product
and Quotient Rules and Higher-Order Derivatives. The
Chain Rule. Implicit Differentiation. Section Project:
Optical Illusions. Derivatives of Inverse Functions.
Related Rates. Newton’s Method. 4. APPLICATIONS
OF DIFFERENTIATION. Extrema on an Interval. Rolle’s
Theorem and the Mean Value Theorem. Increasing and
Decreasing Functions and the First Derivative Test.
Section Project: Rainbows. Concavity and the Second
Derivative Test. Limits at Infinity. A Summary of Curve
Sketching. Optimization Problems. Section Project:
Connecticut River. Differentials. 5. INTEGRATION.
Antiderivatives and Indefinite Integration. Area.
Riemann Sums and Definite Integrals. The Fundamental
Theorem of Calculus. Section Project: Demonstrating
the Fundamental Theorem. Integration by Substitution.
Numerical Integration. The Natural Logarithmic
Function: Integration. Inverse Trigonometric Functions:
Integration. Hyperbolic Functions. Section Project: St.
Louis Arch. 6. DIFFERENTIAL EQUATIONS. Slope Fields
and Euler’s Method. Differential Equations: Growth and
Decay. Differential Equations: Separation of Variables.
The Logistic Equation. First-Order Linear Differential
Equations. Section Project: Weight Loss. PredatorPrey Differential Equations. 7. APPLICATIONS OF
INTEGRATION. Area of a Region Between Two Curves.
Volume: The Disk Method. Volume: The Shell Method.
Section Project: Saturn. Arc Length and Surfaces
www.cengageasia.com
2
of Revolution. Work. Section Project: Tidal Energy.
Moments, Centers of Mass, and Centroids. Fluid Pressure
and Fluid Force. 8. Integration Techniques, L’Hôpital’s
Rule, and Improper Integrals. Basic Integration Rules.
Integration by Parts. Trigonometric Integrals. Section
Project: Power Lines. Trigonometric Substitution. Partial
Fractions. Integration by Tables and Other Integration
Techniques. Indeterminate Forms and L’Hôpital’s Rule.
Improper Integrals. 9. INFINITE SERIES. Sequences.
Series and Convergence. Section Project: Cantor’s
Disappearing Table. The Integral Test and p-Series.
Section Project: The Harmonic Series. Comparisons
of Series. Section Project: Solera Method. Alternating
Series. The Ratio and Root Tests. Taylor Polynomials
and Approximations. Power Series. Representation of
Functions by Power Series. Taylor and Maclaurin Series.
10. CONICS, PARAMETRIC EQUATIONS, AND POLAR
COORDINATES. Conics and Calculus. Plane Curves
and Parametric Equations. Section Projects: Cycloids.
Parametric Equations and Calculus. Polar Coordinates
and Polar Graphs. Section Project: Anamorphic Art. Area
and Arc Length in Polar Coordinates. Polar Equations
of Conics and Kepler’s Laws. 11. VECTORS AND THE
GEOMETRY OF SPACE. Vectors in the Plane. Space
Coordinates and Vectors in Space. The Dot Product
of Two Vectors. The Cross Product of Two Vectors
in Space. Lines and Planes in Space. Section Project:
Distances in Space. Surfaces in Space. Cylindrical
and Spherical Coordinates. 12. VECTOR-VALUED
FUNCTIONS. Vector-Valued Functions. Section Project:
Witch of Agnesi. Differentiation and Integration of
Vector-Valued Functions. Velocity and Acceleration.
Tangent Vectors and Normal Vectors. Arc Length and
Curvature. 13. FUNCTIONS OF SEVERAL VARIABLES.
Introduction to Functions of Several Variables. Limits
and Continuity. Partial Derivatives. Section Project:
Moire Fringes. Differentials. Chain Rules for Functions
of Several Variables. Directional Derivatives and
Gradients. Tangent Planes and Normal Lines. Section
Project: Wildflowers. Extrema of Functions of Two
Variables. Applications of Extrema of Functions of Two
Variables. Section Project: Building a Pipeline. Lagrange
Multipliers. 14. MULTIPLE INTEGRATION. Iterated
Integrals and Area in the Plane. Double Integrals and
Volume. Change of Variables: Polar Coordinates. Center
of Mass and Moments of Inertia. Section Project: Center
of Pressure on a Sail. Surface Area. Section Project:
Capillary Action. Triple Integrals and Applications.
Triple Integrals in Cylindrical and Spherical Coordinates.
Section Project: Wrinkled and Bumpy Spheres. Change
of Variables: Jacobians. 15. VECTOR ANALYSIS. Vector
Fields. Line Integrals. Conservative Vector Fields and
Independence of Path. Green’s Theorem. Section
Project: Hyperbolic and Trigonometric Functions.
Parametric Surfaces. Surface Integrals. Section Project:
Hyperboloid of One Sheet. Divergence Theorem. Stoke’s
Theorem.
© 2011, 1360pp, Hardback, 9780538735513
AP/HS Edition
CALCULUS, 5E
Early Transcendentals Functions
© 2011, 1360pp, Hardback, 9780538497176
CALCULUS I WITH PRECALCULUS,
INTERNATIONAL EDITION, 3E
Ron Larson, The Pennsylvania State University, The Behrend College
CALCULUS I WITH PRECALCULUS, 3e, International
Edition developed for one-year courses, is ideal for
instructors who wish to successfully bring students up
to speed algebraically within precalculus and transition
them into calculus. The Larson Calculus program has
a long history of innovation in the calculus market. It
has been widely praised by a generation of students
and professors for its solid and effective pedagogy
www.cengageasia.com
3
that addresses the needs of a broad range of teaching
and learning styles and environments. Each title is just
one component in a comprehensive calculus course
program that carefully integrates and coordinates
print, media, and technology products for successful
teaching and learning. Two primary objectives guided
the authors in writing this book: to develop precise,
readable materials for students that clearly define
and demonstrate concepts and rules of calculus and
to design comprehensive teaching resources for
and saves the instructor time.
NEW TO THIS EDITION
• Table of Contents Update: Chapter 14 has been
omitted.
• NEW! Chapter Summary gives a concise review of key
terms and concepts covered in each chapter.
• NEW! Chapter Tests have been added to each chapter
and are one page assessments of problems covering
key topics.
• NEW! Explorations, an optional discovery feature,
help students develop intuitive understanding of
calculus concepts. These can be deleted without loss
of continuity.
• UPDATED! Appropriate exercises will be labeled as
Writing About the Concepts.
• NEW! CalcChat.com reference has been added to text
exercise sets.
FEATURES
• The explanations, theorems, and definitions have
been thoroughly and critically reviewed. Exercise
sets have been carefully and extensively examined
to ensure they cover calculus and precalculus topics
appropriately.
appropriately.
• To address the changing needs of today’s
instructors and students and recognizing that
the calculus course is presented in a variety of
teaching and learning environments, the program
resources are available in print and online formats.
CONTENTS
P. PREREQUISITES. Solving Equations. Solving
Inequalities. Graphical Representation of Data.
Graphs of Equations. Linear Equations in Two Variables.
1. FUNCTIONS AND THEIR GRAPHS. Functions.
Analyzing Graphs of Functions. Transformations of
Functions. Combinations of Functions: Composite
Functions. Inverse Functions. Mathematical Modeling
and Variation. 2. POLYNOMIAL AND RATIONAL
FUNCTIONS. Quadratic Functions and Models.
Polynomial Functions of Higher Degree. Polynomial
and Synthetic Division. Complex Numbers. The
Fundamental Theorem of Algebra. Rational Functions.
3. LIMITS AND THEIR PROPERTIES. A Preview of
Calculus. Finding Limits Graphically and Numerically.
Evaluating Limits Analytically. Continuity and OneSided Limits. Infinite Limits. 4. DIFFERENTIATION
Chain Rule. Implicit Differentiation. Related Rates. 5.
APPLICATIONS OF DIFFERENTIATION. Extrema on an
Interval. Rolle’s Theorem and the Mean Value Theorem.
Increasing and Decreasing Functions and the First
Derivative Test. Concavity and the Second Derivative
Test. Limits at Infinity. A Summary of Curve Sketching.
Optimization Problems. Differentials. 6. INTEGRATION.
Theorem of Calculus. Integration by Substitution.
Applications of Integration. 7. EXPONENTIAL AND
LOGARITHMIC FUNCTIONS. Exponential Functions
and Their Graphs. Logarithmic Functions and Their
Graphs. Using Properties of Logarithms. Exponential
and Logarithmic Equations. Exponential and Logarithmic
Models. 8. EXPONENTIAL AND LOGARITHMIC
FUNCTIONS AND CALCULUS. Exponential Functions:
Differentiation and Integration. Logarithmic Functions
and Differentiation. Logarithmic Functions and
Integration. Differential Equations: Growth and
Decay. 9. TRIGONOMETRIC FUNCTIONS. Radian and
Degree Measure. Trigonometric Functions: The Unit
Circle. Right Triangle Trigonometry. Trigonometric
Functions of Any Angle. Graphs of Sine and Cosine
Functions. Graphs of Other Trigonometric Functions.
Inverse Trigonometric Functions. Applications and
Models. 10. ANALYTIC TRIGONOMETRY. Using
www.cengageasia.com
4
Fundamental Identities. Verifying Trigonometric
Identities. Solving Trigonometric Equations. Sum and
Difference Formulas. Multiple-Angle and ProductSum Formulas. 11. TRIGONOMETRIC FUNCTIONS
AND CALCULUS. Limits of Trigonometric Functions.
Trigonometric Functions: Differentiation. Trigonometric
Functions: Integration. Inverse Trigonometric Functions:
Differentiation. Inverse Trigonometric Functions:
Integration. Hyperbolic Functions. 12. TOPICS IN
ANALYTIC GEOMETRY. Introduction to Conics:
Parabolas. Ellipses and Implicit Differentiation.
Hyperbolas and Implicit Differentiation. Parametric
Equations and Calculus. Polar Coordinates and Calculus.
Graphs of Polar Coordinates. Polar Equations of Conics.
13. ADDITIONAL TOPICS IN TRIGONOMETRY. Law of
Sines. Law of Cosines. Vectors in the Plane. Vectors
and Dot Products. Trigonometric Form of a Complex
Number.
© 2012, 1056pp, Paperback, 9780840069207
calculus student. Every edition from the first to the fifth
of Calculus: Early Transcendental Functions, 5/e has
made the mastery of traditional calculus skills a priority,
while embracing the best features of new technology
and, when appropriate, calculus reform ideas.
NEW TO THIS EDITION
• New! Capstone Exercises: The Capstone is a new type
of exercise that appears in every section. These noncomputational exercises synthesize the main concepts
of the section and present them in one exercise. These
exercises are excellent to work through in class to
present a topic for the first time or as review for an
exam. The new Instructor’s Resource Manual offers
teaching tips on how one might use the Capstone
Exercises in class.
• Exercises – revised based on actual usage: New
exercises abound in the fifth edition of CALCULUS:
EARLY TRANSCENTAL FUNCTIONS. Based on
analyses of actual student usage data, the exercise
sets have been overhauled to improve student
understanding. Many exercises were added, some
were revised, and some were removed. The results
are exercise sets that effectively address student
learning needs.
FEATURES
CALCULUS OF A SINGLE VARIABLE, 5E
Early Transcendental Functions
Known for its continued excellence, CALCULUS OF
A SINGLE VARIABLE: EARLY TRANSCENDENTAL
FUNCTIONS, 5/e offers instructors and students
innovative teaching and learning resources. The
Larson team always has two main objectives for text
revisions: to develop precise, readable materials for
students that clearly define and demonstrate concepts
and rules of calculus; and to design comprehensive
teaching resources for instructors that employ proven
pedagogical techniques and save time. The Larson/
Edwards Calculus program offers a solution to address
the needs of any calculus course and any level of
• Exercise sets have been carefully examined and
revised to ensure they cover all calculus topics
appropriately. Many new exercises have been added.
• A variety of exercise types are included in each
exercise set. Questions involving skills, writing,
critical thinking, problem-solving, applications, and
real-data applications are included throughout the
text. Exercises are presented in a variety of question
formats, including matching, free response, true/false,
modeling, and fill-in the blank.
• Putnam Exam Questions—taken from the William
Lowell Putnam Mathematical Competition—offer
challenging problems that often require students
to look for creative solutions; Graphical Analysis
exercises offer the opportunity to analyze graphs;
Think About It exercises require students to use
critical reasoning skills to explore the intricacies of
calculus.
• Explanations, theorems, and definitions in the text
have been thoroughly reviewed to ensure the text is
mathematically precise and easily comprehensible.
www.cengageasia.com
5
• Clear, multi-step examples with worked-out solutions
help students learn difficult mathematical concepts.
Examples correspond to the exercises, serving as a
supportive reference for students. This is the only
text on the market where every example, proof, and
explanation begins and ends on the same page.
CONTENTS
Linear Models and Rates of Change. Functions and
Their Graphs. Fitting Models to Data. Inverse Functions.
Exponential and Logarithmic Functions. 2. LIMITS
Infinite Limits.Section Project: Graphs and Limits
of Trigonometric Functions. 3. DIFFERENTIATION.
Chain Rule. Implicit Differentiation. Section Project:
Optical Illusions. Derivatives of Inverse Functions.
Related Rates. Newton’s Method. 4. APPLICATIONS
OF DIFFERENTIATION. Extrema on an Interval. Rolle’s
Theorem and the Mean Value Theorem. Increasing and
Decreasing Functions and the First Derivative Test.
Section Project: Rainbows. Concavity and the Second
Sketching. Optimization Problems. Section Project:
Connecticut River. Differentials. 5. INTEGRATION.
Integration. Hyperbolic Functions. Section Project:
St. Louis Arch. 6. DIFFERENTIAL EQUATIONS. Slope
Fields and Euler’s Method. Differential Equations:
Growth and Decay. Differential Equations: Separation
of Variables. The Logistic Equation. First-Order Linear
Differential Equations. Section Project: Weight Loss.
Predator-Prey Differential Equations. 7. APPLICATIONS
OF INTEGRATION. Area of a Region Between Two
Curves. Volume: The Disk Method. Volume: The Shell
Method. Section Project: Saturn. Arc Length and
Surfaces of Revolution. Work. Section Project: Tidal
Energy. Moments, Centers of Mass, and Centroids.
Fluid Pressure and Fluid Force. 8. INTEGRATION
TECHNIQUES, L’HOPITAL’S RULE, AND IMPROPER
INTEGRALS. Basic Integration Rules. Integration by
Parts. Trigonometric Integrals. Section Project: Power
Lines. Trigonometric Substitution. Partial Fractions.
Integration by Tables and Other Integration Techniques.
Indeterminate Forms and L’Hôpital’s Rule. Improper
Integrals. 9. INFINITE SERIES. Sequences. Series and
Convergence. Section Project: Cantor’s Disappearing
Table. The Integral Test and p-Series. Section Project: The
Harmonic Series. Comparisons of Series. Section Project:
Solera Method. Alternating Series. The Ratio and Root
Tests. Taylor Polynomials and Approximations. Power
Series. Representation of Functions by Power Series.
Taylor and Maclaurin Series. 10. CONICS, PARAMETRIC
EQUATIONS, AND POLAR COORDINATES. Conics
and Calculus. Plane Curves and Parametric Equations.
Section Projects: Cycloids. Parametric Equations and
Calculus. Polar Coordinates and Polar Graphs. Section
Project: Anamorphic Art. Area and Arc Length in Polar
Coordinates. Polar Equations of Conics and Kepler’s
Laws.
© 2011, 944pp, Hardback, 9780538735520
© 2014, 896pp, Hardback, 9781285060330
www.cengageasia.com
6
Early Transcendental Functions
Known for its continued excellence, CALCULUS OF
A SINGLE VARIABLE: EARLY TRANSCENDENTAL
FUNCTIONS, Sixth Edition, offers instructors and
students innovative teaching and learning resources.
The Larson team always has two main objectives for
text revisions: to develop precise, readable materials for
calculus student. Every edition from the first to the sixth
of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS
has made the mastery of traditional calculus skills
a priority, while embracing the best features of new
technology and, when appropriate, calculus reform
ideas.
NEW TO THIS EDITION
• LarsonCalulus.com-This robust companion website
offers multiple tools and resources. Access to these
features is free. Students can watch videos explaining
concepts or proofs from the book, explore examples,
view three-dimensional graphs, download articles
from math journals, and much more!
• Interactive Examples-Examples throughout the
book are accompanied by interactive examples at
LarsonCalculus.com. These interactive examples
use Wolfram’s free CDF Player and allow students to
explore calculus by manipulating functions or graphs,
and observing the results.
• Proof Videos-Students can watch videos of co-author
Bruce Edwards as he explains the proofs of the
theorems in CALCULUS OF A SINGLE VARIABLE:
EARLY TRANSCENDENTAL FUNCTIONS, Sixth
Edition, at LarsonCalculus.com.
• How Do You See It?-The “How Do You See It?” feature
in each section presents a real-life problem that
students solve by visual inspection using the concepts
learned in the lesson. This exercise is excellent for
classroom discussion or test preparation.
• Remark-These hints and tips reinforce or expand
on concepts, help students learn how to study
mathematics, caution students about common
errors, address special cases, or show alternative or
additional steps to a solution of an example.
• Exercise Sets-The exercise sets have been carefully
and extensively examined to ensure they are rigorous
and relevant and include all topics our users have
suggested. The exercises have been reorganized and
titled so students can better see the connections
between examples and exercises. Multi-step, real-life
exercises reinforce problem-solving skills and mastery
of concepts by giving students the opportunity to
apply the concepts in real-life situations.
• Appendix A (Proofs of Selected Theorems) now
appears in video format on LarsonCalculus.com. The
proofs also appear in text form at CengageBrain.com.
FEATURES
• Applications-Carefully chosen applied exercises and
examples are included throughout to address the
question, “When will I use this?” These applications
are pulled from diverse sources, such as current
events, world data, industry trends, and more, and
relate to a wide range of interests.
• Writing About Concepts-Writing exercises at the
end of each section are designed to test students’
understanding of basic concepts in each section,
encouraging them to verbalize and write answers
and promote technical skills that will be invaluable
in their future careers.
• Theorems-Theorems provide the conceptual
framework for calculus. Theorems are clearly stated
and separated from the rest of the text by boxes for
quick visual reference. Key proofs often follow the
theorem and can be found on LarsonCalculus.com.
CONTENTS
1. PREPARATION FOR CALCULUS. Graphs and
www.cengageasia.com
7
Models. Linear Models and Rates of Change. Functions
and Their Graphs. Fitting Models to Data. Inverse
Functions. Exponential and Logarithmic Functions.
Review Exercises. P.S. Problem Solving. 2. LIMITS
Infinite Limits. Section Project: Graphs and Limits of
Trigonometric Functions. Review Exercises. P.S. Problem
Solving. 3. DIFFERENTIATION. The Derivative and
the Tangent Line Problem. Basic Differentiation Rules
and Rates of Change. Product and Quotient Rules and
Higher-Order Derivatives. The Chain Rule. Implicit
Differentiation. Section Project: Optical Illusions.
Derivatives of Inverse Functions, Related Rates. Newton’s
Method. Review Exercises. P.S. Problem Solving. 4.
Derivative Test. Section Project: Rainbows. Concavity
and the Second Derivative Test. Limits at Infinity. A
Summary of Curve Sketching. Optimization Problems.
Section Project: Connecticut River. Differentials. Review
Exercises. P.S. Problem Solving. 5. INTEGRATION.
Louis Arch. Review Exercises. P.S. Problem Solving. 6.
DIFFERENTIAL EQUATIONS. Slope Fields and Euler’s
Method. Differential Equations: Growth and Decay.
Differential Equations: Separation of Variables. The
Logistic Equation. First-Order Linear Differential
Equations. Section Project: Weight Loss. Predator-Prey
Differential Equations. Review Exercises. P.S. Problem
Solving. 7. APPLICATIONS OF INTEGRATION. Area
of a Region Between Two Curves. Volume: The Disk
Method. Volume: The Shell Method. Section Project:
Saturn. Arc Length and Surfaces of Revolution. Work.
Section Project: Tidal Energy. Moments, Centers of
Mass, and Centroids. Fluid Pressure and Fluid Force.
Review Exercises. P.S. Problem Solving. 8. INTEGRATION
Indeterminate Forms and L’Hopital’s Rule. Improper
Integrals. Review Exercises. P.S. Problem Solving. 9.
INFINITE SERIES. Sequences. Series and Convergence.
Section Project: Cantor’s Disappearing Table. The
Integral Test and p-Series. Section Project: The Harmonic
Series. Comparisons of Series. Section Project: Solera
Method. Alternating Series. The Ratio and Root Tests.
Taylor Polynomials and Approximations. Power Series.
Representation of Functions by Power Series. Taylor and
Maclaurin Series. Review Exercises. P.S. Problem Solving.
and Parametric Equations. Section Project: Cycloids.
and Arc Length in Polar Coordinates. Polar Equations of
Conics and Kepler’s Laws. Review Exercises. P.S. Problem
Solving. Appendix A: Proofs of Selected Theorems
(Web). Appendix B: Integration Tables. Appendix C:
Pre-calculus Review (Web). Appendix C1: Real Numbers
and the Real Number Line. Appendix C2: The Cartesian
Plane. Appendix C3: Review of Trigonometric Functions.
Appendix D: Rotation and the General Second-Degree
Equation (Web). Appendix E: Complex Numbers (Web).
© 2015, 896pp, Hardback, 9781285774794
CALCULUS OF A SINGLE VARIABLE,
HYBRID, 6E
Early Transcendental Functions (with Enhanced
WebAssign Homework and eBook LOE Printed Access
Card for Multi Term Math and Science)
Reflecting Cengage Learning’s commitment to offering
flexible teaching solutions and value for students
and instructors, these hybrid versions feature the
instructional presentation found in the printed text
while delivering end-of-section exercises online in
Enhanced WebAssign®. The result—a briefer printed
text that engages students online! Known for its
www.cengageasia.com
8
continued excellence, CALCULUS OF A SINGLE
VARIABLE: EARLY TRANSCENDENTAL FUNCTIONS,
Sixth Edition offers instructors and students innovative
teaching and learning resources. The Larson team
always has two main objectives for text revisions:
to develop precise, readable materials for students
that clearly define and demonstrate concepts and
rules of calculus; and to design comprehensive
ideas.
NEW TO THIS EDITION
• LarsonCalulus.com – This robust companion website
• Interactive Examples – Examples throughout the
book are accompanied by Interactive Examples at
• Proof Videos – Students can watch videos of coauthor Bruce Edwards as he explains the proofs of
the theorems in CALCULUS OF A SINGLE VARIABLE:
EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition
at LarsonCalculus.com.
• How Do You See It? – The How Do You See It? feature
• Remark – These hints and tips reinforce or expand
upon concepts, help students learn how to study
• Exercise Sets – The exercise sets have been carefully
FEATURES
• Applications – Carefully chosen applied exercises
and examples are included throughout to address the
• Writing About Concepts – Writing exercises at the
• Theorems – Theorems provide the conceptual
CONTENTS
Linear Models and Rates of Change. Functions
Review Exercises. P.S. Problem Solving. 2. LIMITS AND
THEIR PROPERTIES. A Preview of Calculus. Finding
Limits Graphically and Numerically. Evaluating Limits
Analytically. Continuity and One-Sided Limits. Infinite
Limits. Review Exercises. P.S. Problem Solving. 3.
DIFFERENTIATION. The Derivative and the Tangent
Line Problem. Basic Differentiation Rules and Rates of
Change. Product and Quotient Rules and Higher-Order
Derivatives. The Chain Rule. Implicit Differentiation.
Derivatives of Inverse Functions. Related Rates.
Newton’s Method. Review Exercises. P.S. Problem
Solving. 4. APPLICATIONS OF DIFFERENTIATION.
www.cengageasia.com
9
Extrema on an Interval. Rolle’s Theorem and the Mean
Value Theorem. Increasing and Decreasing Functions
and the First Derivative Test. Concavity and the Second
Sketching. Optimization Problems. Differentials. Review
Integration. Hyperbolic Functions. Review Exercises.
P.S. Problem Solving. 6. DIFFERENTIAL EQUATIONS.
Slope Fields and Euler’s Method. Differential Equations:
Differential Equations. Predator-Prey Differential
Equations. Review Exercises. P.S. Problem Solving. 7.
APPLICATIONS OF INTEGRATION. Area of a Region
Between Two Curves. Volume: The Disk Method.
Volume: The Shell Method. Arc Length and Surfaces
of Revolution. Work. Moments, Centers of Mass, and
Centroids. Fluid Pressure and Fluid Force. Review
Exercises. P.S. Problem Solving. 8. INTEGRATION
INTEGRALS. Basic Integration Rules. Integration
by Parts. Trigonometric Integrals. Trigonometric
Substitution. Partial Fractions. Integration by Tables and
Other Integration Techniques. Indeterminate Forms and
L’Hôpital’s Rule. Improper Integrals. Review Exercises.
P.S. Problem Solving. 9. INFINITE SERIES. Sequences.
Series and Convergence. Section Project: Cantor’s
Disappearing Table. The Integral Test and p-Series.
Comparisons of Series. Alternating Series. The Ratio
and Root Tests. Taylor Polynomials and Approximations.
Power Series. Representation of Functions by Power
Series. Taylor and Maclaurin Series. Review Exercises.
P.S. Problem Solving. 10. CONICS, PARAMETRIC
EQUATIONS, AND POLAR COORDINATES. Conics
and Calculus. Plane Curves and Parametric Equations.
and Polar Graphs. Area and Arc Length in Polar
Coordinates. Polar Equations of Conics and Kepler’s
Laws. Review Exercises. P.S. Problem Solving. Appendix
A: Proofs of Selected Theorems (Web). Appendix B:
Integration Tables. Appendix C: Pre-calculus Review.
(Web). Appendix C1: Real Numbers and the Real Number
Line. Appendix C2: The Cartesian Plane. Appendix
C3: Review of Trigonometric Functions. Appendix D:
Rotation and the General Second-Degree Equation
(Web). Appendix E: Complex Numbers (Web).
© 2015, 640pp, Paperback, 9781285777054
HYBRID (WITH ENHANCED WEBASSIGN
HOMEWORK AND EBOOK LOE PRINTED
ACCESS CARD FOR MULTI TERM MATH
AND SCIENCE), 10E
Larson’s CALCULUS OF A SINGLE VARIABLE HYBRID,
Tenth Edition, delivers the same solid and effective
pedagogy as his market-leading hardcover text,
CALCULUS OF A SINGLE VARIABLE, Tenth Edition,
combined with a briefer paperback format that
engages students online with Enhanced WebAssign®.
The HYBRID demonstrates Larson’s commitment to
revolutionizing the way instructors teach and students
learn material by moving all the end-of-section
exercises from the text online as well as incorporating
more real-world applications, ongoing review, and
innovative technology. Each new Larson CALCULUS
OF A SINGLE VARIABLE HYBRID includes immediate
student access to Enhanced WebAssign®. Widely
praised by a generation of students and professors for
its solid and effective pedagogy, the Larson CALCULUS
program is known for addressing the needs of a broad
range of teaching and learning styles and environments.
Each title is just one component in a comprehensive
calculus course program that carefully integrates and
coordinates print, media, and technology products for
successful teaching and learning.
www.cengageasia.com
10
NEW TO THIS EDITION
• NEW HYBRID – The HYBRID provides a cost-effective,
briefer option for students—all end-of-section
exercises are omitted from the text and appear online
only. Each new HYBRID includes immediate access to
Enhanced WebAssign® and the Cengage YouBook.
• NEW Chapter Openers - Each Chapter Opener
highlights five real-life applications of calculus found
throughout the chapter. The applications reference
the examples or exercises featured. You can find a full
listing of the applications in the Index of Applications.
• NEW HOW DO YOU SEE IT? Exercise The How Do You
See It? exercise in each section presents a problem
that you will solve by visual inspection using the
concepts learned in the lesson.
• NEW LarsonCalculus.com - We’ve created a free
website hosting valuable resources. At this website,
you can access the following: Proof Videos – Watch coauthor Bruce Edwards present theorems and explain
their proofs. Calculus Videos – Watch Dana Mosely
explain concepts of calculus. Interactive Examples –
Explore examples using Wolfram’s free CDF player
(plug-in required). Rotatable Graphs – View and
rotate three-dimensional graphs using Wolfram’s
free CDF player (plug-in required). Biographies –
Read biographies of men and women who were
instrumental in creating calculus. Web Appendices
– Read the web-only appendices that accompany
the text. Data Downloads – Use real data to solve
problems.
• Table of Contents Changes - We moved Appendix A
(Proofs of Selected Theorems) to the website www.
LarsonCalculus.com, which also includes videos of
co-author Bruce Edwards explaining these proofs.
and titled so you can better see the connections
between examples and exercises. Multi-step, reallife exercises reinforce problem-solving skills and
mastery of concepts by giving you the opportunity
to apply the concepts in real-life situations. Putnam
Exam questions to push the limits of students’
understanding of calculus. Graphing technology
exercises for students to make us of a graphing utility
to help find solutions.
• Enhanced WebAssign Course: The Larson EWA course
has over 3,900 textbook questions which have been
drawn from the book, and offer more coverage of
problems and topics than most online homework
programs for Calculus. The EWA course for Larson
CALCULUS will present numerous section-level video
lessons by Dana Mosely and animated tutorials. In
addition to these assets, the course includes exerciselevel features: Read It, Watch It, Master It, and Chat
About It links. These tools benefit students with varied
learning styles to ensure they get the most out of their
online learning experience.
• Graded Homework Exercises— Online homework and
tests are evaluated using powerful Maple software to
ensure mathematical accuracy. Instructors control
point values, weighting grades, and whether or not
an item is graded. An electronic gradebook helps
instructors manage course information easily and can
be exported to other files, such as Excel.
• CAS Investigation: Many examples throughout the
book are accompanied by CAS Investigations. These
are collaborative investigations using a computer
algebra system (e.g., Maple) to further explore the
related example. CAS Investigations are located online
and in the Multimedia eBook.
CONTENTS
FEATURES
• REVISED Remarks - To eliminate any possible
confusion, all Study Tips and Notes have been
combined into one feature, Remarks. These hints and
tips can be used to reinforce or expand upon concepts,
help you learn how to study mathematics, caution
you about common errors, address special cases, or
show alternative or additional steps to a solution of
an example.
• REVISED Exercise Sets - The exercise sets have been
carefully and extensively examined to ensure they
are rigorous, relevant, and cover all topics suggested
by our users. The exercises have been reorganized
PREPARATION FOR CALCULUS. Graphs and Models.
Linear Models and Rates of Change. Functions and Their
Graphs. Fitting Models to Data. Review Exercises. P.S.
Problem Solving. 1. LIMITS AND THEIR PROPERTIES.
A Preview of Calculus. Finding Limits Graphically and
Numerically. Evaluating Limits Analytically. Continuity
and One-Sided Limits. Infinite Limits. Section Project:
Graphs and Limits of Trigonometric Functions. Review
Exercises. P.S. Problem Solving. 2. DIFFERENTIATION.
Differentiation Rules and Rates of Change. Product and
Quotient Rules and Higher-Order Derivatives. The Chain
www.cengageasia.com
11
Rule. Implicit Differentiation. Section Project: Optical
Illusions. Related Rates. Review Exercises. P.S. Problem
and the First Derivative Test. Section Project: Rainbows.
Concavity and the Second Derivative Test. Limits at
Infinity. A Summary of Curve Sketching. Optimization
Problems. Section Project: Connecticut River. Newton’s
Method. Differentials. Review Exercises. P.S. Problem
Solving. 4. INTEGRATION. Antiderivatives and Indefinite
Integration. Area. Riemann Sums and Definite Integrals.
The Fundamental Theorem of Calculus. Section Project:
Demonstrating the Fundamental Theorem. Integration
by Substitution. Numerical Integration. Review
Exercises. P.S. Problem Solving. 5. LOGARITHMIC,
EXPONENTIAL, AND OTHER TRANSCENDENTAL
FUNCTIONS. The Natural Logarithmic Function:
Differentiation. The Natural Logarithmic Function:
Integration. Inverse Functions. Exponential Functions:
Differentiation and Integration. Bases Other than e and
Applications. Section Project: Using Graphing Utilities
to Estimate Slope. Inverse Trigonometric Functions:
Separation of Variables and the Logistic Equation.
First-Order Linear Differential Equations. Section
Project: Weight Loss. Review Exercises. P.S. Problem
Solving.
© 2014, 576pp, Paperback, 9781285097886
Larson’s CALCULUS OF A SINGLE VARIABLE, 10E,
International Edition program has a long history of
innovation in the calculus market. It has been widely
its solid and effective pedagogy that addresses the
needs of a broad range of teaching and learning styles
and environments. Each title is just one component in a
comprehensive calculus course program that carefully
integrates and coordinates print, media, and technology
products for successful teaching and learning.
NEW TO THIS EDITION
• NEW Chapter Openers – Each Chapter Opener
www.cengageasia.com
12
• NEW HOW DO YOU SEE IT? Exercise – The How
Do You See It? exercise in each section presents a
problem that you will solve by visual inspection using
the concepts learned in the lesson.
• NEW LarsonCalculus.com – We’ve created a free
problems.
• Table of Contents Changes – We moved Appendix A
FEATURES
• REVISED Remarks – To eliminate any possible
an example.
• REVISED Exercise Sets – The exercise sets have been
exercises for students to make use of a graphing utility
• Enhanced WebAssign Course: The Larson EWA
course has over 3,900 textbook questions which
have been drawn from the book, and offer more
coverage of problems and topics than most online
homework programs for Calculus. The EWA course
for Larson CALCULUS OF A SINGLE VARIABLE, 10E,
International Edition will present numerous sectionlevel video lessons by Dana Mosely and animated
tutorials. In addition to these assets, the course
includes exercise-level features: Read It, Watch It,
Master It, and Chat About It links. These tools benefit
students with varied learning styles to ensure they
get the most out of their online learning experience.
• Graded Homework Exercises: Online homework and
tests are evaluated using powerful Maple software
to ensure mathematical accuracy. Instructors control
point values, weighting grades, and whether or not
and in the eBook.
• Writing Style: Simple, mathematically precise
instruction and directions are clear and easy to
understand for students.
CONTENTS
PREPARATION FOR CALCULUS. Graphs and Models.
www.cengageasia.com
13
Exercises. P.S. Problem Solving. 5. LOGARITHMIC
EXPONENTIAL AND OTHER TRANSCENDENTAL
Section Project: Tidal Energy. Moments Centers of
Mass and Centroids. Fluid Pressure and Fluid Force.
TECHNIQUES L’HOPITAL’S RULE AND IMPROPER
10. CONICS PARAMETRIC EQUATIONS AND POLAR
Solving.
© 2014, 864pp, Paperback, 9781285091105
CALCULUS SINGLE VARIABLE WITH
VECTOR FUNCTIONS, AP*, 7E
James Stewart, McMaster University
© 2012, 948pp, Hardback, 9780840048233
CALCULUS WITH CB COURSESMART
EBOOK, 10E
CB CourseSmart eBook – The ultimate eBook experience
has arrived! Easily access our eBooks with features that
will improve your reading experience, and tools to help
you take notes and organize your studies. The Larson
CALCULUS program has a long history of innovation
www.cengageasia.com
14
in the calculus market. It has been widely praised by a
generation of students and professors for its solid and
effective pedagogy that addresses the needs of a broad
range of teaching and learning styles and environments.
Each title is just one component in a comprehensive
calculus course program that carefully integrates and
coordinates print, media, and technology products for
successful teaching and learning.
NEW TO THIS EDITION
• NEW HOW DO YOU SEE IT? Exercise - The How
Do You See It? exercise in each section presents a
problem that you will solve by visual inspection using
the concepts learned in the lesson.
problems.
FEATURES
an example.
• Second Order Differential Equations: Available online,
this chapter delves into second order differential
equations. This will greatly help engineering and
math majors.
• Enhanced WebAssign Course: The Larson EWA
course has over 3,900 textbook questions which have
been drawn from the book, and offer more coverage
of problems and topics than most online homework
addition to these assets, the course includes exerciselevel features: Read It, Watch It, Master It, and Chat
About It links. These tools benefit students with
varied learning styles to ensure they get the most out
of their online learning experience.
tests are evaluated using powerful Maple software to
ensure mathematical accuracy. Instructors control
point values, weighting grades, and whether of not
and in the Multimedia eBook
CONTENTS
P. PREPARATION FOR CALCULUS. Graphs and Models.
www.cengageasia.com
15
Exercises. P.S. Problem Solving. 5. LOGARITHMIC,
EXPONENTIAL, AND OTHER TRANSCENDENTAL
and Polar Graphs. Section Project: Anamorphic Art.
Area and Arc Length in Polar Coordinates. 10.6 Polar
Equations of Conics and Kepler’s Laws. Review Exercises.
P.S. Problem Solving. 11. VECTORS AND THE GEOMETRY
OF SPACE. Vectors in the Plane. Space Coordinates
and Vectors in Space. The Dot Product of Two Vectors.
The Cross Product of Two Vectors in Space. Lines and
Planes in Space. Section Project: Distances in Space.
Surfaces in Space. Cylindrical and Spherical Coordinates.
Review Exercises. P.S. Problem Solving. 12. VECTORVALUED FUNCTIONS. Vector-Valued Functions.
Section Project: Witch of Agnesi. Differentiation and
Integration of Vector-Valued Functions. Velocity and
Acceleration. Tangent Vectors and Normal Vectors. Arc
Length and Curvature. Review Exercises. P.S. Problem
Solving. 13. FUNCTIONS OF SEVERAL VARIABLES.
Moiré Fringes. Differentials. Chain Rules for Functions of
Several Variables. Directional Derivatives and Gradients.
Tangent Planes and Normal Lines. Section Project:
Wildflowers. Extrema of Functions of Two Variables.
Applications of Extrema of Functions of Two Variables.
Section Project: Building a Pipeline. Lagrange Multipliers.
Review Exercises. P.S. Problem Solving. 14. MULTIPLE
INTEGRATION. Iterated Integrals and Area in the Plane.
Double Integrals and Volume. Change of Variables: Polar
Coordinates. Center of Mass and Moments of Inertia.
Section Project: Center of Pressure on a Sail. Surface
www.cengageasia.com
16
Area. Section Project: Capillary Action. Triple Integrals
and Applications. Triple Integrals in Cylindrical and
Spherical Coordinates. Section Project: Wrinkled and
Bumpy Spheres. Change of Variables: Jacobians. Review
Exercises. P.S. Problem Solving. 15. VECTOR ANALYSIS.
Vector Fields. Line Integrals. Conservative Vector Fields
and Independence of Path. Green’s Theorem. Section
Project: Hyperbolic and Trigonometric Functions.
Parametric Surfaces. Surface Integrals. Section Project:
Hyperboloid of One Sheet. Divergence Theorem.
Stokes’s Theorem. Review Exercises. Section Project: The
Planimeter. P.S. Problem Solving. 16. SECOND ORDER
DIFFERENTIAL EQUATIONS* ONLINE. Exact FirstOrder Equations. Second-Order Homogeneous Linear
Equations. Second-Order Nonhomogeneous Linear
Equations. Series Solutions of Differential Equations.
Review Exercises. P.S. Problem Solving. APPENDIX. A.
Proofs of Selected Theorems. B. Integration Tables. C.
Precalculus Review (Web). C.1 Real Numbers and the
Real Number Line. C.2 The Cartesian Plane. C.3 Review
of Trigonometric Functions. D. Rotation and the General
Second-Degree Equation (Web). E. Complex Numbers
(Web). F. Business and Economic Applications (Web).
Enhanced WebAssign®. The result—a briefer printed
text that engages students online! Designed for
the three-semester engineering calculus course,
CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS,
Sixth Edition, continues to offer instructors and
students innovative teaching and learning resources.
The Larson team always has two main objectives for
text revisions: to develop precise, readable materials for
ideas.
CTE bundled with CM (9789814568876);
CTE bunled with MindTap (9789814568883)
• LarsonCalulus.com - This robust companion website
• Interactive Examples - Examples throughout the
book are accompanied by Interactive Examples at
• Proof Videos - Students can watch videos of coauthor Bruce Edwards as he explains the proofs of the
theorems in CALCULUS: EARLY TRANSCENDENTAL
FUNCTIONS, Sixth Edition at LarsonCalculus.com.
• How Do You See It? - The How Do You See It? feature
• Remark - These hints and tips reinforce or expand
upon concepts, help students learn how to study
© 2014, 832pp, Paperback, 9789814568869
CALCULUS, HYBRID, 6E
Early Transcendental Functions (with Enhanced
Card for Multi Term Math and Science)
and instructors, these hybrid versions feature the
NEW TO THIS EDITION
www.cengageasia.com
17
• Exercise Sets - The exercise sets have been carefully
FEATURES
• Applications - Carefully chosen applied exercises and
examples are included throughout to address the
• Writing About Concepts - Writing exercises at the
• Theorems - Theorems provide the conceptual
CONTENTS
Linear Models and Rates of Change. Functions
Review Exercises. P.S. Problem Solving. 2. LIMITS AND
THEIR PROPERTIES. A Preview of Calculus. Finding
Limits Graphically and Numerically. Evaluating Limits
Analytically. Continuity and One-Sided Limits. Infinite
Limits. Review Exercises. P.S. Problem Solving. 3.
DIFFERENTIATION. The Derivative and the Tangent
Line Problem. Basic Differentiation Rules and Rates of
Change. Product and Quotient Rules and Higher-Order
Derivatives. The Chain Rule. Implicit Differentiation.
Derivatives of Inverse Functions. Related Rates.
Newton’s Method. Review Exercises. P.S. Problem
and the First Derivative Test. Concavity and the Second
Sketching. Optimization Problems. Differentials. Review
Theorem of Calculus.Integration by Substitution.
Integration. Hyperbolic Functions.Review Exercises.
P.S. Problem Solving. 6. DIFFERENTIAL EQUATIONS.
Slope Fields and Euler’s Method. Differential Equations:
Differential Equations. Predator-Prey Differential
Equations. Review Exercises. P.S. Problem Solving. 7.
APPLICATIONS OF INTEGRATION. Area of a Region
Between Two Curves. Volume: The Disk Method.
Volume: The Shell Method. Arc Length and Surfaces
of Revolution. Work. Moments, Centers of Mass, and
Centroids. Fluid Pressure and Fluid Force. Review
Exercises. P.S. Problem Solving. 8. INTEGRATION
TECHNIQUES, L’HÔPITAL’S RULE, AND IMPROPER
INTEGRALS. Basic Integration Rules. Integration
Substitution. Partial Fractions. Integration by Tables
and Other Integration Techniques. Indeterminate
Forms and L’Hôpital’s Rule. Improper Integrals. Review
Exercises. P.S. Problem Solving. 9. INFINITE SERIES.
Sequences. Series and Convergence. The Integral
Test and p-Series. Comparisons of Series. Alternating
Series. The Ratio and Root Tests. Taylor Polynomials
and Approximations. Power Series. Representation
of Functions by Power Series. Taylor and Maclaurin
Series. Review Exercises. P.S. Problem Solving. 10.
CONICS, PARAMETRIC EQUATIONS, AND POLAR
and Parametric Equations. Parametric Equations and
Calculus. Polar Coordinates and Polar Graphs. Area
and Arc Length in Polar Coordinates. Polar Equations
of Conics and Kepler’s Laws. Review Exercises. P.S.
Problem Solving. 11. VECTORS AND THE GEOMETRY
www.cengageasia.com
18
Planes in Space. Surfaces in Space. Cylindrical and
Spherical Coordinates. Review Exercises. P.S. Problem
Solving. 12. VECTOR-VALUED FUNCTIONS. VectorValued Functions. Differentiation and Integration of
Vector-Valued Functions. Velocity and Acceleration.
Tangent Vectors and Normal Vectors. Arc Length and
Curvature. Review Exercises. P.S. Problem Solving. 13.
FUNCTIONS OF SEVERAL VARIABLES. Introduction to
Functions of Several Variables. Limits and Continuity.
Partial Derivatives. Differentials. Chain Rules for
Functions of Several Variables. Directional Derivatives
and Gradients. Tangent Planes and Normal Lines.
Extrema of Functions of Two Variables. Applications
of Extrema of Functions of Two Variables. Lagrange
Multipliers. Review Exercises. P.S. Problem Solving. 14.
MULTIPLE INTEGRATION. Iterated Integrals and Area
in the Plane. Double Integrals and Volume. Change
of Variables: Polar Coordinates. Center of Mass and
Moments of Inertia. Surface Area. Triple Integrals and
Applications. Triple Integrals in Cylindrical and Spherical
Coordinates. Change of Variables: Jacobians. Review
Exercises. P.S. Problem Solving. 15. VECTOR ANALYSIS.
Vector Fields. Line Integrals. Conservative Vector Fields
and Independence of Path. Green’s Theorem. Parametric
Surfaces. Surface Integrals. Divergence Theorem. Stoke’s
Theorem. Review Exercises. P.S. Problem Solving. 16.
ADDITIONAL TOPICS IN DIFFERENTIAL EQUATIONS
(Web). Exact First-Order Equations. Second-Order
Homogeneous Linear Equations. Second-Order
Nonhomogeneous Linear Equations. Series Solutions
of Differential Equations. Review Exercises. P.S. Problem
Solving. Appendix A: Proofs of Selected Theorems
(Web). Appendix B: Integration Tables. Appendix C:
Pre-calculus Review (Web). Appendix C1: Real Numbers
and the Real Number Line. Appendix C2: The Cartesian
Plane. Appendix C3: Review of Trigonometric Functions.
Appendix D: Rotation and the General Second-Degree
Equation (Web). Appendix E: Complex Numbers (Web).
© 2015, 640pp, Paperback, 9781285777023
CALCULUS, HYBRID (WITH ENHANCED
WEBASSIGN HOMEWORK AND EBOOK
LOE PRINTED ACCESS CARD FOR MULTI
TERM MATH AND SCIENCE), 10E
Larson’s CALCULUS HYBRID’ Tenth Edition’ delivers
the same solid and effective pedagogy as his marketleading hardcover text’ CALCULUS’ Tenth Edition’
combined with a briefer paperback format that
engages students online with Enhanced WebAssign®.
The HYBRID demonstrates Larson’s commitment to
revolutionizing the way instructors teach and students
learn material by moving all the end-of-section
exercises from the text online as well as incorporating
more real-world applications’ ongoing review’ and
innovative technology. Each new Larson CALCULUS
HYBRID includes immediate student access to
Enhanced WebAssign®. Widely praised by a generation
of students and professors for its solid and effective
pedagogy’ the Larson CALCULUS program is known
for addressing the needs of a broad range of teaching
print’ media’ and technology products for successful
teaching and learning.
NEW TO THIS EDITION
• NEW HYBRID - The HYBRID provides a cost-effective’
briefer option for students--all end-of-section
only. Each new HYBRID includes immediate access to
Enhanced WebAssign® and the Cengage YouBook.
www.cengageasia.com
19
website hosting valuable resources. At this website’
problems.
LarsonCalculus.com’ which also includes videos of
FEATURES
confusion’ all Study Tips and Notes have been
combined into one feature’ Remarks. These hints and
tips can be used to reinforce or expand upon concepts’
help you learn how to study mathematics’ caution
you about common errors’ address special cases’ or
an example.
are rigorous’ relevant’ and cover all topics suggested
between examples and exercises. Multi-step’ reallife exercises reinforce problem-solving skills and
• Second Order Differential Equations: Available online’
this chapter delves into second order differential
equations. This will greatly help engineering and
math majors.
• Enhanced WebAssign Course: The Larson EWA course
has over 3’900 textbook questions which have been
drawn from the book’ and offer more coverage of
problems and topics than most online homework
addition to these assets’ the course includes exerciselevel features: Read It’ Watch It’ Master It’ and Chat
About It links. These tools benefit students with varied
learning styles to ensure they get the most out of their
online learning experience.
tests are evaluated using powerful Maple software
to ensure mathematical accuracy. Instructors control
point values’ weighting grades’ and whether of not
be exported to other files’ such as Excel.
algebra system (e.g.’ Maple) to further explore the
and in the Multimedia eBook
CONTENTS
P. PREPARATION FOR CALCULUS. Graphs and Models.
www.cengageasia.com
20
Exercises. P.S. Problem Solving. 5. LOGARITHMIC’
EXPONENTIAL’ AND OTHER TRANSCENDENTAL
Section Project: Tidal Energy. Moments’ Centers of
Mass’ and Centroids. Fluid Pressure and Fluid Force.
TECHNIQUES’ L’HOPITAL’S RULE’ AND IMPROPER
10. CONICS’ PARAMETRIC EQUATIONS’ AND POLAR
and Polar Graphs. Section Project: Anamorphic Art.
Area and Arc Length in Polar Coordinates. 10.6 Polar
Equations of Conics and Kepler’s Laws. Review Exercises.
P.S. Problem Solving. 11. VECTORS AND THE GEOMETRY
Planes in Space. Section Project: Distances in Space.
Surfaces in Space. Cylindrical and Spherical Coordinates.
Review Exercises. P.S. Problem Solving. 12. VECTORVALUED FUNCTIONS. Vector-Valued Functions.
Section Project: Witch of Agnesi. Differentiation and
Integration of Vector-Valued Functions. Velocity and
Acceleration. Tangent Vectors and Normal Vectors. Arc
Length and Curvature. Review Exercises. P.S. Problem
Solving. 13. FUNCTIONS OF SEVERAL VARIABLES.
Moiré Fringes. Differentials. Chain Rules for Functions
of Several Variables. Directional Derivatives and
Gradients. Tangent Planes and Normal Lines. Section
Project: Wildflowers. Extrema of Functions of Two
Variables. Applications of Extrema of Functions of Two
Variables. Section Project: Building a Pipeline. Lagrange
Multipliers. Review Exercises. P.S. Problem Solving. 14.
MULTIPLE INTEGRATION. Iterated Integrals and Area
in the Plane. Double Integrals and Volume. Change
of Variables: Polar Coordinates. Center of Mass and
Moments of Inertia. Section Project: Center of Pressure
on a Sail. Surface Area. Section Project: Capillary Action.
Triple Integrals and Applications. Triple Integrals in
Cylindrical and Spherical Coordinates. Section Project:
Wrinkled and Bumpy Spheres. Change of Variables:
Jacobians. Review Exercises. P.S. Problem Solving.
15. VECTOR ANALYSIS. Vector Fields. Line Integrals.
Conservative Vector Fields and Independence of
Path. Green’s Theorem. Section Project: Hyperbolic
and Trigonometric Functions. Parametric Surfaces.
Surface Integrals. Section Project: Hyperboloid of
One Sheet. Divergence Theorem. Stokes’s Theorem.
Review Exercises. Section Project: The Planimeter. P.S.
Problem Solving. 16. SECOND ORDER DIFFERENTIAL
EQUATIONS* ONLINE. Exact First-Order Equations.
Second-Order Homogeneous Linear Equations. SecondOrder Nonhomogeneous Linear Equations. Series
Solutions of Differential Equations. Review Exercises.
www.cengageasia.com
21
P.S. Problem Solving. APPENDIX. A. Proofs of Selected
Theorems. B. Integration Tables. C. Precalculus Review
(Web). C.1 Real Numbers and the Real Number Line.
C.2 The Cartesian Plane. C.3 Review of Trigonometric
Functions. D. Rotation and the General Second-Degree
Equation (Web). E. Complex Numbers (Web). F. Business
and Economic Applications (Web).
© 2014, 864pp, Paperback, 9781285095004
CALCULUS, HYBRID EDITION (WITH
ENHANCED WEBASSIGN WITH EBOOK
FOR MULTI TERM MATH AND SCIENCE),
7E
value for students, these new hybrid versions feature
the same content and coverage found in the full
text while delivering end-of-section exercises online
in Enhanced WebAssign®. Access to Enhanced
WebAssign and the new media-rich Cengage YouBook is
included with every new text, giving you an interactive
learning experience with the convenience of a text that
is both brief and affordable. Success in your calculus
course starts here! James Stewart’s CALCULUS texts
are world-wide best-sellers for a reason: they are clear,
accurate, and filled with relevant, real-world examples.
With CALCULUS, Seventh Edition, Stewart conveys not
only the utility of calculus to help you develop technical
competence, but also gives you an appreciation for the
intrinsic beauty of the subject. His patient examples
and built-in learning aids will help you build your
mathematical confidence and achieve your goals in
the course.
NEW TO THIS EDITION
• TOC change: For this edition, chapters 1 and 2 have
been combined – and some material has been moved
to an appendix—to streamline the presentation of
these early topics.
• Throughout the text, the author has revised the
narrative as necessary to improve clarity and aid in
student comprehension.
• NEW examples, margin notes, applications, and
projects have been added. In addition, new collections
of more challenging exercises called “Problems Plus”
have been added, reinforcing concepts by requiring
students to apply techniques from more than one
chapter of the text. “Problems Plus” sections patiently
show students how to approach a challenging
problem.
• NEW! This edition has been updated with
approximately 25% more exercises than the previous
edition, giving students more opportunities to
practice concepts they have learned.
• NEW “PS” icons denoting problem-solving margin
notes are aimed at increasing instructors’ awareness
of this important aspect of Stewart’s approach.
• UPDATED! Tools for Enriching Calculus—a free,
online, interactive resource that allows Calculus
students to work with animations that deepen their
understanding of key concepts by helping them
visualize the concepts they are learning—has been
updated with new problems and a new Flash design
that is more visually appealing and engaging to
students.
• NEW-AND-IMPROVED! Exclusively from Cengage
Learning, Enhanced WebAssign® offers an extensive
online program for Stewart’s Calculus, 7e, to
encourage the practice that’s so critical for concept
mastery. The meticulously crafted pedagogy and
exercises in our proven texts become even more
effective in Enhanced WebAssign, supplemented by
multimedia tutorial support and immediate feedback
as students complete their assignments. Enhanced
WebAssign for Stewart now includes opportunities
for students to review prerequisite skills and content
both at the start of the course (in conjunction with
four diagnostic tests) and at the beginning of each
section. In addition, at the problem-level, student can
get extra help in the form of “math mentor” feedback
and video solutions.
• NEW! Cengage YouBook is a Flash-based eBook
that is interactive and customizable! Containing all
www.cengageasia.com
22
the content from Stewart’s Calculus, 7e, YouBook
features a text edit tool that allows you to rewrite,
delete, modify, or add to the textbook narrative as
needed. With YouBook, you can quickly re-order
entire chapters and sections or hide any content you
don’t teach to create an eBook that perfectly matches
your syllabus. Additional media assets include
interactive simulations, animations, and video clips
that complement the traditional text presentation.
The YouBook also lets you embed videos of your own
or from YouTube directly into eBook pages.
• NEW! Interested in a simple way to complement
your text and course content with study and practice
materials? Cengage Learning’s CourseMate brings
course concepts to life with interactive learning,
study, and exam preparation tools that support the
printed textbook. Watch student comprehension soar
as your class works with the printed textbook and the
textbook-specific website. CourseMate goes beyond
the book to deliver what you need!
• NEW! Hybrid versions of the text provide a lessexpensive, shorter option for students using EWA.
End-of-section problems are omitted from the text
and appear online only.
CONTENTS
Diagnostic Tests. A Preview of Calculus. 1. FUNCTIONS
AND LIMITS. Four Ways to Represent a Function.
Mathematical Models: A Catalog of Essential Functions.
New Functions from Old Functions. The Tangent and
Velocity Problems. The Limit of a Function. Calculating
Limits Using the Limit Laws. The Precise Definition of a
Limit. Continuity. Review. 2. DERIVATIVES. Derivatives
and Rates of Change. Writing Project: Writing Project:
Early Methods for Finding Tangents. The Derivative
as a Function. Differentiation Formulas. Applied
Project: Building a Better Roller Coaster. Derivatives
of Trigonometric Functions. The Chain Rule. Applied
Project: Where Should a Pilot Start Descent? Implicit
Differentiation. Laboratory Project: Families of Implicit
Curves. Rates of Change in the Natural and Social
Sciences. Related Rates. Linear Approximations and
Differentials. Laboratory Project: Taylor Polynomials.
Review. 3. APPLICATIONS OF DIFFERENTIATION.
Maximum and Minimum Values. Applied Project: The
Calculus of Rainbows. The Mean Value Theorem. How
Derivatives Affect the Shape of a Graph. Limits at
Infinity; Horizontal Asymptotes. Summary of Curve
Sketching. Graphing with Calculus and Calculators.
Optimization Problems. Applied Project: The Shape of
a Can. Newton’s Method. Antiderivatives. Review. 4.
INTEGRALS. Areas and Distances. The Definite Integral.
Discovery Project: Area Functions. The Fundamental
Theorem of Calculus. Indefinite Integrals and the Net
Change Theorem. Writing Project: Newton, Leibniz,
and the Invention of Calculus. The Substitution Rule.
Review. 5. APPLICATIONS OF INTEGRATION. Areas
Between Curves. Applied Project: The Gini Index.
Volume. Volumes by Cylindrical Shells. Work. Average
Value of a Function. Review. 6. INVERSE FUNCTIONS:
EXPONENTIAL, LOGARITHMIC, AND INVERSE
TRIGONOMETRIC FUNCTIONS. Inverse Functions.
Instructors may cover either Sections 6.2-6.4 or Sections
6.2*-6.4*. See the Preface. Exponential Functions and
Their Derivatives. Logarithmic Functions. Derivatives
of Logarithmic Functions. The Natural Logarithmic
Function. The Natural Exponential Function. General
Logarithmic and Exponential Functions. Exponential
Growth and Decay. Inverse Trigonometric Functions.
Applied Project: Where to Sit at the Movies. Hyperbolic
Functions. Indeterminate Forms and l’Hospital’s Rule.
Writing Project: The Origins of l’Hospital’s Rule. Review.
7. TECHNIQUES OF INTEGRATION. Integration by Parts.
Trigonometric Integrals. Trigonometric Substitution.
Integration of Rational Functions by Partial Fractions.
Strategy for Integration. Applied Project: Calculus
and Baseball. Integration Using Tables and Computer
Algebra Systems. Discovery Project: Patterns in
Integrals. Approximate Integration. Improper Integrals.
Review. 8. FURTHER APPLICATIONS OF INTEGRATION.
Arc Length. Discovery Project: Arc Length Contest.
Area of a Surface of Revolution. Discovery Project:
Rotating on a Slant. Applications to Physics and
Engineering. Discovery Project: Complementary
Coffee Cups. Applications to Economics and Biology.
Probability. Review. 9. DIFFERENTIAL EQUATIONS.
Modeling with Differential Equations. Direction Fields
and Euler’s Method. Separable Equations. Applied
Project: How Fast Does a Tank Drain? Applied Project:
Which is Faster, Going Up or Coming Down? Models
for Population Growth. Linear Equations. PredatorPrey Systems. Review. 10. PARAMETRIC EQUATIONS
AND POLAR COORDINATES. Curves Defined by
Parametric Equations. Laboratory Project: Families
of Hypocycloids. Calculus with Parametric Curves.
www.cengageasia.com
23
Laboratory Project: Bézier Curves. Polar Coordinates.
Laboratory Project: Families of Polar Curves. Areas and
Lengths in Polar Coordinates. Conic Sections. Conic
Sections in Polar Coordinates. Review. 11. INFINITE
SEQUENCES AND SERIES. Sequences. Laboratory
Project: Logistic Sequences. Series. The Integral Test and
Estimates of Sums. The Comparison Tests. Alternating
Series. Absolute Convergence and the Ratio and
Root Tests. Strategy for Testing Series. Power Series.
Representations of Functions as Power Series. Taylor
and Maclaurin Series . Laboratory Project: An Elusive
Limit. Writing Project: How Newton Discovered the
Binomial Series. Applications of Taylor Polynomials.
Applied Project: Radiation from the Stars. Review. 12.
VECTORS AND THE GEOMETRY OF SPACE. ThreeDimensional Coordinate Systems. Vectors. The Dot
Product. The Cross Product. Discovery Project: The
Geometry of a Tetrahedron. Equations of Lines and
Planes. Cylinders and Quadric Surfaces. Review. 13.
VECTOR FUNCTIONS. Vector Functions and Space
Curves. Derivatives and Integrals of Vector Functions.
Arc Length and Curvature. Motion in Space: Velocity
and Acceleration. Applied Project: Kepler’s Laws.
Review. 14. PARTIAL DERIVATIVES. Functions of
Several Variables. Limits and Continuity. Partial
Derivatives. Tangent Planes and Linear Approximation.
The Chain Rule. Directional Derivatives and the
Gradient Vector. Maximum and Minimum Values.
Applied Project: Designing a Dumpster. Discovery
Project: Quadratic Approximations and Critical Points.
Lagrange Multipliers. Applied Project: Rocket Science.
Applied Project: Hydro-Turbine Optimization. Review.
15. MULTIPLE INTEGRALS. Double Integrals over
Rectangles. Iterated Integrals. Double Integrals over
General Regions. Double Integrals in Polar Coordinates.
Applications of Double Integrals. Triple Integrals.
Discovery Project: Volumes of Hyperspheres. Triple
Integrals in Cylindrical Coordinates. Discovery Project:
The Intersection of Three Cylinders. Triple Integrals in
Spherical Coordinates. Applied Project: Roller Derby.
Change of Variables in Multiple Integrals. Review. 16.
VECTOR CALCULUS. Vector Fields. Line Integrals.
The Fundamental Theorem for Line Integrals. Green’s
Theorem. Curl and Divergence. Parametric Surfaces
and Their Areas. Surface Integrals. Stokes’ Theorem.
Writing Project: Three Men and Two Theorems. The
Divergence Theorem. Summary. Review. 17. SECOND-
ORDER DIFFERENTIAL EQUATIONS. Second-Order
Linear Equations. Nonhomogeneous Linear Equations.
Applications of Second-Order Differential Equations.
Series Solutions. Review. APPENDIXES. A. Intervals,
Inequalities, and Absolute Values. B. Coordinate
Geometry and Lines. C. Graphs of Second-Degree
Equations. D. Trigonometry. E. Sigma Notation. F. Proofs
of Theorems. G. Graphing Calculators and Computers
. H. Complex Numbers. I. Answers to Odd-Numbered
Exercises.
© 2012, 1080pp, Paperback, 9781133112716
CALCULUS, INTERNATIONAL METRIC
EDITION, 7E
James Stewart’s CALCULUS, 7e, International Metric
Edition texts are widely renowned for their mathematical
precision and accuracy, clarity of exposition, and
outstanding examples and problem sets. Millions of
students worldwide have explored calculus through
Stewart’s trademark style, while instructors have turned
to his approach time and time again. In the Seventh
Edition of CALCULUS, International Metric Edition
Stewart continues to set the standard for the course
while adding carefully revised content. The patient
explanations, superb exercises, focus on problem
solving, and carefully graded problem sets that have
made Stewart’s texts best-sellers continue to provide
a strong foundation for the Seventh Edition. From the
most unprepared student to the most mathematically
gifted, Stewart’s writing and presentation serve to
enhance understanding and build confidence.
NEW TO THIS EDITION
• TOC change: For this edition, Stewart has combined
the material that previously appeared in Chapters
www.cengageasia.com
24
1 and 2. This means that Calculus, 7e, International
Metric Edition and Calculus: Early Transcendentals, 7e,
International Metric Edition have the same number
of chapters, allowing for a single Multivariable text,
rather than two separate ET and LT versions.
• A revised narrative.
problem.
notes demonstrate an increased emphasis on problem
solving.
updated with new problems and is more visually
appealing and engaging to students.
online program for Stewart’s Calculus, 7e, International
Metric Edition to encourage the practice that’s
so critical for concept mastery. The meticulously
crafted pedagogy and exercises in our proven texts
become even more effective in Enhanced WebAssign,
supplemented by multimedia tutorial support and
immediate feedback as students complete their
assignments. Enhanced WebAssign for Stewart now
includes remediation and new Camtasia videos.
FEATURES
• Four carefully crafted diagnostic tests in algebra,
analytic geometry, functions, and trigonometry
appear at the beginning of the text. These provide
students with a convenient way to test their preexisting knowledge and brush up on skill techniques
they need to successfully begin the course. Answers
are included, and students who need to improve will
be referred to points in the text or on the book’s
website where they can seek help.
• Stewart’s writing style speaks clearly and directly to
students, guiding them through key ideas, theorems,
and problem-solving steps, and encouraging them to
think as they read and learn calculus.
CONTENTS
Table of Contents: Diagnostic Tests. A Preview of
Calculus. 1. FUNCTIONS AND LIMITS. Four Ways
to Represent a Function. Mathematical Models: A
Catalog of Essential Functions. New Functions from
Old Functions. The Tangent and Velocity Problems.
The Limit of a Function. Calculating Limits Using
the Limit Laws. The Precise Definition of a Limit.
Continuity. Review. Principles of Problem Solving. 2.
DERIVATIVES. Derivatives and Rates of Change. Writing
Project: Writing Project: Early Methods for Finding
Tangents. The Derivative as a Function. Differentiation
Formulas. Applied Project: Building a Better Roller
Coaster. Derivatives of Trigonometric Functions. The
Chain Rule. Applied Project: Where Should a Pilot
Start Descent? Implicit Differentiation. Laboratory
Project: Families of Implicit Curves. Rates of Change
in the Natural and Social Sciences. Related Rates.
Linear Approximations and Differentials. Laboratory
Project: Taylor Polynomials. Review. Problems Plus.
3. APPLICATIONS OF DIFFERENTIATION. Maximum
and Minimum Values. Applied Project: The Calculus of
Rainbows. The Mean Value Theorem. How Derivatives
Affect the Shape of a Graph. Limits at Infinity; Horizontal
Asymptotes. Summary of Curve Sketching. Graphing
with Calculus and Calculators. Optimization Problems.
Applied Project: The Shape of a Can. Newton’s Method.
Antiderivatives. Review. Problems Plus. 4. INTEGRALS.
Areas and Distances. The Definite Integral. Discovery
Project: Area Functions. The Fundamental Theorem
of Calculus. Indefinite Integrals and the Net Change
www.cengageasia.com
25
Theorem. Writing Project: Newton, Leibniz, and the
Invention of Calculus. The Substitution Rule. Review.
Problems Plus. 5. APPLICATIONS OF INTEGRATION.
Areas Between Curves. Applied Project: The Gini Index.
Value of a Function. Review. Problems Plus. 6. INVERSE
FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND
INVERSE TRIGONOMETRIC FUNCTIONS. Inverse
Functions. Instructors may cover either Sections 6.26.4 or Sections 6.2*-6.4*. See the Preface. Exponential
Functions and Their Derivatives. Logarithmic Functions.
Derivatives of Logarithmic Functions. The Natural
Logarithmic Function. The Natural Exponential
Function. General Logarithmic and Exponential
Functions. Exponential Growth and Decay. Inverse
Trigonometric Functions. Applied Project: Where to Sit
at the Movies. Hyperbolic Functions. Indeterminate
Forms and l’Hospital’s Rule. Writing Project: The
Origins of l’Hospital’s Rule. Review. Problems Plus.
7. TECHNIQUES OF INTEGRATION. Integration
Substitution. Integration of Rational Functions by
Partial Fractions. Strategy for Integration. Applied
Project: Calculus and Baseball. Integration Using
Tables and Computer Algebra Systems. Discovery
Project: Patterns in Integrals. Approximate Integration.
Improper Integrals. Review. Problems Plus. 8. FURTHER
APPLICATIONS OF INTEGRATION. Arc Length.
Discovery Project: Arc Length Contest. Area of a Surface
of Revolution. Discovery Project: Rotating on a Slant.
Applications to Physics and Engineering. Discovery
Project: Complementary Coffee Cups. Applications to
Economics and Biology. Probability. Review. Problems
Plus. 9. DIFFERENTIAL EQUATIONS. Modeling with
Differential Equations. Direction Fields and Euler’s
Method. Separable Equations. Applied Project: How
Fast Does a Tank Drain? Applied Project: Which is Faster,
Going Up or Coming Down? Models for Population
Growth. Linear Equations. Predator-Prey Systems.
Review. Problems Plus. 10. PARAMETRIC EQUATIONS
Sections in Polar Coordinates. Review. Problems Plus.
11. INFINITE SEQUENCES AND SERIES. Sequences.
Laboratory Project: Logistic Sequences. Series. The
Integral Test and Estimates of Sums. The Comparison
Tests. Alternating Series. Absolute Convergence and the
Ratio and Root Tests. Strategy for Testing Series. Power
Series. Representations of Functions as Power Series.
Taylor and Maclaurin Series . Laboratory Project: An
Elusive Limit. Writing Project: How Newton Discovered
the Binomial Series. Applications of Taylor Polynomials.
Applied Project: Radiation from the Stars. Review.
Problems Plus. 12. VECTORS AND THE GEOMETRY
OF SPACE. Three-Dimensional Coordinate Systems.
Vectors. The Dot Product. The Cross Product. Discovery
Project: The Geometry of a Tetrahedron. Equations
of Lines and Planes. Cylinders and Quadric Surfaces.
Review. Problems Plus. 13. VECTOR FUNCTIONS. Vector
Functions and Space Curves. Derivatives and Integrals
of Vector Functions. Arc Length and Curvature. Motion
in Space: Velocity and Acceleration. Applied Project:
Kepler’s Laws. Review. Problems Plus. 14. PARTIAL
DERIVATIVES. Functions of Several Variables. Limits
and Continuity. Partial Derivatives. Tangent Planes
and Linear Approximation. The Chain Rule. Directional
Derivatives and the Gradient Vector. Maximum
and Minimum Values. Applied Project: Designing a
Dumpster. Discovery Project: Quadratic Approximations
and Critical Points. Lagrange Multipliers. Applied
Project: Rocket Science. Applied Project: Hydro-Turbine
Optimization. Review. Problems Plus. 15. MULTIPLE
INTEGRALS. Double Integrals over Rectangles. Iterated
Integrals. Double Integrals over General Regions.
Double Integrals in Polar Coordinates. Applications of
Double Integrals. Triple Integrals. Discovery Project:
Volumes of Hyperspheres. Triple Integrals in Cylindrical
Coordinates. Discovery Project: The Intersection
of Three Cylinders. Triple Integrals in Spherical
Coordinates. Applied Project: Roller Derby. Change of
Variables in Multiple Integrals. Review. Problems Plus.
16. VECTOR CALCULUS. Vector Fields. Line Integrals.
Theorem. Curl and Divergence. Parametric Surfaces and
Their Areas. Surface Integrals. Stokes’ Theorem. Writing
Project: Three Men and Two Theorems. The Divergence
Theorem. Summary. Review. Problems Plus. 17. SECONDORDER DIFFERENTIAL EQUATIONS. Second-Order
www.cengageasia.com
26
Series Solutions. Review. Problems Plus. APPENDIXES.
A. Intervals, Inequalities, and Absolute Values. B.
Coordinate Geometry and Lines. C. Graphs of SecondDegree Equations. D. Trigonometry. E. Sigma Notation.
F. Proofs of Theorems. G. Graphing Calculators and
Computers . H. Complex Numbers. I. Answers to OddNumbered Exercises.
© 2012, 1368pp, Hardback, 9780538498845
CALCULUS: CONCEPTS & CONTEXTS,
HYBRID WITH ENHANCED WEBASSIGN
PRINTED ACCESS CARD, 3 SEMESTER, 4E
and instructors, this new hybrid edition features the
Enhanced WebAssign. The result—a briefer printed text
that engages students online! Stewart’s CALCULUS:
CONCEPTS AND CONTEXTS, FOURTH EDITION offers
a streamlined approach to teaching calculus, focusing
on major concepts and supporting them with precise
definitions, patient explanations, and carefully graded
problems. CALCULUS: CONCEPTS AND CONTEXTS is
highly regarded because this text offers a balance of
theory and conceptual work to satisfy more progressive
programs as well as those who are more comfortable
teaching in a more traditional fashion. This title is just
NEW TO THIS EDITION
• NEW! The hybrid edition of the text provides a less
expensive, shorter option for students. End-of-section
only. The hybrid edition is packaged with Enhanced
WebAssign and the Cengage YouBook.
• Diagnostic tests in Basic Algebra, Analytic Geometry,
Functions, and Trigonometry are now available
in Enhanced WebAssign. Some material has been
rewritten for greater clarity or for better motivation.
• New examples have been added, and examples are
now titled for easier reference. The solutions to some
of the existing examples have been amplified, and in
many cases have been updated to be more timely.
• In response to user feedback, specific areas of content
have either been condensed, moved, or expanded
upon. The material motivating the derivative is
briefer and has been combined into a single section
called Derivatives and Rates of Change. Rates of
Change in the Natural and Social Sciences has been
moved later in Chapter 3 in order to incorporate
more differentiation rules. Coverage of inverse
trigonometric functions has been consolidated in a
single dedicated section (3.6). The former sections
4.6 and 4.7 have been merged into a single section,
with a briefer treatment of optimization problems in
business and economics. There is now a full section
on volumes by cylindrical shells (6.3). Sections 8.7 and
8.8 have been merged into a single section.
• There are new problems in the Focus on Problem
Solving sections, as well as a new project,
Complementary Coffee Cups.
FEATURES
• Conceptual Exercises: The most important way to
foster conceptual understanding is through assigned
problems. Stewart’s CALCULUS: CONCEPTS AND
CONTEXTS offers various types of problems. Some
problems require students to explain the meaning
of basic concepts, while others test conceptual
understanding through verbal description or graphs
and tables. Many exercises combine and compare
graphical, numerical, and algebraic approaches.
• Graded Homework Exercises: Each exercise set is
carefully graded, progressing from basic conceptual
exercises and skill-development problems to more
challenging problems involving applications and
proofs.
• Real World Data: CALCULUS: CONCEPTS AND
CONTEXTS incorporates interesting real-world data
www.cengageasia.com
27
gathered from a variety of contemporary sources to
introduce, motivate, and illustrate the concepts of
calculus.
CONTENTS
Preface. To the Student. Diagnostic Tests. A Preview
of Calculus. 1. FUNCTIONS AND MODELS. Four Ways
to Represent a Function. Mathematical Models: A
Catalog of Essential Functions. New Functions from
Old Functions. Graphing Calculators and Computers.
Exponential Functions. Inverse Functions and
Logarithms. Parametric Curves. Laboratory Project:
Running Circles around Circles. Review. Principles of
Problem Solving. 2. LIMITS AND DERIVATIVES. The
Tangent and Velocity Problems. The Limit of a Function.
Calculating Limits Using the Limit Laws. Continuity.
Limits Involving Infinity. Derivatives and Rates of
Change. Writing Project: Early Methods for Finding
Tangents. The Derivative as a Function. What Does
Review. Focus on Problem Solving. 3. DIFFERENTIATION
RULES. Derivatives of Polynomials and Exponential
Functions. Applied Project: Building a Better Roller
Coaster. The Product and Quotient Rules. Derivatives
of Trigonometric Functions. The Chain Rule. Laboratory
Project: Bézier Curves. Applied Project: Where Should
a Pilot Start Descent? Implicit Differentiation. Inverse
Trigonometric Functions and their Derivatives.
Derivatives of Logarithmic Functions. Discovery
Project: Hyperbolic Functions. Rates of Change in the
Natural and Social Sciences. Linear Approximations and
Review. Focus on Problem Solving. 4. APPLICATIONS
OF DIFFERENTIATION. Related Rates. Maximum
and Minimum Values. Applied Project: The Calculus
of Rainbows. Derivatives and the Shapes of Curves.
Graphing with Calculus and Calculators. Indeterminate
Origins of l’Hospital’s Rule. Optimization Problems.
Antiderivatives. Review. Focus on Problem Solving. 5.
Evaluating Definite Integrals. Discovery Project: Area
Functions. The Fundamental Theorem of Calculus.
Writing Project: Newton, Leibniz, and the Invention of
Calculus. The Substitution Rule. Integration by Parts.
Additional Techniques of Integration. Integration Using
Improper Integrals. Review. Focus on Problem Solving.
6. APPLICATIONS OF INTEGRATION. More about
Areas. Volumes. Discovery Project: Rotating on a Slant.
Volumes by Cylindrical Shells. Arc Length. Discovery
Project: Arc Length Contest. Average Value of a
Function. Applied Project: Where To Sit at the Movies.
Project: Complementary Coffee Cups. Applications
to Economics and Biology. Probability. Review. Focus
on Problem Solving. 7. DIFFERENTIAL EQUATIONS.
Which Is Faster, Going Up or Coming Down? Exponential
Growth and Decay. Applied Project: Calculus and
Baseball. The Logistic Equation. Predator-Prey
Systems. Review. Focus on Problem Solving. 8. INFINTE
Project: Logistic Sequences. Series. The Integral and
Comparison Tests; Estimating Sums. Other Convergence
Tests. Power Series. Representations of Functions as
Power Series. Taylor and Maclaurin Series. Laboratory
Project: An Elusive Limit. Writing Project: How Newton
Discovered the Binomial Series. Applications of Taylor
Polynomials. Applied Project: Radiation from the
Stars. Review. Focus on Problem Solving. 9. VECTORS
AND THE GEOMETRY OF SPACE. Three-Dimensional
Coordinate Systems. Vectors. The Dot Product. The
Cross Product. Discovery Project: The Geometry of a
Tetrahedron. Equations of Lines and Planes. Laboratory
Project: Putting 3D in Perspective. Functions and
Surfaces. Cylindrical and Spherical Coordinates.
Laboratory Project: Families of Surfaces. Review. Focus
on Problem Solving. 10. VECTOR FUNCTIONS. Vector
Functions and Space Curves. Derivatives and Integrals
of Vector Functions. Arc Length and Curvature. Motion
in Space: Velocity and Acceleration. Applied Project:
Kepler’s Laws. Parametric Surfaces. Review. Focus on
Problem Solving. 11. PARTIAL DERIVATIVES. Functions
of Several Variables. Limits and Continuity. Partial
Derivatives. Tangent Planes and Linear Approximations.
The Chain Rule. Directional Derivatives and the Gradient
Vector. Maximum and Minimum Values. Applied
Project: Designing a Dumpster. Discovery Project:
Quadratic Approximations and Critical Points. Lagrange
Multipliers. Applied Project: Rocket Science. Applied
www.cengageasia.com
28
Project: Hydro-Turbine Optimization. Review. Focus
on Problem Solving. 12. MULTIPLE INTEGRALS. Double
Integrals over Rectangles. Iterated Integrals. Double
Integrals over General Regions. Double Integrals in Polar
Coordinates. Applications of Double Integrals. Surface
Area. Triple Integrals. Discovery Project: Volumes
of Hyperspheres. Triple Integrals in Cylindrical and
Discovery Project: The Intersection of Three Cylinders.
Change of Variables in Multiple Integrals. Review. Focus
on Problem Solving. 13. VECTOR CALCULUS. Vector
Fields. Line Integrals. The Fundamental Theorem for
Line Integrals. Green’s Theorem. Curl and Divergence.
Surface Integrals. Stokes’ Theorem. Writing Project:
Three Men and Two Theorems. The Divergence
Theorem. Summary. Review. Focus on Problem Solving.
APPENDIXES. A. Intervals, Inequalities, and Absolute
Values. B. Coordinate Geometry. C. Trigonometry. D.
Precise Definitions of Limits. E. A Few Proofs. F. Sigma
Notation. G. Integration of Rational Functions by Partial
Fractions. H. Polar Coordinates. I. Complex Numbers. J.
Answers to Odd-Numbered Exercises.
© 2013, 1168pp, Paperback, 9781285056548
ESSENTIAL CALCULUS, INTERNATIONAL
METRIC EDITION, 2E
This book is for instructors who think that most calculus
textbooks are too long. In writing the book, James
Stewart asked himself: What is essential for a calculus
course for scientists and engineers? ESSENTIAL
CALCULUS, 2E, International Metric Edition offers a
concise approach to teaching calculus that focuses
on major concepts, and supports those concepts with
precise definitions, patient explanations, and carefully
graded problems. The book is only 900 pages—twothirds the size of Stewart’s other calculus texts, and
yet it contains almost all of the same topics. The author
achieved this relative brevity primarily by condensing
the exposition and by putting some of the features on
the book’s website, www.StewartCalculus.com. Despite
the more compact size, the book has a modern flavor,
covering technology and incorporating material to
promote conceptual understanding, though not as
prominently as in Stewart’s other books. ESSENTIAL
CALCULUS, 2E, International Metric Edition features
the same attention to detail, eye for innovation,
and meticulous accuracy that have made Stewart’s
textbooks the best-selling calculus texts in the world.
NEW TO THIS EDITION
• The book begins with four diagnostic tests in
Basic Algebra, Analytic Geometry, Functions, and
Trigonometry. These tests address the gaps in many
students’ prerequisite skills—and help them start the
course with confidence—by giving them opportunities
to get up to speed or brush up.
• Some material has been rewritten for greater clarity
or for better motivation.
• Based on reviewers’ suggestions, a new section
on surface area has been added to Chapter 7,
“Applications of Integration.”
• Updated data in examples and exercises assures that
the book maintains its currency and relevance.
• More than 35% of the exercises are new, providing
instructors with new assignment options, and
students with an abundance of practice opportunities.
• Enhanced WebAssign® for Stewart’s ESSENTIAL
CALCULUS, 2E, International Metric Edition -is
enhanced with new features and functions. These
include Enhanced Feedback for incorrect problems,
Visualizing Calculus modules and animations,
Lecture Video Problems, and a Show Your Work
feature that gives you the option of seeing students’
detailed solutions. Plus, Cengage YouBook, a Flashbased eBook version of the text that is interactive
and customizable, is fully integrated into Enhanced
WebAssign.
FEATURES
• The text presents a concise approach to calculus for
instructors who want to focus on essential principles
and who feel no need for frills.
www.cengageasia.com
29
• Brevity is achieved through condensed exposition,
fewer examples in some sections, fewer technology
and conceptual problems, and fewer appendixes.
Problems Plus and Projects have been moved to the
author’s website at www.stewartcalculus.com.
• Certain topics, for example, the treatment of the
integral and the remainder term in Taylor Series, are
presented in a manner that is more traditional than
in Stewart’s other books.
• The text presents exponential, logarithmic, and
inverse trigonometric functions late, with the
logarithm defined as an integral. Instructors wishing
to cover such functions earlier should consider
ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS,
2e, International Metric Edition.
CONTENTS
1. FUNCTIONS AND LIMITS. Functions and Their
Representations. A Catalog of Essential Functions.
The Limit of a Function. Calculating Limits. Continuity.
Limits Involving Infinity. 2. DERIVATIVES. Derivatives
and Rates of Change. The Derivative as a Function. Basic
Differentiation Formulas. The Product and Quotient
Rules. The Chain Rule. Implicit Differentiation. Related
Rates. Linear Approximations and Differentials. 3.
APPLICATIONS OF DIFFERENTIATION. Maximum
and Minimum Values. The Mean Value Theorem.
Derivatives and the Shapes of Graphs. Curve
Sketching. Optimization Problems. Newton’s Method.
Antiderivatives. 4. INTEGRALS. Areas and Distances.
The Definite Integral. Evaluating Definite Integrals. The
Fundamental Theorem of Calculus. The Substitution
Rule. 5. INVERSE FUNCTIONS. Inverse Functions.
The Natural Logarithmic Function. The Natural
Exponential Function. General Logarithmic and
Exponential Functions. Exponential Growth and
Decay. Inverse Trigonometric Functions. Hyperbolic
6. TECHNIQUES OF INTEGRATION. Integration by
Parts. Trigonometric Integrals and Substitutions.
Partial Fractions. Integration with Tables and Computer
Algebra Systems. Approximate Integration. Improper
Integrals. 7. APPLICATIONS OF INTEGRATION. Areas
between Curves. Volumes. Volumes by Cylindrical
Shells. Arc Length. Area of a Surface of Revolution.
Applications to Physics and Engineering. Differential
Equations. 8. SERIES. Sequences. Series. The Integral
and Comparison Tests. Other Convergence Tests.
Power Series. Representing Functions as Power Series.
Taylor and Maclaurin Series. Applications of Taylor
Polynomials. 9. PARAMETRIC EQUATIONS AND
POLAR COORDINATES. Parametric Curves. Calculus
with Parametric Curves. Polar Coordinates. Areas and
Lengths in Polar Coordinates. Conic Sections in Polar
Coordinates. 10. VECTORS AND THE GEOMETRY
OF SPACE. Three-Dimensional Coordinate Systems.
Vectors. The Dot Product. The Cross Product. Equations
of Lines and Planes. Cylinders and Quadric Surfaces.
Vector Functions and Space Curves. Arc Length and
Curvature. Motion in Space: Velocity and Acceleration.
11. PARTIAL DERIVATIVES. Functions of Several
Variables. Limits and Continuity. Partial Derivatives.
Tangent Planes and Linear Approximations. The Chain
Rule. Directional Derivatives and the Gradient Vector.
Maximum and Minimum Values. Lagrange Multipliers.
Rectangles. Double Integrals over General Regions.
Double Integrals in Polar Coordinates. Applications
of Double Integrals. Triple Integrals. Triple Integrals in
Cylindrical Coordinates. Triple Integrals in Spherical
Coordinates. Change of Variables in Multiple Integrals.
The Divergence Theorem. Appendix A. Trigonometry.
Appendix B. Proofs. Appendix C. Sigma Notation.
© 2013, 960pp, Paperback, 9781133492566
ESSENTIAL CALCULUS: EARLY
TRANSCENDENTALS, 2E
This book is for instructors who think that most calculus
textbooks are too long. In writing the book, James
Stewart asked himself: What is essential for a threesemester calculus course for scientists and engineers?
www.cengageasia.com
30
ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS,
Second Edition, offers a concise approach to teaching
calculus that focuses on major concepts, and supports
those concepts with precise definitions, patient
explanations, and carefully graded problems. The book
is only 900 pages--two-thirds the size of Stewart’s
other calculus texts, and yet it contains almost all
of the same topics. The author achieved this relative
brevity primarily by condensing the exposition and by
putting some of the features on the book’s website,
www.StewartCalculus.com. Despite the more compact
size, the book has a modern flavor, covering technology
and incorporating material to promote conceptual
understanding, though not as prominently as in
Stewart’s other books. ESSENTIAL CALCULUS: EARLY
TRANSCENDENTALS features the same attention to
detail, eye for innovation, and meticulous accuracy
that have made Stewart’s textbooks the best-selling
calculus texts in the world.
NEW TO THIS EDITION
students’ prerequisite skills--and help them start the
course with confidence--by giving them opportunities
CALCULUS: EARLY TRANSCENDENTALS, Second
Edition--which combines the mathematics content
in this text with the most powerful online homework
solution, WebAssign--is enhanced with new features
and functions. These include Enhanced Feedback for
incorrect problems, Visualizing Calculus modules
and animations, Lecture Video Problems, and a
Show Your Work feature that gives you the option
of seeing students’ detailed solutions. Plus, Cengage
YouBook, a Flash-based eBook version of the text that
is interactive and customizable, is fully integrated into
Enhanced WebAssign.
FEATURES
• Certain topics, for example, the treatment of the
in Stewart’s other books.
• This version of the text presents exponential,
logarithmic, and inverse trigonometric functions
in Chapter Three. Those who wish to cover such
functions later, with the logarithm defined as an
integral, should consider the book entitled simply,
ESSENTIAL CALCULUS.
CONTENTS
INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC,
AND INVERSE TRIGONOMETRIC FUNCTIONS.
Exponential Functions. Inverse Functions and Logarithms.
Derivatives of Logarithmic and Exponential Functions.
Exponential Growth and Decay. Inverse Trigonometric
Functions. Hyperbolic Functions. Indeterminate
Forms and l’Hospital’s Rule. 4. APPLICATIONS OF
DIFFERENTIATION. Maximum and Minimum Values.
The Mean Value Theorem. Derivatives and the Shapes
of Graphs. Curve Sketching. Optimization Problems.
Newton’s Method. Antiderivatives. 5. INTEGRALS. Areas
and Distances. The Definite Integral. Evaluating Definite
Integrals. The Fundamental Theorem of Calculus. The
Substitution Rule. 6. TECHNIQUES OF INTEGRATION.
Integration by Parts. Trigonometric Integrals and
Substitutions. Partial Fractions. Integration with
www.cengageasia.com
31
Tables and Computer Algebra Systems. Approximate
Integration. Improper Integrals. 7. APPLICATIONS
OF INTEGRATION. Areas between Curves. Volumes.
Volumes by Cylindrical Shells. Arc Length. Area of
a Surface of Revolution. Applications to Physics
and Engineering. Differential Equations. 8. SERIES.
Sequences. Series. The Integral and Comparison Tests.
Other Convergence Tests. Power Series. Representing
Functions as Power Series. Taylor and Maclaurin Series.
Applications of Taylor Polynomials. 9. PARAMETRIC
EQUATIONS AND POLAR COORDINATES. Parametric
Curves. Calculus with Parametric Curves. Polar
Coordinates. Areas and Lengths in Polar Coordinates.
Conic Sections in Polar Coordinates. 10. VECTORS
AND THE GEOMETRY OF SPACE. Three-Dimensional
Coordinate Systems. Vectors. The Dot Product. The Cross
Product. Equations of Lines and Planes. Cylinders and
Quadric Surfaces. Vector Functions and Space Curves.
and Acceleration. 11. PARTIAL DERIVATIVES. Functions
of Several Variables. Limits and Continuity. Partial
Derivatives. Tangent Planes and Linear Approximations.
The Chain Rule. Directional Derivatives and the Gradient
Vector. Maximum and Minimum Values. Lagrange
Multipliers. 12. MULTIPLE INTEGRALS. Double Integrals
over Rectangles. Double Integrals over General Regions.
Double Integrals in Polar Coordinates. Applications of
Double Integrals. Triple Integrals. Triple Integrals in
Cylindrical Coordinates. Triple Integrals in Spherical
Coordinates. Change of Variables in Multiple Integrals.
The Divergence Theorem. Appendix A. Trigonometry.
Appendix B. Proofs. Appendix C. Sigma Notation.
Appendix D. The Logarithm Defined as an Integral
© 2013, 960pp, Hardback, 9781133112280
MODELING THE DYNAMICS OF LIFE, 3E
Calculus and Probability for Life Scientists
Frederick R. Adler, University of Utah
Designed to help life sciences students understand
the role mathematics has played in breakthroughs
in epidemiology, genetics, statistics, physiology, and
other biological areas, MODELING THE DYNAMCICS
OF LIFE: CALCULUS AND PROBABILTY FOR LIFE
SCIENTISTS, Third Edition, provides students with a
thorough grounding in mathematics, the language,
and ‘the technology of thought’ with which these
developments are created and controlled. The text
teaches the skills of describing a system, translating
appropriate aspects into equations, and interpreting
the results in terms of the original problem. The text
helps unify biology by identifying dynamical principles
that underlie a great diversity of biological processes.
Standard topics from calculus courses are covered, with
particular emphasis on those areas connected with
modeling such as discrete-time dynamical systems,
differential equations, and probability and statistics.
NEW TO THIS EDITION
• Section 1.7 includes double-log graphs and an
introduction to allometry, the study of power function
relationships among biological measurements.
• Section 2.8 includes examples of implicit differentiation
and related rates with both geometric and dynamical
applications.
• Infinite series are introduced first in a new discussion
of Taylor series in section 3.7, and then studied more
formally in the context of improper integrals in
section 4.7.
• Integration by partial fractions is introduced in section
4.3 and used to solve the logistic differential equation
in section 5.4. Trigonometric substitutions are
presented in a new series of exercises in section 4.3.
• Computing volumes of solids of revolution is
introduced in section 4.6.
www.cengageasia.com
32
FEATURES
• The first chapter includes a review of functions, units,
and linear functions before beginning with the new
topic of discrete-time dynamical systems.
• Partial solutions to all the odd problems are included
in the back of the book, providing valuable guidance
for students at no additional cost.
• The text integrates mathematical content with
modeling, following the process of describing
a system, translating appropriate aspects into
equations, and interpreting results in terms of the
original problem.
• The text introduces and develops mathematical
methods to analyze three kinds of models: discretetime dynamical systems, differential equations, and
stochastic processes.
• Three dynamical principles that underlie diverse
biological processes are woven throughout: growth,
diffusion, and selection. Each theme is studied in turn
with the three kinds of models.
CONTENTS
1. Introduction to Discrete-Time Dynamical Systems. 1.1
Biology and Dynamics. 1.2 Variables. Parameters. and
Functions in Biology. 1.3 The Units and Dimensions of
Measurements and Functions. 1.4 Linear Functions and
Their Graphs. 1.5 Discrete-Time Dynamical Systems.
1.6 Analysis of Discrete-Time Dynamical Systems. 1.7
Expressing Solutions with Exponential Functions. 1.8
Oscillations and Trigonometry. 1.9 A Model of Gas
Exchange in the Lung. 1.10 An Example of Nonlinear
Dynamics. 1.11 An Excitable Systems I: The Heart. 2.
Limits and Derivatives. 2.1 Introduction to Derivatives.
2.2 Limits. 2.3 Continuity. 2.4 Computing Derivatives:
Linear and Quadratic Functions. 2.5 Derivatives of Sums.
Powers. and Polynomials. 2.6 Derivatives of Products
and Quotients. 2.7 The Second Derivative. Curvature.
and Acceleration. 2.8 Derivatives of Exponential
and Logarithmic Functions. 2.9 The Chain Rule. 2.10
Derivatives of Trigonometric Functions. 3. Applications
of Derivatives and Dynamical Systems. 3.1 Stability
and the Derivative. 3.2 More Complicated Dynamics.
3.3 Maximization. 3.4 Reasoning About Functions. 3.5
Limits at Infinity. 3.6 Leading Behavior and L’Hopital’s
Rule. 3.7 Approximating Functions with Lines and
Polynomials. 3.8 Newton’s Method. 3.9 Panting and
Deep Breathing. 4. Differential Equations. Integrals.
and Their Applications. 4.1 Differential Equations. 4.2
Solving Pure-Time Differential Equations. 4.3 Integration
of Special Functions. Integration by Substitution. by
Parts. and by Partial Fractions. 4.4 Integrals and Sums.
4.5 Definite and Indefinite Integrals. 4.6 Applications
of Integrals. 4.7 Improper Integrals. 5. Analysis of
Autonomous Differential Equations. 5.1 Basic Differential
Equations. 5.2 Equilibria and Display of Autonomous
Differential Equations. 5.3 Stable and Unstable Equilibria.
5.4 Solving Autonomous Differential Equations. 5.5 Two
Dimensional Differential Equations. 5.6 The Phase Plane.
5.7 Solutions in the Phase Plane. 5.8 The Dynamics of a
Neuron. 6. Probability Theory and Descriptive Statistics.
6.1 Introduction to Probabilistic Models. 6.2 Stochastic
Models of Diffusion and Genetics. 6.3 Probability
Theory. 6.4 Conditional Probability. 6.5 Independence
and Markov Chains. 6.6 Displaying Probabilities. 6.7
Random Variables. 6.8 Descriptive Statistics. 6.9
Descriptive Statistics for Spread. 7. Probability Models.
7.1 Joint Distributions. 7.2 Covariance and Correlation.
7.3 Sums and Products of Random Variables. 7.4 The
Binomial Distribution. 7.5 Applications of the Binomial
Distribution. 7.6 Waiting Times: Geometric and
Exponential Distributions. 7.7 The Poisson Distribution.
7.8 The Normal Distribution. 7.9 Applying the Normal
Approximation. 8. Introduction to Statistical Reasoning.
8.1 Statistics: Estimating Parameters. 8.2 Confidence
Limits. 8.3 Estimating the Mean. 8.4 Hypothesis
Testing. 8.5 Hypothesis Testing: Normal Theory. 8.6
Comparing Experiments: Normal Theory. 8.7 Analysis of
Contingency Tables and Goodness of Fit. 8.8 Hypothesis
Testing with the Method of Support. 8.9 Regression.
© 2013, 960pp, Hardback, 9780840064189
MULTIVARIABLE CALCULUS, HYBRID
(WITH ENHANCED WEBASSIGN
AND SCIENCE), 7E
flexible teaching solutions and value for students and
instructors, these new hybrid versions feature the
www.cengageasia.com
33
while delivering end-of-section and/or end-of chapter
exercises online in Enhanced WebAssign. The result—a
briefer printed text that engages students online! James
Stewart’s CALCULUS texts are widely renowned for
their mathematical precision and accuracy, clarity of
exposition, and outstanding examples and problem
sets. Millions of students worldwide have explored
calculus through Stewart’s trademark style, while
instructors have turned to his approach time and
time again. In the Seventh Edition of MULTIVARIABLE
CALCULUS, Stewart continues to set the standard
for the course while adding carefully revised content.
The patient explanations, superb exercises, focus on
problem solving, and carefully graded problem sets
that have made Stewart’s texts best-sellers continue
to provide a strong foundation for the Seventh
Edition. From the most unprepared student to the
most mathematically gifted, Stewart’s writing and
presentation serve to enhance understanding and
build confidence. CourseSmart goes beyond traditional
expectations–providing instant, online access to the
textbooks and course materials you need and at a lower
cost to your students. To request an electronic sample
of this Cengage Learning title, go to: www.coursesmart.
com/instructors.
NEW TO THIS EDITION
• TOC change: Chapters 1 and 2 have been combined –
and some material has been moved to an appendix—to
streamline the presentation of these early topics.
problem.
students.
www.cengageasia.com
34
CONTENTS
1 0 . PA R A M E T R I C E Q UAT I O N S A N D P O L A R
COORDINATES. Curves Defined by Parametric
Equations. Laboratory Project: Families of Hypocycloids.
Calculus with Parametric Curves. Laboratory Project:
Bézier Curves. Polar Coordinates. Laboratory Project:
Families of Polar Curves. Areas and Lengths in Polar
Coordinates. Conic Sections. Conic Sections in Polar
Coordinates. Review. 11. INFINITE SEQUENCES AND
SERIES. Sequences. Laboratory Project: Logistic
Sequences. Series. The Integral Test and Estimates
of Sums. The Comparison Tests. Alternating Series.
Absolute Convergence and the Ratio and Root
Tests. Strategy for Testing Series. Power Series.
The Intersection of Three Cylinders . Triple Integrals in
Change of Variables in Multiple Integrals. Review.
16. ECTOR CALCULUS. Vector Fields. Line Integrals.
Divergence Theorem. Summary. Review. 17. SECONDORDER DIFFERENTIAL EQUATIONS. Second-Order
Series Solutions. Review. APPENDIXES. F. Proofs of
Theorems. G. Graphing Calculators and Computers .
H. Complex Numbers. I. Answers to Odd-Numbered
Exercises.
© 2012, 480pp, Paperback, 9781133110835
SINGLE VARIABLE CALCULUS, 7E
Early Transcendentals, Hybrid Edition (with Enhanced
WebAssign with eBook Printed Access Card for Multi
Term Math and Science)
Stewart’s CALCULUS: EARLY TRANSCENDENTALS
texts are widely renowned for their mathematical
Stewart’s trademark style, while instructors have
www.cengageasia.com
35
turned to his approach time and time again. In the
Seventh Edition of SINGLE VARIABLE CALCULUS:
EARLY TRANSCENDENTALS, Stewart continues to
set the standard for the course while adding carefully
revised content. The patient explanations, superb
exercises, focus on problem solving, and carefully
graded problem sets that have made Stewart’s texts
best-sellers continue to provide a strong foundation for
the Seventh Edition. From the most unprepared student
to the most mathematically gifted, Stewart’s writing
and presentation serve to enhance understanding and
com/instructors.
NEW TO THIS EDITION
1 and 2. This means that Calculus, 7e, and Calculus:
Early Transcendentals, 7e, have the same number
rather than two separate ET and LT versions. Chapters
1 and 2 have been combined – and some material
has been moved to an appendix—to streamline the
presentation of these early topics.
problem.
students.
www.cengageasia.com
36
CONTENTS
AND MODELS. Four Ways to Represent a Function.
New Functions from Old Functions. Graphing
Calculators and Computers. Exponential Functions.
Inverse Functions and Logarithms. Review. 2. LIMITS
AND DERIVATIVES. The Tangent and Velocity Problems.
The Limit of a Function. Calculating Limits Using the
Limit Laws. The Precise Definition of a Limit. Continuity.
Limits at Infinity; Horizontal Asymptotes. Derivatives
and Rates of Change. Writing Project: Early Methods for
Finding Tangents. The Derivative as a Function. Review.
3. DIFFERENTIATION RULES. Derivatives of Polynomials
and Exponential Functions. Applied Project: Building a
Better Roller Coaster. The Product and Quotient Rules.
Derivatives of Trigonometric Functions. The Chain Rule.
Applied Project: Where Should a Pilot Start Descent?
Implicit Differentiation. Derivatives of Logarithmic
Functions. Rates of Change in the Natural and Social
Sciences. Exponential Growth and Decay. Related Rates.
Project: Taylor Polynomials. Hyperbolic Functions.
Derivatives Affect the Shape of a Graph. Indeterminate
Forms and L’Hospital’s Rule. Writing Project: The Origins
of l’Hospital’s Rule. Summary of Curve Sketching.
Graphing with Calculus and Calculators. Optimization
Problems. Applied Project: The Shape of a Can. Newton’s
Method. Antiderivatives. Review. 5. INTEGRALS.
6. APPLICATIONS OF INTEGRATION. Areas between
Curves. Volume. Volumes by Cylindrical Shells. Work.
Average Value of a Function. Applied Project: Where
to Sit at the Movies. Review. 7. TECHNIQUES OF
INTEGRATION. Integration by Parts. Trigonometric
Integrals. Trigonometric Substitution. Integration of
Rational Functions by Partial Fractions. Strategy for
Integration. Integration Using Tables and Computer
Project: Which is Faster, Going Up or Coming Down?
Models for Population Growth. Applied Project:
Calculus and Baseball. Linear Equations. Predator-Prey
Systems. Review. 10. PARAMETRIC EQUATIONS AND
POLAR COORDINATES. Curves Defined by Parametric
Bezier Curves. Polar Coordinates. Areas and Lengths
in Polar Coordinates. Conic Sections. Conic Sections in
Polar Coordinates. Review. 11. INFINITE SEQUENCES
AND SERIES. Sequences. Laboratory Project: Logistic
and Maclaurin Series. Laboratory Project: An Elusive
. Binomial Series. Applications of Taylor Polynomials.
APPENDIXES. A. Numbers, Inequalities, and Absolute
Values. B. Coordinate Geometry and Lines. C. Graphs
of Second-Degree Equations. D. Trigonometry. E. Sigma
Notation. F. Proofs of Theorems. G. The Logarithm
Defined as an Integral. H. Complex Numbers. I. Answers
to Odd-Numbered Exercises.
© 2012, 720pp, Paperback, 9781111426705
www.cengageasia.com
37
FEATURES
Early Transcendentals, AP* Edition
© 2012, 912pp, Hardback, 9780840049322
SINGLE VARIABLE CALCULUS
Early Transcendentals
Soo T. Tan, Stonehill College
Known for accuracy, precision, and rigor, Soo Tan now
brings those same qualities to the Calculus course.
With his clear, concise writing style, and use of
relevant, real world examples, Tan introduces abstract
mathematical concepts with his intuitive approach
that captures student interest without compromising
mathematical rigor. In keeping with this emphasis on
conceptual understanding, each exercise set begins
with concept questions and each end-of-chapter review
section includes fill-in-the-blank questions which help
students master the definitions and theorems in each
chapter. Additionally, many questions asking for the
interpretation of graphical, numerical, and algebraic
results are included among both the examples and the
exercise sets.
• Real-life, Relevant Applications: Soo Tan’s intuitive
approach to calculus links the abstract ideas of
calculus with concrete, real-life examples. One such
example—the maglev (magnetic levitation) train
is used as a common thread from limits through
integration, to show students the connection between
all of these concepts.
• Intuitive Presentation Style: By introducing the limit
concept in the context of finding the rate of change
of the maglev, Tan captures student interest from
the very beginning – this approach demonstrates the
relevance of calculus in the real world. Elsewhere in the
text, this intuitive approach is again used to advantage
to introduce and explain some of the fundamental
theorems in calculus, such as the Intermediate Value
Theorem and the Mean Value Theorem.
• Guidance When Students Need It: Comments
appear next to many of the steps and aid in student
understanding. Notes found at the end of many
examples further explain and clarify the example,
and point out subtleties within them. Cautions
advise students on how to avoid common mistakes
and misunderstandings, addressing both student
misconceptions and situations that often lead
students down unproductive paths.
• Emphasis on Concepts in the Exercise Sets: End of
section Concept Questions are designed to test
students’ understanding and encourage students
to explain these concepts in their own words.
Beginning each end of chapter review, Concept
Review Questions give students a chance to check
their knowledge of the basic definitions and concepts.
• Emphasis on Problem-Solving: Problem-Solving
Techniques, at the end of selected chapters, teach
students the tools they need to make seemingly
complex problems easier to solve.
CONTENTS
0. Preliminaries. 1. Limits. 2. The Derivative. 3.
Applications of the Derivative. 4. Integration. 5.
Applications of the Definite Integral. 6. Techniques
of Integration. 7. Differential Equations. 8. Infinite
Sequences and Series. 9. Conic Sections, Parametric
Equations, and Polar Coordinates.
© 2011, 1008pp, Hardback, 9780534465704
www.cengageasia.com
38
Early Transcendentals
James Stewart’s CALCULUS: EARLY TRANSCENDENTALS
com/instructors.
NEW TO THIS EDITION
problem.
www.cengageasia.com
39
CONTENTS
Inverse Functions and Logarithms. Review. Principles
of Problem Solving. 2. LIMITS AND DERIVATIVES.
The Tangent and Velocity Problems. The Limit of a
Function. Calculating Limits Using the Limit Laws.
The Precise Definition of a Limit. Continuity. Limits
at Infinity; Horizontal Asymptotes. Derivatives and
Rates of Change. Writing Project: Early Methods for
Problems Plus. 3. DIFFERENTIATION RULES. Derivatives
of Polynomials and Exponential Functions. Applied
Project: Building a Better Roller Coaster. The Product
and Quotient Rules. Derivatives of Trigonometric
Functions. The Chain Rule. Applied Project: Where
Should a Pilot Start Descent? Implicit Differentiation.
Derivatives of Logarithmic Functions. Rates of Change
in the Natural and Social Sciences. Exponential Growth
and Decay. Related Rates. Linear Approximations and
Hyperbolic Functions. Review. Problems Plus. 4.
Affect the Shape of a Graph. Indeterminate Forms
and L’Hospital’s Rule. Writing Project: The Origins of
l’Hospital’s Rule. Summary of Curve Sketching. Graphing
Areas between Curves. Volume. Volumes by Cylindrical
Shells. Work. Average Value of a Function. Applied
Project: Where to Sit at the Movies. Review. Problems
Plus. 7. TECHNIQUES OF INTEGRATION. Integration
Partial Fractions. Strategy for Integration. Integration
Using Tables and Computer Algebra Systems. Discovery
Method. Separable Equations. Applied Project: Which
is Faster, Going Up or Coming Down? Models for
Population Growth. Applied Project: Calculus and
Baseball. Linear Equations. Predator-Prey Systems.
Laboratory Project: Bezier Curves. Polar Coordinates.
Areas and Lengths in Polar Coordinates. Conic Sections.
Conic Sections in Polar Coordinates. Review. Problems
Plus. 11. INFINITE SEQUENCES AND SERIES. Sequences.
Taylor and Maclaurin Series. Laboratory Project: An
the . Binomial Series. Applications of Taylor Polynomials.
www.cengageasia.com
40
Problems Plus. APPENDIXES. A. Numbers, Inequalities,
and Absolute Values. B. Coordinate Geometry and Lines.
C. Graphs of Second-Degree Equations. D. Trigonometry.
E. Sigma Notation. F. Proofs of Theorems. G. The
Logarithm Defined as an Integral. H. Complex Numbers.
I. Answers to Odd-Numbered Exercises.
© 2012, 936pp, Hardback, 9780538498678
Vol. 1, Early Transcendentals
James Stewart’s CALCULUS: EARLY TRANSCENDENTALS
build confidence.
NEW TO THIS EDITION
problem.
students.
www.cengageasia.com
41
Hyperbolic Functions. Review. Problems Plus. 4.
Affect the Shape of a Graph. Indeterminate Forms
and L’Hospital’s Rule. Writing Project: The Origins
Method. Antiderivatives. Review. Problems Plus. 5.
Theorem of Calculus. Indefinite Integrals and the Net
Change Theorem. Writing Project: Newton, Leibniz,
and the Invention of Calculus. The Substitution
Rule. Review. Problems Plus. 6. APPLICATIONS OF
INTEGRATION. Areas between Curves. Volume.
Volumes by Cylindrical Shells. Work. Average Value of
a Function. Applied Project: Where to Sit at the Movies.
Review. APPENDIXES. A. Numbers, Inequalities, and
Absolute Values. B. Coordinate Geometry and Lines. C.
Graphs of Second-Degree Equations. D. Trigonometry. E.
Sigma Notation. F. Proofs of Theorems. G. The Logarithm
© 2012, 600pp, Hardback, 9780538498692
CONTENTS
Inverse Functions and Logarithms. Review. Principles
of Problem Solving. 2. LIMITS AND DERIVATIVES.
The Tangent and Velocity Problems. The Limit of a
Function. Calculating Limits Using the Limit Laws.
The Precise Definition of a Limit. Continuity. Limits
at Infinity; Horizontal Asymptotes. Derivatives and
Rates of Change. Writing Project: Early Methods for
Problems Plus. 3. DIFFERENTIATION RULES. Derivatives
of Polynomials and Exponential Functions. Applied
Project: Building a Better Roller Coaster. The Product
and Quotient Rules. Derivatives of Trigonometric
Functions. The Chain Rule. Applied Project: Where
Should a Pilot Start Descent? Implicit Differentiation.
Derivatives of Logarithmic Functions. Rates of Change
in the Natural and Social Sciences. Exponential Growth
and Decay. Related Rates. Linear Approximations and
Concepts & Contexts, Hybrid (with Enhanced WebAssign
with eBook LOE Printed Access Card for One-Term Math
and Science)
www.cengageasia.com
42
NEW TO THIS EDITION
• NEW! The hybrid edition of the text provides a lessexpensive, shorter option for students. End-of-section
FEATURES
proofs.
calculus.
CONTENTS
Preface. To the Student. A Preview of Calculus. 1.
FUNCTIONS AND MODELS. Four Ways to Represent a
Function. Mathematical Models: A Catalog of Essential
Functions. New Functions from Old Functions. Graphing
Inverse Functions and Logarithms. Parametric Curves.
Laboratory Project: Running Circles around Circles.
Review. Principles of Problem Solving. 2. LIMITS AND
DERIVATIVES. The Tangent and Velocity Problems.
the Limit Laws. Continuity. Limits Involving Infinity.
Derivatives and Rates of Change. Writing Project:
as a Function. Review. Focus on Problem Solving. 3.
DIFFERENTIATION RULES. Derivatives of Polynomials
and Exponential Functions. Applied Project: Building
a Better Roller Coaster. The Product and Quotient
Rules. Derivatives of Trigonometric Functions. The
Chain Rule. Laboratory Project: Bézier Curves. Applied
Differentiation. Inverse Trigonometric Functions and
their Derivatives. Derivatives of Logarithmic Functions.
Discovery Project: Hyperbolic Functions. Rates of
Change in the Natural and Social Sciences. Linear
Approximations and Differentials. Laboratory Project:
Taylor Polynomials. Review. Focus on Problem Solving.
www.cengageasia.com
43
4. APPLICATIONS OF DIFFERENTIATION. Related
Rates. Maximum and Minimum Values. Applied Project:
The Calculus of Rainbows. Derivatives and the Shapes
of Curves. Graphing with Calculus and Calculators.
Indeterminate Forms and l’Hospital’s Rule. Writing
Project: The Origins of l’Hospital’s Rule. Optimization
Problems. Applied Project: The Shape of a Can.
Newton’s Method. Antiderivatives. Review. Focus on
Problem Solving. 5. INTEGRALS. Areas and Distances.
The Definite Integral. Evaluating Definite Integrals.
Theorem of Calculus. Writing Project: Newton, Leibniz,
Rule. Integration by Parts. Additional Techniques of
Review. Focus on Problem Solving. 6. APPLICATIONS OF
INTEGRATION. More about Areas. Volumes. Discovery
Project: Rotating on a Slant. Volumes by Cylindrical
Shells. Arc Length. Discovery Project: Arc Length
Contest. Average Value of a Function. Applied Project:
Where To Sit at the Movies. Applications to Physics
and Engineering. Discovery Project: Complementary
Probability. Review. Focus on Problem Solving. 7.
DIFFERENTIAL EQUATIONS. Modeling with Differential
Equations. Direction Fields and Euler’s Method.
Separable Equations. Applied Project: How Fast Does
a Tank Drain? Applied Project: Which Is Faster, Going
Up or Coming Down? Exponential Growth and Decay.
Applied Project: Calculus and Baseball. The Logistic
Equation. Predator-Prey Systems. Review. Focus on
Problem Solving. 8. INFINTE SEQUENCES AND SERIES.
Sequences. Laboratory Project: Logistic Sequences.
Series. The Integral and Comparison Tests; Estimating
Sums. Other Convergence Tests. Power Series.
Representations of Functions as Power Series. Taylor and
Maclaurin Series. Laboratory Project: An Elusive Limit.
Writing Project: How Newton Discovered the Binomial
Series. Applications of Taylor Polynomials. Applied
Project: Radiation from the Stars. Review. Focus on
Problem Solving. APPENDIXES. A. Intervals, Inequalities,
and Absolute Values. B. Coordinate Geometry. C.
Trigonometry. D. Precise Definitions of Limits. E. A Few
Proofs. F. Sigma Notation. G. Integration of Rational
Functions by Partial Fractions. H. Polar Coordinates.
I. Complex Numbers. J. Answers to Odd-Numbered
Exercises.
© 2013, 624pp, Paperback, 9781133627159
SINGLE VARIABLE CALCULUS, HYBRID
REPRINT (WITH ENHANCED WEBASSIGN
WITH EBOOK FOR MULTI TERM MATH
AND SCIENCE), 7E
value for students, these new hybrid versions feature
the same content and coverage found in the full
text while delivering end-of-section exercises online
in Enhanced WebAssign®. Access to Enhanced
WebAssign and the new media-rich Cengage YouBook is
included with every new text, giving you an interactive
learning experience with the convenience of a text that
is both brief and affordable. Success in your calculus
course starts here! James Stewart’s CALCULUS texts
are world-wide best-sellers for a reason: they are clear,
accurate, and filled with relevant, real-world examples.
With SINGLE VARIABLE CALCULUS, Seventh Edition,
Stewart conveys not only the utility of calculus to help
you develop technical competence, but also gives you
an appreciation for the intrinsic beauty of the subject.
His patient examples and built-in learning aids will help
you build your mathematical confidence and achieve
your goals in the course!
NEW TO THIS EDITION
these early topics.
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44
problem.
students.
CONTENTS
A Preview of Calculus. 1. FUNCTIONS AND LIMITS. Four
Ways to Represent a Function. Mathematical Models: A
Catalog of Essential Functions. New Functions from Old
Functions. The Tangent and Velocity Problems. The Limit
of a Function. Calculating Limits Using the Limit Laws.
The Precise Definition of a Limit. Continuity. Review. 2.
Project: Families of Implicit Curves. Rates of Change in
the Natural and Social Sciences. Related Rates. Linear
Taylor Polynomials. Review. 3. APPLICATIONS OF
Applied Project: The Calculus of Rainbows. The Mean
Value Theorem. How Derivatives Affect the Shape of
a Graph. Limits at Infinity; Horizontal Asymptotes.
Summary of Curve Sketching. Graphing with Calculus
and Calculators. Optimization Problems. Applied Project:
The Shape of a Can. Newton’s Method. Antiderivatives.
Review. 4. INTEGRALS. Areas and Distances. The
Definite Integral. Discovery Project: Area Functions. The
Fundamental Theorem of Calculus. Indefinite Integrals
and the Net Change Theorem. Writing Project: Newton,
Leibniz, and the Invention of Calculus. The Substitution
Rule. Review. 5. APPLICATIONS OF INTEGRATION.
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Value of a Function. Review. 6. INVERSE FUNCTIONS:
EXPONENTIAL, LOGARITHMIC, AND INVERSE
TRIGONOMETRIC FUNCTIONS. Inverse Functions.
(Instructors may cover either Sections 6.2-6.4 or Sections
6.2*-6.4*. See the Preface.). Exponential Functions and
Logarithmic and Exponential Function. Exponential
7. TECHNIQUES OF INTEGRATION. Integration by Parts.
Trigonometric Integrals. Trigonometric Substitution.
Integration of Rational Functions by Partial Fractions.
Strategy for Integration. Applied Project: Calculus
and Baseball. Integration Using Tables and Computer
Which is Faster, Going Up or Coming Down? Models
for Population Growth. Linear Equations. PredatorPrey Systems. Review. 10. PARAMETRIC EQUATIONS
Sections in Polar Coordinates. Review. 11. INFINITE
Project: Logistic Sequences. Series. The Integral Test and
Estimates of Sums. The Comparison Tests. Alternating
Series. Absolute Convergence and the Ratio and
Root Tests. Strategy for Testing Series. Power Series.
APPENDIXES. A. Intervals, Inequalities, and Absolute
of Second-Degree Equations. D. Trigonometry. E.
Sigma Notation. F. Proofs of Theorems. G. Graphing
Calculators and Computers. H. Complex Numbers. I.
© 2012, 744pp, Paperback, 9781133112112
SINGLE VARIABLE CALCULUS,
INTERNATIONAL METRIC EDITION, 7E
James Stewart’s CALCULUS, 7e, International Metric
Edition texts are widely renowned for their mathematical
Stewart’s trademark style, while instructors have turned
to his approach time and time again. In the Seventh
Edition of SINGLE VARIABLE CALCULUS, International
Metric Edition, Stewart continues to set the standard
build confidence.
NEW TO THIS EDITION
www.cengageasia.com
46
these early topics.
problem.
students.
online program for Stewart’s Calculus, 7e, International
Metric Edition to encourage the practice that’s
assignments. Enhanced WebAssign for Stewart
now includes opportunities for students to review
prerequisite skills and content both at the start of
the course (in conjunction with four diagnostic tests)
and at the beginning of each section. In addition, at
the problem-level, student can get extra help in the
form of “math mentor” feedback and video solutions.
• NEW! Cengage YouBook is a Flash-based eBook that
is interactive and customizable! Containing all the
content from Stewart’s Calculus, 7e, International
Metric Edition, YouBook features a text edit tool that
allows you to rewrite, delete, modify, or add to the
textbook narrative as needed. With YouBook, you can
quickly re-order entire chapters and sections or hide
any content you don’t teach to create an eBook that
perfectly matches your syllabus. Additional media
assets include interactive simulations, animations,
and video clips that complement the traditional
text presentation. The YouBook also lets you embed
videos of your own or from YouTube directly into
eBook pages.
FEATURES
CONTENTS
Ways to Represent a Function. Mathematical Models:
A Catalog of Essential Functions. New Functions from
Project: Families of Implicit Curves. Rates of Change
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47
in the Natural and Social Sciences. Related Rates.
Project: Taylor Polynomials. Review. Problems Plus.
3. APPLICATIONS OF DIFFERENTIATION. Maximum
Affect the Shape of a Graph. Limits at Infinity; Horizontal
Asymptotes. Summary of Curve Sketching. Graphing
Value of a Function. Review. Problems Plus. 6. INVERSE
FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND
INVERSE TRIGONOMETRIC FUNCTIONS. Inverse
Functions. (Instructors may cover either Sections 6.26.4 or Sections 6.2*-6.4*. See the Preface.). Exponential
Functions and Their Derivatives. Logarithmic Functions.
Derivatives of Logarithmic Functions. The Natural
Logarithmic Function. The Natural Exponential
Function. General Logarithmic and Exponential
Function. Exponential Growth and Decay. Inverse
Trigonometric Functions. Applied Project: Where to Sit
at the Movies. Hyperbolic Functions. Indeterminate
Origins of l’Hospital’s Rule. Review. Problems Plus.
7. TECHNIQUES OF INTEGRATION. Integration
Partial Fractions. Strategy for Integration. Applied
Project: Calculus and Baseball. Integration Using
Taylor and Maclaurin Series. Laboratory Project: An
Problems Plus. APPENDIXES. A. Intervals, Inequalities,
E. Sigma Notation. F. Proofs of Theorems. G. Graphing
© 2012, 960pp, Hardback, 9780538498852
SINGLE VARIABLE CALCULUS, VOLUME
1, 7E
James Stewart’s CALCULUS texts are widely renowned
for their mathematical precision and accuracy, clarity of
exposition, and outstanding examples and problem sets.
Millions of students worldwide have explored calculus
through Stewart’s trademark style, while instructors
have turned to his approach time and time again. In
the Seventh Edition of SINGLE VARIABLE CALCULUS,
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48
NEW TO THIS EDITION
problem.
students.
FEATURES
CONTENTS
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49
Tangents.The Derivative as a Function. Differentiation
the Natural and Social Sciences. Related Rates.
Project: Taylor Polynomials. Review. Problems Plus. 3.
APPLICATIONS OF DIFFERENTIATION.
Maximum and Minimum Values. Applied Project:
The Calculus of Rainbows. The Mean Value Theorem.
How Derivatives Affect the Shape of a Graph. Limits
at Infinity; Horizontal Asymptotes. Summary of Curve
Optimization Problems. Applied Project: The Shape
of a Can. Newton’s Method. Antiderivatives. Review.
Problems Plus. 4. INTEGRALS. Areas and Distances. The
INTEGRATION. Areas Between Curves. Applied Project:
The Gini Index. Volumes. Volumes by Cylindrical Shells.
Work. Average Value of a Function. Applied Project:
Calculus and Baseball. Review. Problems Plus. Appendix
A: Intervals, Inequalities, and Absolute Values.
Appendix B: Coordinate Geometry and Lines. Appendix
C: Graphs of Second-Degree Equations. Appendix D:
Trigonometry. Appendix E: Sigma Notation. Appendix F:
Proofs of Theorems. Appendix G: Graphing Calculators
and Computers. Appendix H: Complex Numbers.
Appendix I: Answers to Odd-Numbered Exercises.
© 2012, 504pp, Hardback, 9780538497848
2, 7E
NEW TO THIS EDITION
problem.
www.cengageasia.com
50
students.
FEATURES
CONTENTS
4. INTEGRALS. Areas and Distances. The Definite
Integral. Discovery Project: Area Functions. The
The Gini Index. Volume. Volumes by Cylindrical Shells.
Work. Average Value of a Function. Review. Problems
Plus. 6. INVERSE FUNCTIONS: Exponential, Logarithmic,
and Inverse Trigonometric Functions. Inverse Functions.
Problems Plus. 7. TECHNIQUES OF INTEGRATION.
Integration by Parts. Trigonometric Integrals.
Trigonometric Substitution. Integration of Rational
Functions by Partial Fractions. Strategy for Integration.
Applied Project: Calculus and Baseball. Integration
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51
© 2012, 648pp, Hardback, 9780538497855
SINGLE VARIABLE CALCULUS: CONCEPTS
& CONTEXTS, HYBRID WITH ENHANCED
WEBASSIGN PRINTED ACCESS CARD, 3
SEMESTER, 4E
NEW TO THIS EDITION
www.cengageasia.com
52
FEATURES
proofs.
calculus.
CONTENTS
Preface. To the Student. A Preview of Calculus. 1.
FUNCTIONS AND MODELS. Four Ways to Represent a
Function. Mathematical Models: A Catalog of Essential
Functions. New Functions from Old Functions. Graphing
Inverse Functions and Logarithms. Parametric Curves.
Laboratory Project: Running Circles around Circles.
Review. Principles of Problem Solving. 2. LIMITS AND
DERIVATIVES. The Tangent and Velocity Problems.
the Limit Laws. Continuity. Limits Involving Infinity.
Derivatives and Rates of Change. Writing Project:
as a Function. Review. Focus on Problem Solving. 3.
DIFFERENTIATION RULES. Derivatives of Polynomials
and Exponential Functions. Applied Project: Building
a Better Roller Coaster. The Product and Quotient
Rules. Derivatives of Trigonometric Functions. The
Chain Rule. Laboratory Project: Bézier Curves. Applied
Differentiation. Inverse Trigonometric Functions and
their Derivatives. Derivatives of Logarithmic Functions.
Discovery Project: Hyperbolic Functions. Rates of
Change in the Natural and Social Sciences. Linear
Taylor Polynomials. Review. Focus on Problem Solving.
4. APPLICATIONS OF DIFFERENTIATION. Related
Rates. Maximum and Minimum Values. Applied Project:
The Calculus of Rainbows. Derivatives and the Shapes
of Curves. Graphing with Calculus and Calculators.
Indeterminate Forms and l’Hospital’s Rule. Writing
Project: The Origins of l’Hospital’s Rule. Optimization
Problems. Applied Project: The Shape of a Can.
Newton’s Method. Antiderivatives. Review. Focus on
Problem Solving. 5. INTEGRALS. Areas and Distances.
The Definite Integral. Evaluating Definite Integrals.
Theorem of Calculus. Writing Project: Newton, Leibniz,
Rule. Integration by Parts. Additional Techniques of
Review. Focus on Problem Solving. 6. APPLICATIONS OF
INTEGRATION. More about Areas. Volumes. Discovery
Project: Rotating on a Slant. Volumes by Cylindrical
Shells. Arc Length. Discovery Project: Arc Length
Contest. Average Value of a Function. Applied Project:
Where To Sit at the Movies. Applications to Physics
and Engineering. Discovery Project: Complementary
Probability. Review. Focus on Problem Solving. 7.
DIFFERENTIAL EQUATIONS. Modeling with Differential
Equations. Direction Fields and Euler’s Method.
Separable Equations. Applied Project: How Fast Does
a Tank Drain? Applied Project: Which Is Faster, Going
Up or Coming Down? Exponential Growth and Decay.
Applied Project: Calculus and Baseball. The Logistic
Equation. Predator-Prey Systems. Review. Focus on
Problem Solving. 8. INFINTE SEQUENCES AND SERIES.
Sequences. Laboratory Project: Logistic Sequences.
Series. The Integral and Comparison Tests; Estimating
Sums. Other Convergence Tests. Power Series.
Representations of Functions as Power Series. Taylor and
Maclaurin Series. Laboratory Project: An Elusive Limit.
Writing Project: How Newton Discovered the Binomial
Series. Applications of Taylor Polynomials. Applied
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53
Project: Radiation from the Stars. Review. Focus on
Problem Solving. APPENDIXES. A. Intervals, Inequalities,
and Absolute Values. B. Coordinate Geometry. C.
Trigonometry. D. Precise Definitions of Limits. E. A Few
Proofs. F. Sigma Notation. G. Integration of Rational
Functions by Partial Fractions. H. Polar Coordinates.
I. Complex Numbers. J. Answers to Odd-Numbered
Exercises.
© 2013, 624pp, Paperback, 9781285056654
SINGLE VARIABLE ESSENTIAL CALCULUS,
INTERNATIONAL METRIC EDITION, 2E
This book is for instructors who think that most
calculus textbooks are too long. In writing the book,
James Stewart asked himself: What is essential for a
calculus course for scientists and engineers? SINGLE
VARIABLE ESSENTIAL CALCULUS, 2E, International
Metric Edition offers a concise approach to teaching
calculus that focuses on major concepts, and supports
those concepts with precise definitions, patient
explanations, and carefully graded problems. The book
is only 550 pages—two-fifths the size of Stewart’s other
calculus texts (CALCULUS, 7E, International Metric
Edition and CALCULUS: EARLY TRANSCENDENTALS,
7E, International Metric) and yet it contains almost all
of the same topics. The author achieved this relative
brevity primarily by condensing the exposition and by
putting some of the features on the book’s website,
www.StewartCalculus.com. Despite the more compact
size, the book has a modern flavor, covering technology
and incorporating material to promote conceptual
understanding, though not as prominently as in
Stewart’s other books. SINGLE VARIABLE ESSENTIAL
CALCULUS, 2E, International Metric Edition features
the same attention to detail, eye for innovation,
and meticulous accuracy that have made Stewart’s
textbooks the best-selling calculus texts in the world.
NEW TO THIS EDITION
students’ prerequisite skills—and help them start the
course with confidence—by giving them opportunities
• Enhanced WebAssign® for Stewart’s SINGLE
VARIABLE ESSENTIAL CALCULUS, 2E, International
Metric Edition -is enhanced with new features and
functions. These include Enhanced Feedback for
Enhanced WebAssign.
FEATURES
author’s website www.stewartcalculus.com.
• Certain topics, such as the treatment of the integral
and the remainder term in Taylor Series, are presented
in a manner that is more traditional than Stewart’s
other books.
www.cengageasia.com
54
late, with the logarithm defined as an integral.
Those wishing to cover such functions earlier
should consider, ESSENTIAL CALCULUS: EARLY
TRANSCENDENTALS, 2e, International Metric Edition.
CONTENTS
and Minimum Values. The Mean Value Theorem.
Derivatives and the Shapes of Graphs. Curve
Sketching. Optimization Problems. Newton’s Method.
Antiderivatives. 4. INTEGRALS. Areas and Distances.
The Definite Integral. Evaluating Definite Integrals. The
Fundamental Theorem of Calculus. The Substitution
Rule. 5. INVERSE FUNCTIONS. Inverse Functions.
The Natural Logarithmic Function. The Natural
Exponential Function. General Logarithmic and
Exponential Functions. Exponential Growth and
Decay. Inverse Trigonometric Functions. Hyperbolic
6. TECHNIQUES OF INTEGRATION. Integration by
Parts. Trigonometric Integrals and Substitutions.
Partial Fractions. Integration with Tables and Computer
Algebra Systems. Approximate Integration. Improper
Integrals. 7. APPLICATIONS OF INTEGRATION. Areas
between Curves. Volumes. Volumes by Cylindrical
Shells. Arc Length. Area of a Surface of Revolution.
Applications to Physics and Engineering. Differential
Equations. 8. SERIES. Sequences. Series. The Integral
and Comparison Tests. Other Convergence Tests.
Power Series. Representing Functions as Power Series.
Taylor and Maclaurin Series. Applications of Taylor
Polynomials. 9. PARAMETRIC EQUATIONS AND
POLAR COORDINATES. Parametric Curves. Calculus
with Parametric Curves. Polar Coordinates. Areas and
Lengths in Polar Coordinates. Conic Sections in Polar
Coordinates. Appendix A: Trigonometry. Appendix B:
Proofs. Appendix C: Sigma Notation.
© 2013, 648pp, Paperback, 9781133528623
SINGLE VARIABLE ESSENTIAL CALCULUS:
EARLY TRANSCENDENTALS, 2E
This book is for instructors who think that most
calculus textbooks are too long. In writing the book,
James Stewart asked himself: What is essential for
a three-semester calculus course for scientists and
engineers? SINGLE VARIABLE ESSENTIAL CALCULUS:
EARLY TRANSCENDENTALS, Second Edition, offers a
concise approach to teaching calculus that focuses
on major concepts, and supports those concepts with
precise definitions, patient explanations, and carefully
graded problems. The book is only 600 pages--less
than half the size of Stewart’s other calculus texts
(CALCULUS, Seventh Edition and CALCULUS: EARLY
TRANSCENDENTALS, Seventh Edition) and yet it
contains almost all of the same topics. The author
achieved this relative brevity primarily by condensing
the exposition and by putting some of the features
on the book’s website, www.StewartCalculus.com.
Despite the more compact size, the book has a
modern flavor, covering technology and incorporating
material to promote conceptual understanding,
though not as prominently as in Stewart’s other books.
SINGLE VARIABLE ESSENTIAL CALCULUS: EARLY
TRANSCENDENTALS features the same attention to
detail, eye for innovation, and meticulous accuracy
that have made Stewart’s textbooks the best-selling
calculus texts in the world.
NEW TO THIS EDITION
• The book begins with four diagnostic tests--in
Trigonometry--addressing the gaps in many students’
prerequisite skills by giving them opportunities to get
up to speed at the beginning of the Calculus course.
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55
CALCULUS: EARLY TRANSCENDENTALS, 2nd
Edition--which combines the mathematics content
in this text with the most powerful online homework
solution, WebAssign--is enhanced with new features
and functions. These include Enhanced Feedback for
Enhanced WebAssign.
FEATURES
• Certain topics, or example, the treatment of the
Stewart’s other books.
in Chapter Three. Those who wish to cover such
functions later, with the logarithm defined as an
integral, should consider the book entitled simply,
ESSENTIAL CALCULUS.
INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC,
AND INVERSE TRIGONOMETRIC FUNCTIONS.
Exponential Functions. Inverse Functions and Logarithms.
Derivatives of Logarithmic and Exponential Functions.
Exponential Growth and Decay. Inverse Trigonometric
Functions. Hyperbolic Functions. 3.7 Indeterminate
Forms and l’Hospital’s Rule 4. APPLICATIONS OF
The Mean Value Theorem. Derivatives and the Shapes
of Graphs. Curve Sketching. Optimization Problems.
Newton’s Method. Antiderivatives. 5. INTEGRALS. Areas
and Distances. The Definite Integral. Evaluating Definite
Integrals. The Fundamental Theorem of Calculus. The
Substitution Rule. 6. TECHNIQUES OF INTEGRATION.
Integration by Parts. Trigonometric Integrals and
Substitutions. Partial Fractions. Integration with
Tables and Computer Algebra Systems. Approximate
Integration. Improper Integrals. 7. APPLICATIONS
OF INTEGRATION. Areas between Curves. Volumes.
Volumes by Cylindrical Shells. Arc Length. Area of
a Surface of Revolution. Applications to Physics
and Engineering. Differential Equations. 8. SERIES.
Sequences. Series. The Integral and Comparison Tests.
Other Convergence Tests. Power Series. Representing
Functions as Power Series. Taylor and Maclaurin Series.
Applications of Taylor Polynomials. 9. PARAMETRIC
EQUATIONS AND POLAR COORDINATES. Parametric
Curves. Calculus with Parametric Curves. Polar
Coordinates. Areas and Lengths in Polar Coordinates.
Conic Sections in Polar Coordinates. Appendix A.
Trigonometry Appendix B. Proofs Appendix C. Sigma
Notation Appendix D. The Logarithm Defined as an
Integral
© 2013, 648pp, Hardback, 9781133112785
CONTENTS
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56
Developmental Mathematics
STUDENT SOLUTIONS MANUAL FOR
LARSON/EDWARDS’ CALCULUS OF A
SINGLE VARIABLE, 10TH, 10E
Need a leg up on your homework or help to prepare
for an exam? The Student Solutions Manual contains
worked-out solutions for all odd-numbered exercises
in Calculus of a Single Variable 10e (Chapters P-11
of Calculus 10e). It is a great resource to help you
understand how to solve those tough problems.
© 2014, 648pp, Paperback, 9781285085715
STUDENT SOLUTIONS MANUAL
FOR LARSON/EDWARDS’ CALCULUS
OF A SINGLE VARIABLE: EARLY
TRANSCENDENTAL FUNCTIONS, 6TH, 6E
This manual contains worked-out solutions for all oddnumbered exercises in Larson/Edwards’s CALCULUS
OF A SINGLE VARIABLE: EARLY TRANSCENDENTAL
FUNCTIONS, Sixth Edition (Chapters 1-10 of CALCULUS:
EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition).
ELEMENTARY TECHNICAL
MATHEMATICS, 11E
Dale Ewen, Parkland Community College; C. Robert Nelson,
Champaign Centennial High School
ELEMENTARY TECHNICAL MATHEMATICS Eleventh
Edition is written to help students with minimal math
background successfully prepare for technical, trade,
allied health, or Tech Prep programs. The authors
focus on fundamental concepts in basic arithmetic
including the metric system and measurement,
algebra, geometry, trigonometry, and statistics, which
are supported by thousands of examples, exercises,
and applications surrounding such fields as industrial
and construction trades, electronics, agriculture/
horticulture, allied health, CAD/drafting, HVAC,
welding, auto/diesel service, aviation, natural resources,
culinary arts, business/personal finance, and others.
For this revision, the authors have added over 150
new exercises, 30 new examples, new applications
categories, and a new appendix on simple inequalities.
The goal of ELEMENTARY TECHNICAL MATHEMATICS
is to engage students and provide them with the math
background they need to succeed in future courses
and careers.
NEW TO THIS EDITION
• New categories of applications: culinary arts and
business and personal finance.
• New and revised applications in agriculture with
horticulture added, auto/diesel service, and allied
health.
• New Appendix C on Simple Inequalities.
• 150 new exercises. 30 new examples.
© 2015, 640pp, Paperback, 9781285774800
www.cengageasia.com
57
FEATURES
• This book features a large number of applications
from a wide variety of technical areas noted by
marginal icons, including industrial and construction
trades, electronics, agriculture/horticulture, allied
health, CAD/drafting, HVAC, welding, auto/diesel
service, aviation, natural resources, culinary arts, and
business/personal finance. Marginal icons are used to
call attention to the applications, making it easier for
instructors and students to benefit from them.
• Each chapter opener presents basic information about
a technical career.
• The inside covers contain useful, frequently referenced
information—such as metric system prefixes, English
weights and measures, metric and English conversion,
and formulas from geometry.
• Chapter 1 reviews basic concepts in such a way that
students or the entire class can easily study only those
sections they need to review.
• The use of a scientific calculator has been integrated in
an easy to use format throughout the text to reflect its
nearly universal use in technical classes and on the job.
• Includes signed number drills exercises to assist
students in learning addition, subtraction, and
multiplication on signed numbers.
CONTENTS
1. BASIC CONCEPTS. Unit1A Review of Operations
with Whole Numbers. 1.1 Review of Basic Operations.
1.2 Order of Operations. 1.3 Area and Volume. 1.4
Formulas. 1.5 Prime Factorization Divisibility. Unit 1A:
Review. Unit 1B Review of Operations with Fractions. 1.6
Introduction to Fractions. 1.7 Addition and Subtraction
of Fractions. 1.8 Multiplication and Division of Fractions.
1.9 The U.S. System of Weights and Measures. Unit 1B:
Review. Unit 1C Review of Operations with Decimal
Fractions and Percent. 1.10 Addition and Subtraction
of Decimal Fractions. 1.11 Rounding Numbers. 1.12
Multiplication and Division of Decimal Fractions. 1.13
Percent. 1.14 Part, Base, and Rate. 1.15 Powers and Roots.
1.16 Application Involving Percent: Business and Personal
Finance. Unit 1C: Review. Chapter 1: Group Activities.
Chapter 1: Summary. Chapter 1: Review. Chapter 1: Test.
2. SIGNED NUMBERS AND POWERS OF 10. 2.1 Addition
of Signed Numbers. 2.2 Subtraction of Signed Numbers.
2.3 Multiplication and Division of Signed Numbers.
2.4 Signed Fractions. 2.5 Powers of 10. 2.6 Scientific
Notation. 2.7 Engineering Notation. Chapter 2: Group
Activities. Chapter 2: Summary. Chapter 2: Review.
Chapter 2: Test. Chapter 1-2: Cumulative Review. 3. THE
METRIC SYSTEM. 3.1 Introduction to the Metric System.
3.2 Length. 3.3 Mass and Weight. 3.4 Volume and Area.
3.5 Time, Current, and Other Units. 3.6 Temperature. 3.7
Metric and U.S. Conversion. Chapter 3: Group Activities.
Chapter 3: Summary. Chapter 3: Review. Chapter 3:
Test. 4. MEASUREMENT. 4.1 Approximate Numbers
and Accuracy. 4.2 Precision and Greatest Possible
Error. 4.3 The Vernier Caliper. 4.4 The Micrometer
Caliper. 4.5 Addition and Subtraction of Measurements.
4.6 Multiplication and Division of Measurements. 4.7
Relative Error and Percent of Error. 4.8 Color Code
of Electrical Resistors. 4.9 Reading Scales. Chapter
4: Group Activities. Chapter 4: Summary. Chapter
4: Review. Chapter 4: Test. Chapter 1-4: Cumulative
Review. 5. POLYNOMIALS: AN INTRODUCTION TO
ALGEBRA. 5.1 Fundamental Operations. 5.2 Simplifying
Algebraic Expressions. 5.3 Addition and Subtraction
of Polynomials. 5.4 Multiplication of Monomials.
5.5 Multiplication of Polynomials. 5.6 Division by a
Monomial. 5.7 Division by a Polynomial. Chapter
5: Group Activities. Chapter 5: Summary. Chapter
5: Review. Chapter 5: Test. 6. EQUATIONS AND
FORMULAS. 6.1 Equations. 6.2 Equations with Variables
in Both Members. 6.3 Equations with Parentheses.
6.4 Equations with Fractions. 6.5 Translating Words
into Algebraic Symbols. 6.6 Applications Involving
Equations. 6.7 Formulas. 6.8 Substituting Data into
Formulas. 6.9 Reciprocal Formulas Using a Calculator.
Chapter 6: Group Activities. Chapter 6: Summary.
Chapter 6: Review. Chapter 6: Test. Chapters 1-6:
Cumulative Review. 7. RATIO AND PROPORTION. 7.1
Ratio. 7.2 Proportion. 7.3 Direct Variation. 7.4 Inverse
Variation. Chapter 7: Group Activities. Chapter 7:
Summary. Chapter 7: Review. Chapter 7: Test. 8.
GRAPHING LINEAR EQUATIONS. 8.1 Linear Equations
with Two Variables. 8.2 Graphing Linear Equations. 8.3
The Slope of a Line. 8.4 The Equation of a Line. Chapter
8: Group Activities. Chapter 8: Summary. Chapter 8:
Review. Chapter 8: Test. Chapters 1-8: Cumulative
Review. 9. SYSTEMS OF LINEAR EQUATIONS. 9.1
Solving Pairs of Linear Equations by Graphing. 9.2
Solving Pairs of Linear Equations by Addition. 9.3
Solving Pairs of Linear Equations by Substitution.
9.4 Applications Involving Pairs of Linear Equations.
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58
Chapter 9: Review. Chapter 9: Test. 10. FACTORING
ALGEBRAIC EXPRESSIONS. 10.1 Finding Monomial
Factors. 10.2 Finding the Product of Two Binomials
Mentally. 10.3 Finding Binomial Factors. 10.4 Special
Products. 10.5 Finding Factors of Special Products.
10.6 Factoring General Trinomials. Chapter 10: Group
Chapter 10: Test. Chapters 1-10: Cumulative Review.
11. QUADRATIC EQUATIONS. 11.1 Solving Quadratic
Equations by Factoring. 11.2 The Quadratic Formula.
11.3 Applications Involving Quadratic Equations. 11.4
Graphs of Quadratic Equations. 11.5 Imaginary Numbers.
Chapter 11: Review. Chapter 11: Test. 12. GEOMETRY.
12.1 Angles and Polygons. 12.2 Quadrilaterals. 12.3
Triangles. 12.4 Similar Polygons. 12.5 Circles. 12.6
Radian Measure. 12.7 Prisms. 12.8 Cylinders. 12.9
Pyramids and Cones. 12.10 Spheres. Chapter 12: Group
Chapter 12: Test. Chapters 1-12: Cumulative Review. 13.
RIGHT TRIANGLE TRIGONOMETRY. 13.1 Trigonometric
Ratios. 13.2 Using Trigonometric Ratios to Find Angles.
13.3 Using Trigonometric Ratios to Find Sides. 13.4
Solving Right Triangles. 13.5 Applications Involving
Trigonometric Ratios. Chapter 13: Group Activities.
Chapter 13: Summary. Chapter 13: Review. Chapter
13: Test. 14. TRIGONOMETRY WITH ANY ANGLE. 14.1
Sine and Cosine Graphs. 14.2 Period and Phase Shift.
14.3 Solving Oblique Triangles: Law of Sines. 14.4 Law
of Sines: The Ambiguous Case. 14.5 Solving Oblique
Triangles: Law of Cosines. Chapter 14: Group Activities.
Chapter 14: Summary. Chapter 14: Review. Chapter
14: Test. Chapters 1-14: Cumulative Review. 15. BASIC
STATISTICS. 15.1 Bar Graphs. 15.2 Circle Graphs. 15.3 Line
Graphs. 15.4 Other Graphs. 15.5 Mean Measurement.
15.6 Other Average Measurements and Percentiles. 15.7
Range and Standard Deviation. 15.8 Grouped Data. 15.9
Standard Deviation for Grouped Data. 15.10 Statistical
Process Control. 15.11 Other Graphs for Statistical
Data. 15.12 Normal Distribution. 15.13 Probability. 15.14
Independent Events. Chapter 15: Group Activities.
Chapter 15: Summary. Chapter 15: Review. Chapter 15:
Test. 16. BINARY AND HEXADECIMAL NUMBERS. 16.1
Introduction to Binary Numbers. 16.2 Addition of Binary
Numbers. 16.3 Subtraction of Binary Numbers. 16.4
Multiplication of Binary Numbers. 16.5 Conversion from
Decimal to Binary System. 16.6 Conversion from Binary
to Decimal System. 16.7 Hexadecimal System. 16.8
Addition and Subtraction of Hexadecimal Numbers. 16.9
Binary to Hexadecimal Conversion. 16.10 Hexadecimal
Code for Colors. Chapter 16: Group Activities. Chapter
16: Summary. Chapter 16: Review. Chapter 16: Test.
Chapters 1-16: Cumulative Review. Appendix A: Tables.
Table 1: Formulas from Geometry. Table 2: Electrical
Symbols. Appendix B: Exponential Equations. Appendix
C: Simple Inequalities Appendix D: Instructor’s Answer
Key to All Exercises.
© 2015, 640pp, Paperback, 9781285199191
INTERMEDIATE ALGEBRA,
INTERNATIONAL EDITION
Laura Bracken, Lewis-Clark State College; Ed Miller, Lewis-Clark State
College
INTERMEDIATE ALGEBRA, International Edition offers
a practical approach to the study of intermediate
algebra concepts, consistent with the needs of today’s
student. The authors help students to develop a solid
understanding of functions by revisiting key topics
related to functions throughout the text. They put
special emphasis on the worked examples in each
section, treating them as the primary means of
instruction, since students rely so heavily on examples to
complete assignments. Many of the applications (both
within the examples and exercises) are also uniquely
designed so that students have an experience that is
more true to life—students must read information as it
appears in headline news sources and extract only the
relevant information needed to solve a stated problem.
This promotes the text’s focus on developing better
study habits, problem solving and critical thinking
skills along with orienting students to think and reason
mathematically. Through INTERMEDIATE ALGEBRA,
International Edition, students will not only be better
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59
prepared for future math courses, they will be better
prepared to solve problems and answer questions they
encounter in their own lives.
FEATURES
• Functions early and often. The authors introduce
several key concepts related to functions in Chapter
3 and then revisited in more depth in later chapters,
where appropriate. The concepts include domain,
range, maximum, minimum, zeros, evaluating
functions, and translating functions. These concepts
appear as soon as students complete their review
of elementary algebra and their initial work with
polynomials.
• Applications with data in “as is” form. Many of
the application exercises and examples reference
information taken directly from headline news,
research studies, or reports. The excerpts contain
information that is relevant to solve the problems as
well as extraneous information that requires students
to read and think critically, rather than randomly “plug
and chug.” No bigger than “texts” or “tweets,” these
authentic excerpts help students develop the skill of
using information found in every day media to solve
problems and make decisions not only in Intermediate
Algebra, but in their own lives.
• Five Steps Framework for Problem Solving. Based on
the work of George Polya, the Five Steps provide a
framework for solving application problems and are
used consistently throughout the textbook to solve a
wide variety of problems. Putting the Five Steps to use
will help students overcome any trepidation, so that
they can confidently unravel application problems,
no matter their type.
• Success in College Mathematics. To help students
better understand the culture of college, these
chapter opener narratives address topics such
as personal responsibility, study skills, and time
management. Follow-up exercises appear at the end
of each section to help students reflect on their own
attitudes and habits so that they can improve their
performance and ensure success.
• Examples with step-by-step explanation. Each step
of the worked examples is accompanied by an
annotation that explains how the solution progresses,
from the first line to the final answer. Color-coding and
boldface are also used to help students easily identify
the operation that occurs in each step.
• Side-by-side Examples. Some of the processes used
to solve arithmetic equations can be directly applied
to solve algebraic equations. Accordingly, some of
the worked examples are set up with an arithmetic
equation and a parallel algebraic equation side-byside. In this format, students can more readily see
how each step of the solution to one equation mimics
the other and how they can apply what they already
know to something new.
• Practice Problems. Following a set of worked
examples in each section are a short set of Practice
Problems that mirror the examples. Students can use
the Practice Problems to check their understanding
of the concepts or skills presented.
• Problem Solving: Practice and Review. Found in the
majority of the section-ending exercise sets are a set
of four applications-based exercises called ProblemSolving: Practice and Review. Because these problems
do not necessarily involve the concepts or skills taught
in the section, students need to think critically about
the information and relationships in the problem.
• Find the Mistake. Each section-ending exercise set
includes Find the Mistake exercises. In each of these
exercises, students are asked to identify the error and
then rework the problem correctly. By including these
exercises the authors cultivate greater self-sufficiency
on the part of students—encouraging them to develop
the skills they need to correct their own work.
• Learning the Language of Math. Vocabulary matching
exercises that appear before the section-ending
exercises as well as writing exercises that appear
within the section-ending exercises help students
improve their knowledge of vocabulary and notation.
CONTENTS
1. FUNDAMENTALS OF ALGEBRA. Success in
College Mathematics: Personal Responsibility. Sets
and Numerical Expressions. Algebraic Expressions.
Equations and Inequalities in One Variable. Scientific
Notation and Unit Analysis. Applications and Problem
Solving. Slope and Linear Equations in Two Variables.
Writing the Equation of a Line. Linear Inequalities
in Two Variables. Study Plan for Review of Chapter
1. Chapter Test. 2. POLYNOMIALS AND ABSOLUTE
VALUE. Success in College Mathematics: Studying for
Tests. Adding, Subtracting, and Multiplying Polynomial
Expressions. Factoring Polynomials: Greatest Common
Factor and Grouping. Factoring Trinomials: Trinomials
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60
and a Strategy for Factoring Completely. Polynomial
Equations. Absolute Value Equations. Conjunctions,
Disjunctions, and Absolute Value Inequalities. Study
Plan for Review of Chapter 2. Chapter Test. 3. RELATIONS
AND FUNCTIONS. Success in College Mathematics:
Problem Solving. Introduction to Relations and
Functions. Linear and Constant Functions. Quadratic
and Cubic Functions. Polynomial Models. Absolute
Value Functions. Translation of Polynomial Functions.
Study Plan for Review of Chapter 3. Chapter Test.
Cumulative Review Chapters 1-3. 4. SYSTEM OF
LINEAR EQUATIONS. Success in College Mathematics:
Finding and Learning from Mistakes. Systems of Linear
Equations. Algebraic Methods. Applications. Systems
of Linear Equations in Three Variables. Matrix Methods.
Systems of Linear Inequalities. Study Plan for Review of
Chapter 4. Chapter Test. 5. RATIONAL EXPRESSIONS,
EQUATIONS AND FUNCTIONS. Success in College
Mathematics: Making Connections. Simplifying,
Multiplying, and Dividing Rational Expressions. Adding
and Subtracting Rational Expressions. Complex Rational
Expressions. Rational Equations in One Variable. Rational
Functions. Variation. Division of Polynomials; Synthetic
Division. Rational Inequalities. Study Plan for Review
of Chapter 5. Chapter Test. 6. RADICAL EXPRESSIONS,
EQUATIONS AND FUNCTIONS. Success in College
Mathematics: Keys for Success Introduction to Radicals.
Adding, Subtracting, Multiplying and Simplifying
Radical Expressions. Dividing Radical Expressions and
Conjugates. Rational Exponents. Radical Equations.
Radical Functions. Study Plan for Review of Chapter
6. Chapter Test. Cumulative Review Chapters 4-6.
7. QUADRATIC EXPRESSIONS, EQUATIONS AND
FUNCTIONS. Success in College Mathematics: Planning
for the Future. Complex Numbers. Solving Quadratic
Equations. Completing the Square. Quadratic Formula.
Quadratic Functions. Vertex Form of a Quadratic
Function. Quadratic Inequalities. Study Plan for Review
of Chapter 7. Chapter Test. 8. EXPONENTIAL AND
LOGARITHMIC EXPRESSIONS, EQUATIONS AND
FUNCTIONS. Success in College Mathematics: Final
Exams. Operations with Functions and One-to-One
Functions. Exponential Functions. Inverse Functions
and Logarithmic Functions. Natural Logarithms and
Logarithm Rules. Applications. Exponential Equations.
Logarithmic Equations. Study Plan for Review of Chapter
8. Chapter Test. 9. CONIC SECTIONS SYSTEMS OF NON-
LINEAR EQUATIONS. Success in College Mathematics:
Why Study Mathematics? Distance Formula, Midpoint
Formula, and Circles. Ellipses. Parabolas. Hyperbolas.
Systems of Non-Linear Equations in Two Variables.
Study Plan for Review of Chapter 7. Chapter Test.
Cumulative Review Chapters 7-9. 10. SEQUENCES,
SERIES AND THE BINOMIAL THEOREM. Success in
College Mathematics: Final Exams. Sequences and
Series. Arithmetic Sequences. Geometric Sequences.
The Binomial Theorem. Study Plan for Review of Chapter
10. Chapter Test. APPENDIX. A1: Reasonability and
Problem Solving. A2: Determinants and Cramer’s Rule.
A3: Developing the Equations of Conic Sections
© 2014, 1040pp, Paperback, 9781133365204
KAUFMANN/SCHWITTERS ALGEBRA FOR
COLLEGE STUDENTS, 10TH, 10E
Kaufmann/Schwitters
The Student Solutions Manual provides worked-out
solutions to the odd-numbered problems in the text.
© 2015, 608pp, Paperback, 9781285863979
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61
Discrete Mathematics
DISCRETE MATHEMATICS
Introduction to Mathematical Reasoning
Susanna S. Epp, DePaul University
Susanna Epp’s DISCRETE MATHEMATICS: AN
INTRODUCTION TO MATHEMATICAL REASONING,
provides the same clear introduction to discrete
mathematics and mathematical reasoning as her
highly acclaimed DISCRETE MATHEMATICS WITH
APPLICATIONS, but in a compact form that focuses on
core topics and omits certain applications usually taught
in other courses. The book is appropriate for use in a
discrete mathematics course that emphasizes essential
topics or in a mathematics major or minor course that
serves as a transition to abstract mathematical thinking.
The ideas of discrete mathematics underlie and are
essential to the science and technology of the computer
age. This book offers a synergistic union of the major
themes of discrete mathematics together with the
reasoning that underlies mathematical thought.
Renowned for her lucid, accessible prose, Epp explains
complex, abstract concepts with clarity and precision,
helping students develop the ability to think abstractly
as they study each topic. In doing so, the book provides
students with a strong foundation both for computer
science and for other upper-level mathematics courses.
FEATURES
• Epp addresses difficulties in understanding logic
and language with very concrete and easy-toconceptualize examples, helping students with a
variety of backgrounds better comprehend basic
mathematical reasoning, and enabling them to
construct sound mathematical arguments.
• A large number of exercises provide ample practice for
students, with numerous applied problems covering
an impressive array of applications.
• Worked examples are developed in intuitive problemsolution format. Proof solutions are developed in two
steps, with discussion on how one might come to
devise the proof oneself followed by a concise version
of the proof,enabling students of different levels to
work at their own pace with adequate support and
additional help for those who need it.
• Margin notes highlight issues of particular importance
and help students avoid common mistakes.
• “Test Yourself” questions with answers at the end of
each section provide immediate feedback to students
regarding their understanding of basic concepts.
CONTENTS
1. SPEAKING MATHEMATICALLY. Variables. The
Language of Sets. The Language of Relations and
Functions. 2. THE LOGIC OF COMPOUND STATEMENTS.
Logical Form and Logical Equivalence. Conditional
Statements. Valid and Invalid Arguments. 3. THE
LOGIC OF QUANTIFIED STATEMENTS. Predicates and
Quantified Statements I. Predicates and Quantified
Statements II. Statements with Multiple Quantifiers.
Arguments with Quantified Statements. 4. ELEMENTARY
NUMBER THEORY AND METHODS OF PROOF. Direct
Proof and Counterexample I: Introduction. Direct
Proof and Counterexample II: Rational Numbers.
Direct Proof and Counterexample III: Divisibility.
Direct Proof and Counterexample IV: Division into
Cases and the Quotient-Remainder Theorem. Indirect
Argument: Contradiction and Contraposition. Indirect
Argument: Two Classical Theorems. 5. SEQUENCES,
MATHEMATICAL INDUCTION, AND RECURSION.
Sequences. Mathematical Induction I. Mathematical
Induction II. Strong Mathematical Induction and
the Well-Ordering Principle. Defining Sequences
Recursively. Solving Recurrence Relations by Iteration.
6. SET THEORY. Set Theory: Definitions and the Element
Method of Proof. Set Identities. Disproofs and Algebraic
Proofs. Boolean Algebras and Russell’s Paradox. 7.
PROPERTIES OF FUNCTIONS. Functions Defined on
General Sets. One-to-one, Onto, and Inverse Functions.
Composition of Functions. Cardinality and Sizes of
Infinity. 8. PROPERTIES OF RELATIONS. Relations
on Sets. Reflexivity, Symmetry, and Transitivity.
Equivalence Relations. Modular Arithmetic and Zn. The
Euclidean Algorithm and Applications. 9. COUNTING.
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Counting and Probability. The Multiplication Rule.
Counting Elements of Disjoint Sets: The Addition
Rule. The Pigeonhole Principle. Counting Subsets
of a Set: Combinations. Pascal’s Formula and the
Binomial Theorem. 10. GRAPHS AND TREES. Graphs:
An Introduction. Trails, Paths, and Circuits. Matrix
Representations of Graphs. Isomorphisms of Graphs.
Trees: Examples and Basic Properties. Rooted Trees.
© 2011, 648pp, Hardback, 9780495826170
• Includes worked-out exercises in each section to
illustrate crucial problem solving techniques.
• Supplies a rich collection of examples and visual
diagrams that clearly illustrate key concepts.
CONTENTS
CHAPTER 1. Foundations: Sets, Logic, and Algorithms.
 CHAPTER 2. Integers and Mathematical Induction.
 CHAPTER 3. Relations and Posets. CHAPTER
4 Matrices and Closures of Relations. CHAPTER 5.
Functions. CHAPTER 6. Congruences. CHAPTER
7. Counting Principles. CHAPTER 8. Discrete
Probability. CHAPTER 9. Recurrence Relations.
 CHAPTER 10. Algorithms and Time Complexity.
 CHAPTER 11 Graph Theory. CHAPTER 12. Trees
and Networks. CHAPTER 13. Boolean Algebra
and Combinatorial Circuits. CHAPTER 14. Finite
Automata and Languages.  
© 2010, 880pp, Hardback, 9789814296359
DISCRETE MATHEMATICS
Theory and Applications (Revised Edition)
D.S. Malik, Creighton University; M. K. Sen, University of Calcutta
Discrete Mathematics: Theory
and Applications (Revised Edition) offers a
refreshing alternative for the undergraduate Discrete
Mathematics course. In this revised text, the authors,
Dr. Malik and Dr. Sen, employ a classroom-tested,
student-focused approach that is conducive to effective
learning. Each chapter motivates students through the
use of real-world, concrete examples. Ample exercise
sets provide alternative practice to allow students to
apply what they learn, while programming exercises in
each chapter allow opportunities for computer science
application. This text is a true blend of theory and
applications.
NEW TO THIS EDITION
• A new chapter on discrete probability.
FEATURES
• Designed for an undergraduate course in Discrete
Mathematics, mainly for students in mathematics or
in computer science.
• Provides over 100 exercises and a rich set of
programming exercises per chapter.
DISCRETE MATHEMATICS WITH
APPLICATIONS, INTERNATIONAL
EDITION, 4E
Susanna S. Epp, DePaul University
Susanna Epp’s DISCRETE MATHEMATICS WITH
APPLICATIONS, 4e, International Edition provides a
clear introduction to discrete mathematics. Renowned
for her lucid, accessible prose, Epp explains complex,
abstract concepts with clarity and precision. This
book presents not only the major themes of discrete
mathematics, but also the reasoning that underlies
mathematical thought. Students develop the ability
to think abstractly as they study the ideas of logic
and proof. While learning about such concepts as
logic circuits and computer addition, algorithm
analysis, recursive thinking, computability, automata,
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63
cryptography, and combinatorics, students discover
that the ideas of discrete mathematics underlie and are
essential to the science and technology of the computer
age. Overall, Epp’s emphasis on reasoning provides
students with a strong foundation for computer science
and upper-level mathematics courses.
NEW TO THIS EDITION
• A new Chapter 1 introduces students to some of
the precise language that is a foundation for much
mathematical thought, and is intended as a warm-up
before addressing topics in more depth later on.
• New material on the definition of sound argument,
trailing quantifiers, infinite unions and intersections,
and Dijkstra’s shortest path algorithm.
• Expanded discussion of writing proofs and avoiding
common mistakes in proof-writing.
• Increased coverage of functions of more than one
variable and functions acting on sets.
• New margin notes are provided to provide better
context-sensitive help highlighting issues of particular
importance.
FEATURES
• Epp addresses inherent difficulties in understanding
logic and language with very concrete and easyto-conceptualize examples, an approach that
helps students with a variety of background better
comprehend basic mathematical reasoning, and
enables them to construct sound mathematical
arguments.
• Around 2500 exercises providing ample practice for
students, with numerous applied problems covering
an impressive array of applications.
• Over 500 worked examples in problem-solution
format. Proof solutions are intuitively developed in
two steps, a discussion on how to approach the proof
and a summary of the solution, to allow students
the choice or quicker or more deliberate instruction
depending on how well they understand the problem.
• Flexible organization, allowing instructors the ability
to mix core and optional topics easily to suit a wide
variety of discrete math course syllabi and topic focus.
• Features, definitions, theorems, and exercise types are
clearly marked and easily navigable, making the book
an excellent reference that students will want to keep
and continually refer back to in their later courses.
CONTENTS
1. SPEAKING MATHEMATICALLY. Variables. The
Language of Sets. The Language of Relations
and Functions. 2. THE LOGIC OF COMPOUND
STATEMENTS. Logical Form and Logical Equivalence.
Conditional Statements. Valid and Invalid Arguments.
Application: Digital Logic Circuits. Application: Number
Systems and Circuits for Addition. 3. THE LOGIC OF
QUANTIFIED STATEMENTS. Predicates and Quantified
Statements I. Predicates and Quantified Statements II.
Statements with Multiple Quantifiers. Arguments with
Quantified Statements. 4. ELEMENTARY NUMBER
THEORY AND METHODS OF PROOF. Direct Proof
and Counterexample I: Introduction. Direct Proof and
Counterexample II: Rational Numbers. Direct Proof
and Counterexample III: Divisibility. Direct Proof
and Counterexample IV: Division into Cases and
the Quotient-Remainder Theorem. Direct Proof and
Counterexample V: Floor and Ceiling. Indirect Argument:
Contradiction and Contraposition. Indirect Argument:
Two Classical Theorems. Application: Algorithms. 5.
SEQUENCES, MATHEMATICAL INDUCTION, AND
RECURSION. Sequences. Mathematical Induction
I. Mathematical Induction II. Strong Mathematical
Induction and the Well-Ordering Principle. Application:
Correctness of Algorithms. Defining Sequences
Recursively. Solving Recurrence Relations by Iteration.
Second-Order Linear Homogeneous Recurrence
Relations with Constant Coefficients. General Recursive
Definitions and Structural Induction. 6. SET THEORY.
Set Theory: Definitions and the Element Method of
Proof. Properties of Sets. Disproofs and Algebraic
Proofs. Boolean Algebras, Russell’s Paradox, and the
Halting Problem. 7. FUNCTIONS. Functions Defined
on General Sets. One-to-one, Onto, Inverse Functions.
Composition of Functions. Cardinalitywith Applications
to Computability. 8. RELATIONS. Relations on Sets.
Reflexivity, Symmetry, and Transitivity. Equivalence
Relations. Modular Arithmetic with Applications to
Cryptography. Partial Order Relations. 9. COUNTING
AND PROBABILITY. Introduction. Possibility Trees
and the Multiplication Rule. Counting Elements of
Disjoint Sets: The Addition Rule. The Pigeonhole
Principle. Counting Subsets of a Set: Combinations.
r-Combinations with Repetition Allowed. Pascal’s
Formula and the Binomial Theorem. Probability Axioms
and Expected Value. Conditional Probability, Bayes’
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64
Formula, and Independent Events. 10. GRAPHS AND
TREES. Graphs: Definitions and Basic Properties. Trails,
Paths, and Circuits. Matrix Representations of Graphs.
Isomorphisms of Graphs. Trees. Rooted Trees. Spanning
Trees and a Shortest Path Algorithm. 11. ANALYZING
ALGORITHM EFFICIENCY. Real-Valued Functions of a
Real Variable and Their Graphs. Application: Analysis
of Algorithm Efficiency I. Exponential and Logarithmic
Functions: Graphs and Orders. Application: Efficiency of
Algorithms II. 12. REGULAR EXPRESSIONS AND FINITE
STATE AUTOMATA. Formal Languages and Regular
Expressions. Finite-State Automata. Simplifying FiniteState Automata.
© 2011, 984pp, Paperback, 9780495826163
MATHEMATICS, 3E
A Discrete Introduction
Edward R. Scheinerman, The Johns Hopkins University
MATHEMATICS: A DISCRETE INTRODUCTION
teaches students the fundamental concepts in discrete
mathematics and proof-writing skills. With its clear
presentation, the text shows students how to present
cases logically beyond this course. All of the material is
directly applicable to computer science and engineering,
but it is presented from a mathematician’s perspective.
Students will learn that discrete mathematics is very
useful, especially those whose interests lie in computer
science and engineering, as well as those who plan to
study probability, statistics, operations research, and
other areas of applied mathematics.
NEW TO THIS EDITION
• This edition has been revised based on input
from reviewers and users, as well as the author’s
understanding of the course. This includes correcting
and adding to the existing content.
• Featuring more than 25% increase in problems.
Some of these new problems, which are included in
problem sets and chapter tests, are interrelated to
develop ideas across chapters, providing a stronger
understanding of the materiel.
FEATURES
• Self-Tests: A self-test appears at the end of every
chapter. The problems are of various degrees of
difficulty, and complete answers appear in Appendix
B.
• Induction: The sections on mathematical induction
have been reworked with new motivational material,
more examples, and more problems. The induction
section is now essentially independent of the proof
by smallest counterexample section.
• The book includes sections covering topics such as
recurrence relations and combinatorial proof.
• The introductory section, “Joy,” motivates students by
describing the pleasure of doing mathematics.
• Proof Templates: Proof templates appear throughout
the book and give students the basic skeleton of the
proof as well as boilerplate language.
• Growing Proofs: The author teaches students how to
write proofs by instructing them to begin their proofs
by first writing the first sentence and next writing the
last sentence. Students then work the proof from both
ends until they meet in the middle.
• Mathspeak: Marginal notes explain many of the
idiosyncrasies of mathematical English.
• Hints: Appendix A contains an extensive collection of
hints (and some answers when necessary) that point
students in the correct direction.
CONTENTS
1. FUNDAMENTALS. Joy. Speaking (and Writing)
of Mathetimatics. Definition. Theorem. Proof.
Counterexample. Boolean Algebra. Self Test. 2.
COLLECTIONS. Lists. Factorial. Sets I: Introduction,
Subsets. Quantifiers. Sets II: Operations. Combinatorial
Proof: Two Examples. Self Test. 3. COUNTING
AND RELATIONS. Relations. Equivalence Relations.
Partitions. Binomial Coefficients. Counting Multisets.
Inclusion-Exclusion. Self Test. 4. MORE PROOF.
Contradiction. Smallest Counterexample. Induction.
Recurrence Relations. Self Test. 5. FUNCTIONS.
Functions. The Pigeonhole Principle. Composition.
Permutations. Symmetry. Assorted Notation. Self Test.
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65
6. PROBABILITY. Sample Space. Events. Conditional
Probability and Independence. Random Variables.
Expectation. Self Test. 7. NUMBER THEORY. Dividing.
Greatest Common Divisor. Modular Arithmetic. The
Chinese Remainder Theorem. Factoring. Self Test. 8.
ALGEBRA. Groups. Group Isomorphism. Subgroups.
Fermat’s Little Theorem. Public-Key Cryptography
I: Introduction. Public-Key Cryptography II: Rabin’s
Method. Public-Key Cryptography III: RSA. Self Test.
9. GRAPHS. Graph Theory Fundamentals. Subgraphs.
Connection. Trees. Eulerian Graphs. Coloring. Planar
Graphs. Self Test. 10. PARTIALLY ORDERED SETS.
Partially Ordered Sets Fundamentals. Max and Min.
Linear Orders. Linear Extensions. Dimension. Lattices.
Self Test. APPENDICES. Lots of Hints and Comments;
Some Answers. Solutions to Self Tests. Glossary.
Fundamentals. Index.
© 2013, 504pp, Hardback, 9780840049421
Finite Mathematics /
Applied Calculus
APPLIED CALC (WITH COURSEMATE
PRINTED ACCESS CARD), 2E
Frank Wilson, Chandler-Gilbert Community College
Created through a “student-tested, faculty-approved”
review process APPLIED CALC, 2nd edition is an
engaging and accessible solution to accommodate
the diverse lifestyles of today’s learners at a valuebased price. Geared toward business and social
science majors, this text helps students develop the
analytical thinking skills they need to be successful
in the workplace. Straightforward language and an
award-winning writing style promote conceptual
understanding of mathematical topics and real-world
contexts. An innovative combination of content
delivery both in print and online provides a core
text and a wealth of comprehensive multimedia
teaching and learning assets, including end-ofchapter review cards, downloadable flashcards and
practice problems, online video tutorials, solutions to
exercises aimed at supplementing learning outside of
the classroom. Also available is Cengage Learning’s
Enhanced WebAssign®—a complete online homework
management system for students and professors.
NEW TO THIS EDITION
• Chapter 1 “Functions and Models” has been revised
and expanded to provide a more in-depth review of
prerequisite material.
• Answers to odd-numbered problems are included in
the text.
• The text contains many new and updated real-life
applications.
FEATURES
• Every 4LTR Press solution comes complete with an
engaging print textbook, tear-out review cards, an
interactive digital solution (CourseMate), and an
eBook all of which were directly influenced from
student focus groups, surveys, and interviews.
• Shorter, comprehensive chapters in a modern design
present content in a more engaging and accessible
format without minimizing coverage for your course.
• Tear-out Tech Cards in both the Student and Instructor
Editions contain tips on using graphing calculators.
• Instructor Prep Cards in the Instructor’s Edition make
preparation simple with detachable cards for each
chapter, offering a quick overview of chapter content,
including Concept Overview, Key Words, and Concept
Challenges for Students.
• Every 4LTR Press solution comes with CourseMate,
the interactive digital component that offers a full
suite of unique learning tools that appeal to different
learning styles. Quizzes, flashcards, lecture videos,
solution videos, extra practice exercises, and more are
only a click away. *(please make sure the resources
you list pertain to your title and are available.)*
• All of the content and resources you expect with a
supplements package that is second to none including
PowerLecture (an instructor CD/DVD), Cengage
Learning Testing Powered by Cognero, an Instructor’s
Edition, an e-book, an online Instructor’s Solutions
Manual, and an online Student Solutions Manual.
www.cengageasia.com
66
CONTENTS
1. FUNCTIONS AND MODELS. 1.1 Functions 1.2 Linear
Functions 1.3 Quadratic Functions 1.4 Polynomial
and Rational Functions 1.5 Exponential Functions and
Logarithms 1.6 Function Modeling and Combining
Functions. 2. THE DERIVATIVE. 2.1 Average Rate of
Change 2.2 Limits and Instantaneous Rates of Change
2.3 The Derivative as a Slope: Graphical Methods
2.4 The Derivative as a Function: Algebraic Method
2.5 Interpreting the Derivative 3. DIFFERENTIATION
TECHNIQUES. 3.1 Basic Derivative Rules 3.2 The
Product and Quotient Rules 3.3 The Chain Rule
3.4 Exponential and Logarithmic Rules 3.5 Implicit
Differentiation 4. DERIVATIVE APPLICATIONS. 4.1
Maxima and Minima 4.2 Applications of Maxima and
Minima 4.3 Concavity and the Second Derivative
4.4 Related Rates. 5. THE INTEGRAL. 5.1 Indefinite
Integrals 5.2 Integration by Substitution 5.3 Using
Sums to Approximate Area 5.4 The Definite Integral 5.5
The Fundamental Theorem of Calculus. 6. ADVANCED
INTEGRATION TECHNIQUES AND APPLICATIONS. 6.1
Integration by Parts 6.2 Area Between Two Curves 6.3
Differential Equations and Applications 6.4 Differential
Equations: Limited Growth and Logistic Growth
Models. 7. MULTIVARIABLE FUNCTIONS AND PARTIAL
DERIVATIVES. 7.1 Multivariable Functions 7.2 Partial
Derivatives 7.3 Multivariable Maxima and Minima 7.4
Constrained Maxima and Minima and Applications.
© 2015, 288pp, Paperback, 9781285061825
APPLIED CALC (WITH MATHEMATICS
COURSEMATE WITH EBOOK PRINTED
ACCESS CARD)
Frank Wilson, Chandler-Gilbert Community College
review process Applied CALC is an engaging and
accessible solution to accommodate the diverse
lifestyles of today’s learners at a value-based price.
Geared toward business and social science majors,
this text equips students with the analytical tools
and technological skills they need to be successful in
the workplace. Straightforward language and writing
style promote conceptual understanding, and the
incorporation of real-life applications, examples, and
data helps engage students--even those with minimal
interest in mathematics. An innovative combination
of content delivery both in print and online provides a
core text and a wealth of comprehensive multimedia
FEATURES
• An innovative combination of content delivered both
in print and online provides a core text and a wealth
of comprehensive multimedia teaching and learning
assets based on input from student focus groups,
surveys, and interviews.
• Detachable Review Cards for each chapter provide
students a portable study tool containing information
to prepare for class and for tests, including section
objectives, definitions of key terms, and section
summaries.
• Detachable Tech Cards in both the Student and
Instructor Editions contain tips on using graphing
calculators.
• Detachable Instructor Prep Cards for each chapter
make preparation simple by offering section
objectives, teaching tips (including common student
errors, suggested homework assignments, and time
management tips), and Make It Real projects.
• A full suite of unique learning tools that appeal to
different learning styles is available to students with
the purchase of a new book. Interactive quizzes,
videos, extra examples and problems, flashcards,
answers and solutions, and more are only a click away.
www.cengageasia.com
67
PowerLecture (an instructor CD/DVD), an Instructor’s
Edition, an e-book, an online Instructor’s Manual, and
an online Student’s Solutions Manual.
• Exclusively from Cengage Learning, Enhanced
WebAssign® offers an extensive online program for
Applied Calculus to encourage the practice that’s
assignments.
CONTENTS
1. FUNCTIONS AND LINEAR MODELS. 1.1 Functions.
Function Notation. Graphs of Functions. Domain and
Range. Exercises. 1.2 Linear Functions. Intercepts.
Linear Equations. Finding the Equation of a Line.
Other Forms of Linear Equations. Graphing Linear
Functions. Exercises. 2. NONLINEAR MODELS. 2.1
Quadratic Function Models. Exercises. 2.2 Exponential
Function Models. Exponential Function Graphs.
Properties of Exponents. Finding an Exponential
Function from a Table. Using Exponential Regression
to Model Data. Finding an Exponential Function from
a Verbal Description. Exercises. 3. THE DERIVATIVE.
3.1 Average Rate of Change. Graphical Interpretation
of the Difference Quotient. Exercises. 3.2 Limits and
Instantaneous Rates of Change. Limits. Exercises. 3.3
The Derivative as a Slope: Graphical Methods. TangentLine Approximations. Numerical Derivatives. Exercises.
3.4 The Derivative as a Function: Algebraic Method.
Estimating Derivatives. Exercises. 3.5 Interpreting
the Derivative. Exercises. 4. DIFFERENTIATION
TECHNIQUES. 4.1 Basic Derivative Rules. Derivative
Notation. The Constant Rule. The Power Rule. Constant
Multiple Rule. Sum and Difference Rule. Exercises. 4.2
The Product and Quotient Rules. Exercises. 4.3 The
Chain Rule. Composition of Functions. The Chain Rule.
Chain Rule: Alternative Form. Exercises. 4.4 Exponential
and Logarithmic Rules. Exponential Rule. Logarithmic
Rule. Exercises. 4.5 Implicit Differentiation. Exercises.
5. DERIVATIVE APPLICATIONS. 5.1 Maxima and
Minima. Continuity. Relative and Absolute Extrema.
Critical Values. The First Derivative Test. Exercises. 5.2
Applications of Maxima and Minima. Revenue, Cost, and
Profit. Area and Volume. Exercises. 5.3 Concavity and the
Second Derivative. Concavity. The Second Derivative
Test. Point of Diminishing Returns. Position, Velocity,
and Acceleration. Curve Sketching. Exercises. 5.4
Related Rates. Exercises. 6. THE INTEGRAL. 6.1 Indefinite
Integrals. Basic Integration Rules. Indefinite Integral
Applications. Exercises. 6.2 Integration by Substitution.
Differentials. Integration by Substitution. Exercises. 6.3
Using Sums to Approximate Area. Exercises. 6.4 The
Definite Integral. Summation Notation. The Definite
Integral. Definite Integral Properties. Exercises. 6.5 The
Fundamental Theorem of Calculus. Changing Limits of
Integration. Exercises. 7. ADVANCED INTEGRATION
TECHNIQUES AND APPLICATIONS. 7.1 Integration
by Parts. Exercises. 7.2 Area Between Two Curves.
Difference of Accumulated Changes. Exercises. 7.3
Differential Equations and Applications. Newton’s
Law of Heating and Cooling. Exercises. 7.4 Differential
Equations: Limited Growth and Logistic Growth
Models. Limited Growth Model. Logistic Growth
Model. Exercises. 8. MULTIVARIABLE FUNCTIONS AND
PARTIAL DERIVATIVES. 8.1 Multivariable Functions.
Exercises. 8.2 Partial Derivatives. Cross Sections of a
Surface. Second-Order Partial Derivatives. Exercises.
8.3 Multivariable Maxima and Minima. Exercises. 8.4
Constrained Maxima and Minima and Applications.
Graphical Interpretation of Constrained Optimization
Problems. Exercises.
© 2012, 256pp, Paperback, 9780840065636
Coming Soon!
APPLIED CALCULUS FOR THE
MANAGERIAL, LIFE, AND SOCIAL
SCIENCES, 9E
A Brief Approach, International Edition
A traditional book with a modern feel, market-leading
APPLIED CALCULUS FOR THE MANAGERIAL, LIFE,
AND SOCIAL SCIENCES: A BRIEF APPROACH, 9e,
www.cengageasia.com
68
International Edition teaches by application and
uses real-world examples to motivate students. It
combines solid theory with innovative technology,
includes a robust supplement package, and offers
unmatched flexibility that caters to both traditional
and modern practitioners. Accessible for majors and
non-majors alike, the new Ninth Edition utilizes an
intuitive approach that marries real-life instances to
what would otherwise be abstract concepts. This is the
focus of new and insightful Portfolio features, which
highlight the careers of actual persons and discuss
how they incorporate math into their daily operations.
Numerous exercises, including Diagnostic Tests, ensure
that students have a solid understanding of textbook
information before advancing to the next topic. Plus,
algebra review notes which refer to the Preliminaries
chapter appear where you need them, when you need
them. And by offering a powerful array of supplements
such as Enhanced WebAssign®, the new Ninth Edition
enables students to maximize their study time and
succeed in class.
NEW TO THIS EDITION
• Over 100 new and updated student-friendly
applications. Topics include: global defense spending,
public transportation budget deficit, cost of the
Health Care Bill, brain cancer survival rate, small car
market share, Case-Shiller Home Price Index, rate of
business failures, solar panel production, seat belt use,
Mexico’s hedging tactic, medical costs for veterans,
and bounced-check charges.
• Four new Portfolio features illustrate mathematics
in the workplace. Among those interviewed are the
Senior Vice President of Supply at Earthbound Farms
and an Antibody Assay Developer at Ventana Medical.
FEATURES
• Motivating real-world applications: With more than
100 new and updated applications, Tan’s exercises
build student interest and illustrate the real-world
relevance of mathematics.
• Algebra review when you need it: Diagnostic Tests
begin the Preliminaries chapter, offering students a
chance to see which algebra skills they need to review
before beginning regular coursework. Additionally,
algebra review notes, keyed to the review chapter,
appear where you need them, when you need them.
• Study Tabs that work: Convenient color-coded Study
Tabs, similar to Post-It® notes, make it easy for
students to flag pages that they want to revisit later.
• Solution videos and tutorials: Available on CourseMate,
these videos directly correspond to exercises found
within the text and provide additional instruction,
including a Graphing Calculator Tutorial.
• Math for life: Real-world applications in the areas
of business, economics, behavioral, life, physical,
and social sciences bring relevance to mathematical
results and make chapter concepts come to life for
students. In addition, Portfolio interviews show
how professionals use mathematics in their daily
operations. Applied examples are clearly marked with
photo icons that link to the list of applications.
• Flexibility: Optional coverage offers instructors
different ways to tailor technology to their course
needs. For example, “Using Technology” sections
show how graphing utilities can facilitate the analysis
and solution of complicated problems. “Exploring
with Technology” questions also pop up throughout
the text in special boxes. And, “Modeling with Data”
exercises feature in many of the “Using Technology”
subsections, showing students how some of the
functions found in the exercises are constructed.
• Complete exercise sets: Section exercise sets include
“Concept” questions, and chapter reviews contain fillin-the-blank “Concept Review” questions. Additional
routine and true-false questions have been added as
well.
• Thorough: Detailed illustrations support examples and
exercises, ensuring student understanding. “Explore
and Discuss” questions take concepts a step further
and spark student discussion. Other pedagogical tools
that help students master the material include: “SelfCheck” exercises in every section, “Notes” to clarify
more mathematical ideas, “Cautions” highlighting
common pitfalls, and more.
CONTENTS
Preface. 1. PRELIMINARIES. Precalculus Review I.
Precalculus Review II. The Cartesian Coordinate System.
Straight Lines. Chapter 1 Summary of Principal Formulas
and Terms. Chapter 1 Concept Review Questions.
Chapter 1 Review Exercises. Chapter 1 Before Moving
On. 2. FUNCTIONS, LIMITS, AND THE DERIVATIVE.
Functions and Their Graphs. The Algebra of Functions.
Functions and Mathematical Models. Portfolio. Using
Technology: Finding the Points of Intersection of Two
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69
Graphs and Modeling. Limits. Using Technology: Finding
the Limit of a Function. One-Sided Limits and Continuity.
Using Technology: Finding the Points of Discontinuity of
a Function. The Derivative. Using Technology: Graphing
a Function and Its Tangent Line. Chapter 2 Summary
of Principal Formulas and Terms. Chapter 2 Concept
Review Questions. Chapter 2 Review Exercises. Chapter
2 Before Moving On. 3. DIFFERENTIATION. Basic Rules
of Differentiation. Using Technology: Finding the Rate of
Change of a Function. The Product and Quotient Rules.
Using Technology: The Product and Quotient Rules. The
Chain Rule. Using Technology: Finding the Derivative of
a Composite Function. Marginal Functions in Economics.
Higher-Order Derivatives. Using Technology: Finding
the Second Derivative of a Function at a Given Point.
Implicit Differentiation and Related Rates. Differentials.
Using Technology: Finding the Differential of a Function.
Chapter 3 Summary of Principal Formulas and Terms.
Chapter 3 Concept Review Questions. Chapter 3
Review Exercises. Chapter 3 Before Moving On. 4.
APPLICATIONS OF THE DERIVATIVE. Applications
of the First Derivative. Using Technology: Using the
First Derivative to Analyze a Function. Applications of
the Second Derivative. Using Technology: Finding the
Inflection Points of a Function. Curve Sketching. Using
Technology: Analyzing the Properties of a Optimization
I. Using Technology: Finding the Absolute Extrema of
a Function. Optimization II. Chapter 4 Summary of
Principal Terms. Chapter 4 Concept Review Questions.
On. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. Using Technology. Logarithmic
Functions. Compound Interest. Using Technology:
Finding the Accumulated Amount of an Investment, the
Effective Rate of Interest, and the Present Value of an
Investment. Differentiation of Exponential Functions.
Using Technology. Differentiation of Logarithmic
Functions. Exponential Functions as Mathematical
Models. Portfolio. Using Technology: Analyzing
Mathematical Models. Chapter 5 Summary of Principal
Formulas and Terms. Chapter 5 Concept Review
Questions. Chapter 5 Review Exercises. Chapter 5 Before
Moving On. 6. INTEGRATION. Antiderivatives and the
Rules of Integration. Integration by Substitution. Area
and the Definite Integral. The Fundamental Theorem
of Calculus. Portfolio. Using Technology: Evaluating
Definite Integrals. Evaluating Definite Integrals.
Using Technology: Evaluating Integrals for PiecewiseDefined Functions. Area between Two Curves. Using
Technology: Finding the Area between Two Curves.
Applications of the Definite Integral to Business and
Economics. Using Technology: Business and Economic
Applications/Technology Exercises. Chapter 6 Summary
6 Before Moving On. 7. ADDITIONAL TOPICS IN
INTEGRATION. Integration by Parts. Integration Using
Tables of Integrals. Numerical Integration. Improper
Integrals. Applications of Calculus to Probability.
Chapter 7 Concept Review Questions. Chapter 7 Review
Exercises. Chapter 7 Before Moving On. 8. CALCULUS
OF SEVERAL VARIABLES. Functions of Several Variables.
Partial Derivatives. Portfolio. Using Technology: Finding
Partial Derivatives at a Given Point. Maxima and Minima
of Functions of Several Variables. The Method of Least
Squares. Using Technology: Finding an Equation of LeastSquares Line. Constrained Maxima and Minima and the
Method of Lagrange Multipliers. Double Integrals.
Exercises. Chapter 8 Before Moving On. Appendix
A. The Inverse of a Function. The Graphs of Inverse
Functions. Functions That Have Inverses. Finding the
Inverse of a Function. Appendix B. Indeterminant Forms
and l’Hôpital’s Rule. The Indeterminant Forms 0/0 and
∞/ ∞. Index.
© 2012, 688pp, Paperback, 9781111427733
Coming Soon!
SCIENCES, 9E
Well known for accuracy, Soo Tan’s APPLIED CALCULUS
FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES,
Ninth Edition balances applications, pedagogy, and
technology to provide students the context they need
to stay motivated in the course and interested in the
material. Accessible for majors and non-majors alike,
www.cengageasia.com
70
the text uses an intuitive approach that introduces
abstract concepts through examples drawn from
common, real-life experiences to which students can
relate. It also draws applications from readers’ fields
of interest. In addition, insightful Portfolios highlight
the careers of real people and discuss how they
incorporate math into their daily professional activities.
Numerous exercises ensure that students have a solid
understanding of concepts before advancing to the
next topic. Algebra review notes, keyed to the review
chapter Preliminaries, appear where and when students
need them. The text’s exciting array of supplements,
including Enhanced WebAssign®, equips students with
extensive learning support to help them make the most
of their study time. Available with InfoTrac® Student
Collections http://gocengage.com/infotrac.
NEW TO THIS EDITION
applications: Topics include global defense spending,
public transportation budget deficits, cost of the
Health Care Bill, brain cancer survival rates, small car
market share, the Case-Shiller Home Price Index, the
rate of business failures, solar panel production, seat
belt use, Mexico’s hedging tactic, medical costs for
veterans, and bounced-check charges.
• Four New Portfolios: Illustrating the value of
mathematics in the workplace, this feature includes
new interviews with professionals such as the Senior
Vice President of Supply at Earthbound Farms and a
Research Associate at Stanford University’s Hopkins
Marine Station.
FEATURES
• Algebra review when it’s needed: A Diagnostic Test
begins the Preliminaries chapter, offering students a
appear where and when students need them.
the book’s website, these videos directly correspond
to exercises found in the text and provide additional
instruction, including a Graphing Calculator Tutorial.
students. In addition, Portfolio interviews show how
professionals use mathematics in their daily activities.
Applied examples are clearly marked with photo icons
that link them to the list of applications.
and solution of complicated problems. “Exploring with
Technology” boxes throughout the text offer students
the opportunity to use technology to further explore
mathematical concepts. And, “Modeling with Data”
exercises, featured in many of the “Using Technology”
subsections, show students how some of the functions
found in the exercises are constructed.
well.
that help students master the material include “SelfCheck” exercises in every section, “Notes” to clarify
mathematical ideas, and “Cautions” that highlight
common pitfalls.
CONTENTS
1. PRELIMINARIES. Precalculus Review I. Precalculus
Review II. The Cartesian Coordinate System. Straight
Lines. 2. FUNCTIONS, LIMITS, AND THE DERIVATIVE.
Functions and Mathematical Models. Limits. OneSided Limits and Continuity. The Derivative. 3.
DIFFERENTIATION. Basic Rules of Differentiation.
The Product and Quotient Rules. The Chain Rule.
Marginal Functions in Economics. Higher-Order
Derivatives. Implicit Differentiation and Related Rates.
Differentials. 4. APPLICATIONS OF THE DERIVATIVE.
www.cengageasia.com
71
Applications of the First Derivative. Applications of the
Second Derivative. Curve Sketching. Optimization I.
Optimization II. 5. EXPONENTIAL AND LOGARITHMIC
FUNCTIONS. Exponential Functions. Logarithmic
Functions. Compound Interest. Differentiation of
Exponential Functions. Differentiation of Logarithmic
Models. 6. INTEGRATION. Antiderivatives and the
and the Definite Integral. The Fundamental Theorem of
Calculus. Evaluating Definite Integrals. Area between
Two Curves. Applications of the Definite Integral to
Business and Economics. 7. ADDITIONAL TOPICS
IN INTEGRATION. Integration by Parts. Integration
Using Tables of Integrals. Numerical Integration.
Improper Integrals. Volumes of Solids of Revolution.
8. CALCULUS OF SEVERAL VARIABLES. Functions
of Several Variables. Partial Derivatives. Maxima
and Minima of Functions of Several Variables. The
Method of Least Squares. Constrained Maxima and
Minima and the Method of Lagrange Multipliers. Total
Differentials. Double Integrals. Applications of Double
Integrals. 9. DIFFERENTIAL EQUATIONS. Differential
Equations. Separation of Variables. Applications
of Separable Differential Equations. Approximate
Solutions of Differential Equations. 10. PROBABILITY
AND CALCULUS. Probability Distributions of Random
Variables. Expected Value and Standard Deviation.
Normal Distributions. 11. TAYLOR POLYNOMIALS
AND INFINITE SERIES. Taylor Polynomials. Infinite
Sequences. Infinite Series. Series with Positive Numbers.
Power Series and Taylor Series. More on Taylor Series.
Newton’s Method. 12. TRIGONOMETRIC FUNCTIONS.
Measurement of Angles. The Trigonometric Functions.
Differentiation of Trigonometric Functions. Integration
of Trigonometric Functions APPENDIX A. The Inverse of
a Function. The Graphs of Inverse Functions. Functions
That Have Inverses. Finding the Inverse of a Function.
APPENDIX B. Indeterminate Forms and l’Hôpital’s Rule.
The Indeterminate Forms 0/0 and infinity/infinity.
APPENDIX C. The Standard Normal Distribution.
Answers to Odd-Numbered Exercises. Index.
© 2014, 896pp, Hardback, 9781133607717
SCIENCES, 10E
A Brief Approach
APPLIED CALCULUS FOR THE MANAGERIAL, LIFE,
AND SOCIAL SCIENCES: A BRIEF APPROACH, Tenth
Edition balances modern applications, solid pedagogy,
and the latest technology to engage students and keep
them motivated in the course. Suitable for majors and
non-majors alike, the text uses an intuitive approach
that teaches concepts through examples drawn from
real-life situations from students’ fields of interest. In
addition, insightful Portfolios highlight the careers of
real people and discuss how they incorporate math into
their daily professional activities. Numerous exercises,
including a Diagnostic Test, ensure that students have a
concrete understanding of concepts before advancing
to the next topic. The text’s pedagogical features
coupled with an exciting array of supplements equip
students with the tools they need to make the most of
their study time and to succeed in the course.
NEW TO THIS EDITION
• New and updated applications.
• New and updated examples.
• New and updated exercises.
• Increased emphasis on prerequisite skills in the
accompanying Enhanced WebAssign course with the
addition of Just-in-Time and Quick Prep Exercises.
FEATURES
• Motivating real-world applications: Included in the
10th edition are more than 100 new and updated
modern applications to motivate students and to
illustrate the relevance of mathematics in everyday
life. Topics include: Mobile Devise Usage; U.S. Public
www.cengageasia.com
72
Debt; Outsourcing of Jobs; Inflation; Bank Failures;
Social Networks; Gini Index; and Isoquants.
• Portfolio features outlining the real-life experiences
of a variety of professionals who use mathematics
Senior Vice President of Supply at Earthbound Farms
and a Principal Software Engineer at Iron Mountain.
• Technology experiences: “Modeling with Data”
exercises appear in many of the Using Technology
subsections, giving students an inside look at how
the author constructed the functions found in the
exercises.
• Algebra review when you need it: A Diagnostic Test at
the start of the Preliminaries chapter offers students a
algebra review notes, keyed to the Preliminaries
chapter, appear where you need them, when you
need them.
with Technology” questions emerge throughout the
text in special boxes. And, “Modeling with Data”
CONTENTS
Business and Economics. 7. ADDITIONAL TOPICS IN
INTEGRATION. Integration by Parts. Integration Using
Tables of Integrals. Numerical Integration. Improper
Integrals. Applications of Calculus to Probability. 8.
CALCULUS OF SEVERAL VARIABLES. Functions of
Several Variables. Partial Derivatives. Maxima and
Minima of Functions of Several Variables. The Method
of Least Squares. Constrained Maxima and Minima and
the Method of Lagrange Multipliers. Total Differentials.
Double Integrals.
© 2015, 704pp, Hardback, 9781285464640
SCIENCES, HYBRID EDITION, 9E
that engages students online! Well known for accuracy,
Soo Tan’s APPLIED CALCULUS FOR THE MANAGERIAL,
LIFE, AND SOCIAL SCIENCES, Ninth Edition balances
applications, pedagogy, and technology to provide
www.cengageasia.com
73
students the context they need to stay motivated in
the course and interested in the material. Accessible for
majors and non-majors alike, the text uses an intuitive
approach that introduces abstract concepts through
examples drawn from common, real-life experiences
to which students can relate. It also draws applications
from readers’ fields of interest. In addition, insightful
Portfolios highlight the careers of real people and
discuss how they incorporate math into their daily
professional activities. Numerous exercises ensure
that students have a solid understanding of concepts
before advancing to the next topic. Algebra review
notes, keyed to the review chapter Preliminaries,
appear where and when students need them. The text’s
exciting array of supplements, including Enhanced
WebAssign®, equips students with extensive learning
support to help them make the most of their study time.
NEW TO THIS EDITION
applications: Topics include global defense spending,
public transportation budget deficits, cost of the
Health Care Bill, brain cancer survival rates, small car
market share, the Case-Shiller Home Price Index, the
rate of business failures, solar panel production, seat
belt use, Mexico’s hedging tactic, medical costs for
veterans, and bounced-check charges.
• New Portfolios: Illustrating the value of mathematics
in the workplace, this feature includes new interviews
with professionals such as the Senior Vice President
of Supply at Earthbound Farms and an Antibody Assay
Developer at Ventana Medical.
FEATURES
• Algebra review when it’s needed: A Diagnostic Test
begins the Preliminaries chapter, offering students a
appear where and when students need them.
the book’s website, these videos directly correspond
to exercises found in the text and provide additional
students. In addition, Portfolio interviews show how
professionals use mathematics in their daily activities.
Applied examples are clearly marked with photo icons
that link them to the list of applications.
and solution of complicated problems. “Exploring with
Technology” boxes throughout the text offer students
the opportunity to use technology to further explore
mathematical concepts. And, “Modeling with Data”
exercises, featured in many of the “Using Technology”
subsections, show students how some of the functions
found in the exercises are constructed.
that help students master the material include “SelfCheck” exercises in every section, “Notes” to clarify
mathematical ideas, and “Cautions” that highlight
common pitfalls.
CONTENTS
www.cengageasia.com
74
Business and Economics. 7. ADDITIONAL TOPICS
IN INTEGRATION. Integration by Parts. Integration
Using Tables of Integrals. Numerical Integration.
Improper Integrals. Volumes of Solids of Revolution.
of Several Variables. Partial Derivatives. Maxima
and Minima of Functions of Several Variables. The
Method of Least Squares. Constrained Maxima and
Minima and the Method of Lagrange Multipliers. Total
Differentials. Double Integrals. Applications of Double
Integrals. 9. DIFFERENTIAL EQUATIONS. Differential
Equations. Separation of Variables. Applications
of Separable Differential Equations. Approximate
Solutions of Differential Equations. 10. PROBABILITY
AND CALCULUS. Probability Distributions of Random
Variables. Expected Value and Standard Deviation.
Normal Distributions. 11. TAYLOR POLYNOMIALS
AND INFINITE SERIES. Taylor Polynomials. Infinite
Sequences. Infinite Series. Series with Positive Numbers.
Power Series and Taylor Series. More on Taylor Series.
Newton’s Method. 12. TRIGONOMETRIC FUNCTIONS.
Measurement of Angles. The Trigonometric Functions.
Differentiation of Trigonometric Functions. Integration
of Trigonometric Functions APPENDIX A. The Inverse of
a Function. The Graphs of Inverse Functions. Functions
That Have Inverses. Finding the Inverse of a Function.
APPENDIX B. Indeterminate Forms and l’Hôpital’s Rule.
The Indeterminate Forms 0/0 and infinity/infinity.
APPENDIX C. The Standard Normal Distribution.
Answers to Odd-Numbered Exercises. Index.
© 2014, 704pp, Paperback, 9781285082691
APPLIED CALCULUS, BRIEF HYBRID
(WITH ENHANCED WEBASSIGN WITH
EBOOK LOE PRINTED ACCESS CARD FOR
ONE-TERM MATH AND SCIENCE), 6E
Geoffrey C. Berresford, Long Island University; Andrew M. Rockett,
Long Island University
Enhanced WebAssign. The result—a briefer printed
text that engages students online! This text for the
one-semester applied or business calculus course
uses intriguing real-world applications to engage
students’ interest and show them the practical side of
calculus. The book’s many applications are related to
finance, business, and such general-interest topics as
the learning curves in airplane production, the age of
the Dead Sea Scrolls, Apple and Oracle stock prices,
the distance traveled by sports cars, lives saved by
seat belts, and the cost of a congressional victory. The
Sixth Edition maintains the hallmark features that
have made BRIEF APPLIED CALCULUS so popular:
contemporary and interesting applications; careful
and effective use of technology, including graphing
calculator and spreadsheet coverage; constant
pedagogical reinforcement through section summaries,
chapter summaries, annotated examples, and extra
practice problems; Just-in-Time algebra review material;
and a variety of exercises and assignment options
including Applied Exercises, Conceptual Exercises, and
Explorations and Excursions.
NEW TO THIS EDITION
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75
only. The Hybrid Edition is packaged with Enhanced
• New exercises have been added, enhancing in
particular the number and quality of business
applications. Exercises and examples have also been
updated with the most current real data available.
• An icon now identifies Just-in-Time Review material,
which provides students with helpful algebra guidance
via blue annotations to the right of the mathematics
in every example throughout the text.
• A new design and new artwork improve the
presentation and flow of material, and boost the
aesthetic appeal of the book for today’s learners.
FEATURES
BRIEF APPLIED CALCULUS, 6th Edition, to encourage
the practice that’s so critical for concept mastery.
The pedagogy and exercises in this proven text
supplemented by multimedia tutorial assistance (e.g.,
Read It eBook pages, Watch It videos, and Master
It tutorials) and immediate feedback as students
complete their assignments. Assign as many as
2,300 problems that match your text’s end-of-section
exercises.
• Many of the book’s contemporary and interesting
applications use real, sourced data from a wide range
of fields including athletics, biomedical sciences,
environmental sciences, management science and
business, personal finance and management, social
and behavioral sciences, and topics of general interest.
A globe icon identifies real-world examples.
• Sourced exercises establish factual basis and enable
further research.
• Regression (modeling) exercises in Chapter 1 ask
students to use calculators to fit equations to actual
data, and illustrate the methods used to develop the
models in applied exercises throughout the book.
Students can also benefit from optional examples
on linear regression, power regression, quadratic
regression, and exponential regression.
• The book presents substantial treatment of limits
involving infinity, graphing rational functions, and
elasticity of demand. In addition to these expanded
applications, more challenging exercises are included
as well as a complete proof of the Chain Rule based
on Carathédory’s definition of the derivative.
• Brief Examples, located immediately to the right of the
boxes that summarize results, illustrate and provide
immediate reinforcement of the concepts.
CONTENTS
1. FUNCTIONS. Real Numbers, Inequalities, and Lines.
Exponents. Functions: Linear and Quadratic. Functions:
Polynomial, Rational, and Exponential. 2. DERIVATIVES
AND THEIR USES. Limits and Continuity. Rates of
Change, Slopes, and Derivatives. Some Differentiation
Formulas. The Product and Quotient Rules. HigherOrder Derivatives. The Chain Rule and the Generalized
Power Rule. Nondifferentiable Functions. 3. FURTHER
APPLICATIONS OF DERIVATIVES. Graphing Using
the First Derivative. Graphing Using the First and
Second Derivatives. Optimization. Further Applications
of Optimization. Optimizing Lot Size and Harvest
Size. Implicit Differentiation and Related Rates. 4.
EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. Logarithmic Functions.
Differentiation of Logarithmic and Exponential
Functions. Two Applications to Economics: Relative
Rates and Elasticity of Demand. 5. INTEGRATION AND
ITS APPLICATIONS. Antiderivatives and Indefinite
Integrals. Integration Using Logarithmic and Exponential
Functions. Definite Integrals and Areas. Further
Applications of Definite Integrals: Average Value and
Area Between Curves. Two Applications to Economics:
Consumers’ Surplus and Income Distribution. Integration
by Substitution. 6. INTEGRATION TECHNIQUES.
Integration by Parts. Integration Using Tables. Improper
Integrals. Numerical Integration. Differential Equations.
Further Applications of Differential Equations: Three
Models of Growth. 7. CALCULUS OF SEVERAL
VARIABLES. Functions of Several Variables. Partial
Derivatives. Optimizing Functions of Several Variables.
Least Squares. Lagrange Multipliers and Constrained
Optimization. Total Differentials and Approximate
Changes. Multiple Integrals.
© 2013, 504pp, Paperback, 9781133364801
www.cengageasia.com
76
APPLIED CALCULUS, HYBRID, 6E
Stefan Waner, Hofstra University
that engages students online! Full of relevant, diverse,
and current real-world applications, Stefan Waner and
Steven Costenoble’s APPLIED CALCULUS, Sixth Edition
helps your students relate to mathematics. A large
number of the applications are based on real, referenced
data from business, economics, the life sciences, and
the social sciences. Thorough, clearly delineated
spreadsheet and TI Graphing Calculator instruction
appears throughout the text. The Technology Notes and
Technology Guides are optional, allowing you to include
any amount of technology instruction in your courses.
Acclaimed for accuracy and readability, APPLIED
CALCULUS appeals to, and is appropriate for, all types
of teaching and learning styles. Resources, such as the
accompanying author website, allow the text to support
a range of course formats, from traditional lectures to
strictly online courses.
NEW TO THIS EDITION
• Current Applications: Many examples and exercises
based on dated information have been replaced
by updated versions; those based on unique or
historically interesting data have been kept. New
and updated real data applications reflect topics
that are of intense current interest or of general
interest to contemporary students, such as Facebook,
XBoxes, iPhones, Androids, iPads, foreclosure rates,
the housing crisis, subprime mortgages, the BP 2011
Gulf oil spill, and the U.S. stock market “flash crash”
in May 2010. The inside back cover lists corporations
referenced in the applications.
• Connection Between Functions and Equations:
Chapter 1 now discusses the common practice of
representing functions as equations and vice versa;
for instance, a cost equation like C = 10x + 50 can
be thought of as defining a cost function C(x) = 10x
+ 50. The authors encourage students to see this
connection and equip them to be able to switch from
one interpretation to the other.
• Discussion of Functions in Context: Coverage of
functions and models in Section 1.2 now includes
a discussion of the algebra of functions presented
through the context of important applications rather
than as an abstract concept. This allows students to
see from the outset why it’s important to learn about
sums, products, etc. of functions rather than simply
how to manipulate them.
• Chapter 3: The material on limits now includes
extensive discussions of when, and why, substitution
can be used to obtain a limit. The book now also
follows the usual convention of allowing only onesided limits at endpoints of domains. This approach
also applies to derivatives, where the text now
disallows derivatives at endpoints of domains, as is
the normal convention.
• Chapter 4: The closed-form formula for the derivative
of |x|, introduced in Section 4.1, is now more fully
integrated into the text, as is that for its antiderivative
(in Chapter 6).
• Chapter 6: The sections on antiderivatives and
substitution have been reorganized and streamlined,
and now include discussion of the closed-form
antiderivative of |x| as well as new exercises
featuring absolute values. The definite integral is now
introduced in the realistic context of the volume of
oil released in an oil spill comparable in size to the BP
2011 Gulf oil spill.
• Chapter 8: The discussion of level curves in Section 8.1
is now more extensive, and includes added examples
and exercises.
• Case Studies: A number of the Case Studies at the
ends of the chapters have been extensively revised
with updated real data, and continue to reflect topics
of current interest, such as spending on housing
construction, modeling tax revenues, and pollution
control.
www.cengageasia.com
77
• Chapter Review Exercises: Chapter review exercise
sets have been expanded to be more representative
of the material within the chapter. Students will
appreciate the applications in these exercises, all of
which revolve around the fictitious online bookseller,
OHaganBooks.com, and the various (and often
amusing) travails of company CEO John O’Hagan and
his business associate Marjory Duffin. In addition,
numerous new conceptual Communication and
Reasoning exercises include many dealing with
common student errors and misconceptions.
• More Flexible Technology Guides: End-of-chapter
Technology Guides now discuss the use of
spreadsheets in general rather than focusing
exclusively on Microsoft® Excel. This enables readers
to use any of the several alternatives now available,
such as Google’s online Google Sheets®, Open
Office®, and Apple’s Numbers®.
Calculus. 7. FURTHER INTEGRATION TECHNIQUES
AND APPLICATIONS OF THE INTEGRAL. Integration
by Parts. Area Between Two Curves and Applications.
Averages and Moving Averages. Applications to
Business and Economics: Consumers’ and Producers’
Surplus and Continuous Income Streams. Improper
Integrals and Applications. Differential Equations and
Applications. 8. FUNCTIONS OF SEVERAL VARIABLES.
Functions of Several Variables from the Numerical,
Algebraic, and Graphical Viewpoints. Partial Derivatives.
Maxima and Minima. Constrained Maxima and Minima
and Applications. Double Integrals and Applications. 9.
TRIGONOMETRIC MODELS. Trigonometric Functions,
Models, and Regression. Derivatives of Trigonometric
Functions and Applications. Integrals of Trigonometric
Functions and Applications.
© 2014, 544pp, Paperback, 9781285056401
CONTENTS
0. PRECALCULUS REVIEW. Real Numbers. Exponents
and Radicals. Multiplying and Factoring Algebraic
Equations. Rational Expressions. Solving Polynomial
Equations. Solving Miscellaneous Equations. The
Coordinate Plane. 1. FUNCTIONS AND APPLICATIONS.
Functions from the Numerical, Algebraic, and Graphical
Viewpoints. Functions and Models. Linear Functions
and Models. Linear Regression. 2. NONLINEAR
FUNCTIONS AND MODELS. Quadratic Functions and
Models. Exponential Functions and Models. Logarithmic
Functions and Models. Logistic Functions and Models. 3.
INTRODUCTION TO THE DERIVATIVE. Limits: Numerical
and Graphical Approaches. Limits and Continuity.
Limits: Algebraic Approach. Average Rate of Change.
Derivatives: Numerical and Graphical Viewpoints.
Derivatives: Algebraic Viewpoint. 4. TECHNIQUES
OF DIFFERENTIATION. Derivatives of Powers, Sums,
and Constant Multiples. A First Application: Marginal
Analysis. The Product and Quotient Rules. The Chain
Rule. Derivatives of Logarithmic and Exponential
Functions. Implicit Differentiation. 5. APPLICATIONS
OF THE DERIVATIVE. Maxima and Minima. Applications
of Maxima and Minima. Higher Order Derivatives:
Acceleration and Concavity. Analyzing Graphs. Related
Rates. Elasticity. 6. THE INTEGRAL. The Indefinite
Integral. Substitution. The Definite Integral: Numerical
and Graphical Approaches. The Definite Integral:
Algebraic Approach and the Fundamental Theorem of
APPLIED CALCULUS, HYBRID EDITION
ONE-TERM MATH AND SCIENCE), 6E
text that engages students online! This text for the
one- or two-semester applied or business calculus
course uses intriguing real-world applications to engage
students’ interest and show them the practical side
of calculus. The book’s many applications are related
to finance, business, and such general-interest topics
www.cengageasia.com
78
as learning curves in airplane production, the age of
the Dead Sea Scrolls, Apple and Oracle stock prices,
the distance traveled by sports cars, lives saved by
seat belts, and the cost of a congressional victory. The
Sixth Edition maintains the hallmark features that have
made APPLIED CALCULUS so popular: contemporary
and interesting applications; careful and effective
use of technology, including graphing calculator
and spreadsheet coverage; constant pedagogical
reinforcement through section summaries, chapter
summaries, annotated examples, and extra practice
problems; Just-in-Time algebra review material;
NEW TO THIS EDITION
only. The Hybrid Edition is packaged with Enhanced
FEATURES
WebAssign® offers an extensive online program
for APPLIED CALCULUS, 6th Edition, to encourage
the practice that’s so critical for concept mastery.
The pedagogy and exercises in this proven text
supplemented by multimedia tutorial assistance (e.g.,
Read It eBook pages, Watch It videos, and Master
It tutorials) and immediate feedback as students
complete their assignments. Assign as many as
2,300 problems that match your text’s end-of-section
exercises.
further research.
CONTENTS
Rates and Elasticity of Demand. 5. INTEGRATION
AND ITS APPLICATIONS. Antiderivatives and
Indefinite Integrals. Integration Using Logarithmic
and Exponential Functions. Definite Integrals and
Areas. Further Applications of Definite Integrals:
www.cengageasia.com
79
Average Value and Area Between Curves. Two
Applications to Economics: Consumers’ Surplus and
Income Distribution. Integration by Substitution. 6.
INTEGRATION TECHNIQUES. Integration by Parts.
Integration Using Tables. Improper Integrals. Numerical
Integration. 7. CALCULUS OF SEVERAL VARIABLES.
Functions of Several Variables. Partial Derivatives.
Optimizing Functions of Several Variables. Least Squares.
Lagrange Multipliers and Constrained Optimization.
Total Differentials and Approximate Changes. Multiple
Integrals. 8. TRIGONOMETRIC FUNCTIONS. Triangles,
Angles, and Radian Measure. Sine and Cosine Functions.
Derivatives of Sine and Cosine Functions. Integrals
of Sine and Cosine Functions. Other Trigonometric
Functions. 9. DIFFERENTIAL EQUATIONS. Separation
of Variables. Further Applications of Differential
Equations: Three Models of Growth. First-Order Linear
Differential Equations. Approximate Solutions of
Differential Equations: Euler’s Method. 10. SEQUENCES
AND SERIES. Geometric Series. Taylor Polynomials.
Taylor Series. Newton’s Method. 11. PROBAILITY.
Discrete Probability. Continuous Probability. Uniform
and Exponential Random Variables. Normal Random
Variables.
© 2013, 688pp, Paperback, 9781133364771
of the Supreme Court, water shortage, the fastest
pitch in baseball, and pollution and the depletion of
natural resources. The Sixth Edition maintains the
hallmark features that have made APPLIED CALCULUS,
International Edition so popular: contemporary
NEW TO THIS EDITION
FEATURES
APPLIED CALCULUS, INTERNATIONAL
EDITION, 6E
This text for the applied or business calculus course
students’ interest and show them the practical side
of calculus. The book’s many applications are related
to finance, business, and such general-interest topics
as the growing population of Africa, the composition
for APPLIED CALCULUS, 6E, International Edition to
mastery. The pedagogy and exercises in this proven
text become even more effective in Enhanced
WebAssign, supplemented by multimedia tutorial
assistance (e.g., Read It eBook pages, Watch It videos,
and Master It tutorials) and immediate feedback as
students complete their assignments.
further research.
www.cengageasia.com
80
• Optional Graphing Calculator Explorations and
exercises explore new topics, allow students to
easily carry out otherwise messy calculations, or
show the limitations and pitfalls of technology. To
allow for optional use of the graphing calculator,
the Calculator Explorations are boxed, and an icon
identifies exercises that require a graphing calculator.
CONTENTS
Applications to Economics: Consumers’ Surplus and
Income Distribution. Integration by Substitution. 6.
INTEGRATION TECHNIQUES. Integration by Parts.
Integration. 7. CALCULUS OF SEVERAL VARIABLES.
Optimizing Functions of Several Variables. Least Squares.
Lagrange Multipliers and Constrained Optimization.
Total Differentials and Approximate Changes. Multiple
Integrals. 8. TRIGONOMETRIC FUNCTIONS. Triangles,
Angles, and Radian Measure. Sine and Cosine Functions.
Derivatives of Sine and Cosine Functions. Integrals
of Sine and Cosine Functions. Other Trigonometric
Functions. 9. DIFFERENTIAL EQUATIONS. Separation
of Variables. Further Applications of Differential
Equations: Three Models of Growth. First-Order Linear
Differential Equations. Approximate Solutions of
Differential Equations: Euler’s Method. 10. SEQUENCES
AND SERIES. Geometric Series. Taylor Polynomials.
Taylor Series. Newton’s Method. 11. PROBABILITY.
Discrete Probability. Continuous Probability. Uniform
and Exponential Random Variables. Normal Random
Variables.
© 2013, 912pp, Paperback, 9781133103936
Rates and Elasticity of Demand. 5. INTEGRATION
AND ITS APPLICATIONS. Antiderivatives and
Indefinite Integrals. Integration Using Logarithmic
and Exponential Functions. Definite Integrals and
Areas. Further Applications of Definite Integrals:
Average Value and Area Between Curves. Two
APPLIED CALCULUS, INTERNATIONAL
EDITION, 6E
Stefan Waner, Hofstra University; Steven Costenoble, Hofstra
University
Full of relevant, diverse, and current real-world
applications, Stefan Waner and Steven Costenoble’s
APPLIED CALCULUS, 6E, International Edition helps
your students relate to mathematics. A large number of
the applications are based on real, referenced data from
business, economics, the life sciences, and the social
sciences. Thorough, clearly delineated spreadsheet and
www.cengageasia.com
81
TI Graphing Calculator instruction appears throughout
the text. The Technology Notes and Technology Guides
are optional, allowing you to include any amount of
technology instruction in your courses. Acclaimed
for accuracy and readability, APPLIED CALCULUS, 6E,
International Edition appeals to, and is appropriate for,
all types of teaching and learning styles. Resources,
such as the accompanying author website, allow
the text to support a range of course formats, from
traditional lectures to strictly online courses.
NEW TO THIS EDITION
based on dated information have been replaced
by updated versions; those based on unique or
historically interesting data have been kept. New
and updated real data applications reflect topics
that are of intense current interest or of general
interest to contemporary students, such as Facebook,
the housing crisis, subprime mortgages, the BP 2011
Gulf oil spill, and the U.S. stock market “flash crash”
in May 2010. The inside back cover lists corporations
referenced in the applications.
• Chapter 3: The material on limits now includes
extensive discussions of when, and why, substitution
can be used to obtain a limit. The book now also
follows the usual convention of allowing only onesided limits at endpoints of domains. This approach
also applies to derivatives, where the text now
disallows derivatives at endpoints of domains, as is
the normal convention.
(in Chapter 6).
antiderivative of |x| as well as new exercises
• Chapter 8: The discussion of level curves in Section 8.1
is now more extensive, and includes added examples
and exercises.
• Case Studies: A number of the Case Studies at the
ends of the chapters have been extensively revised
with updated real data, and continue to reflect topics
of current interest, such as spending on housing
construction, modeling tax revenues, and pollution
control.
exclusively on Microsoft® Excel. This enables readers
to use any of the several alternatives now available,
such as Google’s online Google Sheets®, Open
Office®, and Apple’s Numbers®.
CONTENTS
www.cengageasia.com
82
and Models. Linear Regression. 2. NONLINEAR
Algebraic Approach and the Fundamental Theorem of
Calculus. 7. FURTHER INTEGRATION TECHNIQUES
AND APPLICATIONS OF THE INTEGRAL. Integration
by Parts. Area Between Two Curves and Applications.
© 2014, 768pp, Paperback, 9781133936695
Coming Soon!
APPLIED MATHEMATICS FOR THE
SCIENCES, HYBRID (WITH ENHANCED
WEBASSIGN WITH EBOOK LOE PRINTED
ACCESS CARD FOR ONE-TERM MATH
AND SCIENCE), 6E
that engages students online! A traditional book with a
modern feel, market-leading APPLIED MATHEMATICS
FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES,
Sixth Edition, teaches by application and uses realworld examples to motivate students. It combines
solid theory with innovative technology, includes a
robust supplement package, and offers unmatched
flexibility that caters to both traditional and modern
practitioners. Accessible for majors and non-majors
alike, the new Sixth Edition utilizes an intuitive
approach that marries real-life instances to what would
otherwise be abstract concepts. This is the focus of
new and insightful Portfolios, which highlight the
careers of real people and discuss how they use math
in their professions. Numerous exercises ensure that
students have a solid understanding of concepts before
advancing to the next topic. By offering a powerful array
of supplements such as Enhanced WebAssign®, the
new Sixth Edition enables students to maximize their
study time and succeed in class.
NEW TO THIS EDITION
• NEW! The hybrid edition of the text provides a less-
www.cengageasia.com
83
expensive, shorter option for students. End-of-section
• The sixth edition includes many new and updated
student-friendly applications. Topics include: worker
efficiency, optics, inventory control, air pollution,
public transportation budget deficit, brain cancer
survival rate, motion of cars, Case-Shiller Home Price
Index, solar panel production, and federal lobbying.
• Eight new Portfolios illustrate the real-life experiences
of a variety of professionals who use mathematics in
the workplace. Among those interviewed are the City
Manager of Fanfoto, Senior Vice President of Supply at
Earthbound Farms, and a Principal Software Engineer
at Iron Mountain.
• Updated Excel coverage enhances the student
experience.
• Complement your text and course content with
study and practice materials. Cengage Learning’s
CourseMate brings course concepts to life with
interactive learning, study, and exam preparation tools
that support the printed textbook. Watch student
comprehension soar as your class works with the
printed textbook and the textbook-specific website.
CourseMate goes beyond the book to deliver what
you need!
FEATURES
exercises.
• Solution videos and tutorials: Available on the
CourseMate, these videos directly correspond to
exercises found within the text and provide additional
CONTENTS
Preface. 1. FUNDAMENTALS OF ALGEBRA. Real
Numbers.Polynomials.Factoring Polynomials. Rational
Expressions. Integral Exponents. Solving Equations.
Rational Exponents and Radicals. Quadratic Equations.
Inequalities and Absolute Value.Chapter 1 Summary of
Principal Formulas and Terms. Chapter 1 Concept Review
Moving On. 2. FUNCTIONS AND THEIR GRAPHS. The
Cartesian Coordinate System. Equations of Lines. Using
Technology: Graphing Straight Lines. Functions and
Their Graphs. Using Technology: Graphing a Function.
The Algebra of Functions. Linear Functions. Quadratic
Functions. Portfolio. Using Technology: Constructing
Matehmatical Models from Raw Data. Functions and
Mathematical Models. Portfolio. Chapter 1 Summary of
Moving On. 3. EXPONENTIAL AND LOGARITHMIC
FUNCTIONS. Exponential Functions. Using TEchnology.
Logarithmic Functions. Exponential Functions as
Mathematical Models. Portfolio. Using Technology:
Analyzing Matematical Models. 4. MATHEMATICS
OF FINANCE. Compound Interest. Using Technology:
Finding the Accumulated Amount of an Investment,
the Effective Rate of Interest, and the Present Value
of an Investment. Annuities. Using Technology:
Finding the Amount of an Annuity. Amortization and
Sinking Funds. Using Technology: Amortizing a Loan.
Arithmetic and Geometric Progressions. Chapter 4
Summary of Principal Formulas and Terms. Chapter
4 Concept Review Questions. Chapter 4 Review
Exercises. Chapter 4 Before Moving On. 5. SYSTEMS
OF LINEAR EQUATIONS AND MATRICES. Systems
of Linear Equations: An Introduction. Systems of
Linear Equations: Unique Solutions. Using Technology:
Systems of Linear Equations: Unique Solutions.
Systems of Linear Equations: Underdetermined
and Overdetermined Systems. Using Technology:
Systems of Linear Equations: Underdetermined and
Overdetermined Systems. Matrices. Using Technology:
Matrix Operations. Multiplication of Matrices. Using
Technology: Matrix Multiplication. The Inverse of a
Square Matrix. Using Technology: Finding the Inverse
of a Square Matrix. Chapter 5 Summary of Principal
www.cengageasia.com
84
Moving On. 6. LINEAR PROGRAMMING Graphing
Systems of Linear Inequalities in Two Variables.
Linear Programming Problems. Graphical Solutions of
Linear Programming Problems. The Simplex Method:
Standard Maximization Problems. Portfolio. Using
Technology: The Simplex Method: Solving Maximization
Problems. The Simplex Method: Standard Minimization
Problems. Using Technology: The Simplex Method:
Solving Minimization Problems. Chapter 6 Summary
6 Before Moving On. 7. SETS AND PROBABILITY. Sets
and Set Operations. The Number of Elements in a Finite
Set. The Multiplication Principle. Permutations and
Combinations. Portfolio. Using Technology: Evaluating
n!, P (n,r) and C (n,r). Experiments, Sample Spaces, and
Events. Definition of Probability. Rules of Probability.
ADDITIONAL TOPICS IN PROBABILITY. Use of Counting
Techniques in Probability. Conditional Probability and
Independent Events. Bayes’ Theorem. Distributions
of Random Variables. Using Technology: Graphing a
Histogram. Expected Value. Portfolio. Variance and
Standard Deviation. Using Technology: Finding the
Mean and Standard Deviation. Chapter 8 Summary
8 Before Moving On. 9. THE DERIVATIVE. Limits. Using
Technology: Finding the Limit of a Function. One-Sided
Limits and Continuity. Using Technology: Finding the
Points of Discontinuity of a Function. The Derivative.
Using Technology: Graphing a Function and Its Tangent
Line. Basic Rules of Differentiation. Using Technology:
Finding the Rate of Change of a Function. The Product
and Quotient Rules; Higher-Order Derivatives. Using
Technology: The Product and Quotient Rules. The
Chain Rule. Using Technology: Finding the Derivative
of a Composite Function. Differentiation of Exponential
and Logarithmic Functions. Using Technology. Marginal
Functions in Economics. Chapter 9 Concept Review
Questions. Chapter 9 Review Exercises. Chapter
9 Before Moving On. 10. APPLICATIONS OF THE
DERIVATIVE. Applications of the First Derivative.
Using Technology: Using the First Derivative to Analyze
a Function. Applications of the Second Derivative.
Using Technology: Finding the Inflection Points of
a Function. Curve Sketching. Using Technology:
Analyzing the Properties of a Function. Optimization
On. 11. INTEGRATION. Antiderivatives and the Rules
of Integration. Integration by Substitution. Area and
the Definite Integral. The Fundamental Theorem of
Calculus. Portfolio. Using Technology: Evaluating
11 Before Moving On. 12. CALCULUS OF SEVERAL
Derivatives. Portfolio. Using Technology: Finding Partial
Derivatives at a Given Point. Maxima and Minima of
Functions of Several Variables. Chapter 12 Summary
12 Before Moving On.
© 2013, 752pp, Paperback, 9781133364856
APPLIED MATHEMATICS FOR THE
SCIENCES, INTERNATIONAL EDITION, 6E
A traditional book with a modern feel, market-leading
APPLIED MATHEMATICS FOR THE MANAGERIAL,
LIFE, AND SOCIAL SCIENCES, 6E, International Edition
teaches by application and uses real-world examples
to motivate students. It combines solid theory with
innovative technology, includes a robust supplement
www.cengageasia.com
85
package, and offers unmatched flexibility that caters to
both traditional and modern practitioners. Accessible
for majors and non-majors alike, the new Sixth Edition
utilizes an intuitive approach that marries real-life
instances to what would otherwise be abstract
concepts. This is the focus of new and insightful
Portfolios, which highlight the careers of real people
and discuss how they use math in their professions.
Numerous exercises ensure that students have a solid
understanding of concepts before advancing to the
next topic. By offering a powerful array of supplements
such as Enhanced WebAssign®, the new Sixth Edition
enables students to maximize their study time and
succeed in class.
NEW TO THIS EDITION
• The sixth edition includes many new and updated
student-friendly applications. Topics include: worker
efficiency, optics, inventory control, air pollution,
public transportation budget deficit, brain cancer
survival rate, motion of cars, Case-Shiller Home Price
Index, solar panel production, and federal lobbying.
• Eight new Portfolios illustrate the real-life experiences
of a variety of professionals who use mathematics in
the workplace. Among those interviewed are the City
Manager of Fanfoto, Senior Vice President of Supply at
Earthbound Farms, and a Principal Software Engineer
at Iron Mountain.
• Updated Excel coverage enhances the student
experience.
• Complement your text and course content with
study and practice materials. Cengage Learning’s
CourseMate brings course concepts to life with
CourseMate goes beyond the book to deliver what
you need!
FEATURES
exercises.
well.
CONTENTS
1. FUNDAMENTALS OF ALGEBRA. Real Numbers.
Polynomials. Factoring Polynomials. Rational
Expressions. Integral Exponents. Solving Equations.
Rational Exponents and Radicals. Quadratic Equations.
Inequalities and Absolute Value. Chapter 1 Summary of
Moving On. 2. FUNCTIONS AND THEIR GRAPHS. The
Cartesian Coordinate System. Equations of Lines. Using
Technology: Graphing Straight Lines. Functions and
Their Graphs. Using Technology: Graphing a Function.
The Algebra of Functions. Linear Functions. Quadratic
Functions. Portfolio. Using Technology: Constructing
Mathematical Models from Raw Data. Functions and
Mathematical Models. Portfolio. Chapter 1 Summary of
www.cengageasia.com
86
Moving On. 3. EXPONENTIAL AND LOGARITHMIC
FUNCTIONS. Exponential Functions. Using Technology.
Logarithmic Functions. Exponential Functions as
Mathematical Models. Portfolio. Using Technology:
Analyzing Mathematical Models. 4. MATHEMATICS
OF FINANCE. Compound Interest. Using Technology:
the Effective Rate of Interest, and the Present Value
of an Investment. Annuities. Using Technology:
Finding the Amount of an Annuity. Amortization and
Sinking Funds. Using Technology: Amortizing a Loan.
Arithmetic and Geometric Progressions. Chapter 4
OF LINEAR EQUATIONS AND MATRICES. Systems
of Linear Equations: An Introduction. Systems of
Linear Equations: Unique Solutions. Using Technology:
Systems of Linear Equations: Unique Solutions.
Systems of Linear Equations: Underdetermined
and Overdetermined Systems. Using Technology:
Systems of Linear Equations: Underdetermined and
Overdetermined Systems. Matrices. Using Technology:
Matrix Operations. Multiplication of Matrices. Using
Technology: Matrix Multiplication. The Inverse of a
Square Matrix. Using Technology: Finding the Inverse
of a Square Matrix. Chapter 5 Summary of Principal
Moving On. 6. LINEAR PROGRAMMING Graphing
Systems of Linear Inequalities in Two Variables.
Linear Programming Problems. Graphical Solutions of
Linear Programming Problems. The Simplex Method:
Standard Maximization Problems. Portfolio. Using
Technology: The Simplex Method: Solving Maximization
Problems. The Simplex Method: Standard Minimization
Problems. Using Technology: The Simplex Method:
Solving Minimization Problems. Chapter 6 Summary
6 Before Moving On. 7. SETS AND PROBABILITY. Sets
and Set Operations. The Number of Elements in a Finite
Set. The Multiplication Principle. Permutations and
Combinations. Portfolio. Using Technology: Evaluating
n!, P (n,r) and C (n,r). Experiments, Sample Spaces, and
Events. Definition of Probability. Rules of Probability.
ADDITIONAL TOPICS IN PROBABILITY. Use of Counting
Techniques in Probability. Conditional Probability and
Independent Events. Bayes’ Theorem. Distributions
of Random Variables. Using Technology: Graphing a
Histogram. Expected Value. Portfolio. Variance and
Standard Deviation. Using Technology: Finding the
Mean and Standard Deviation. Chapter 8 Summary
8 Before Moving On. 9. THE DERIVATIVE. Limits. Using
Technology: Finding the Limit of a Function. One-Sided
Limits and Continuity. Using Technology: Finding the
Points of Discontinuity of a Function. The Derivative.
Using Technology: Graphing a Function and Its Tangent
Line. Basic Rules of Differentiation. Using Technology:
Finding the Rate of Change of a Function. The Product
and Quotient Rules; Higher-Order Derivatives. Using
Technology: The Product and Quotient Rules. The
Chain Rule. Using Technology: Finding the Derivative
of a Composite Function. Differentiation of Exponential
and Logarithmic Functions. Using Technology. Marginal
Functions in Economics. Chapter 9 Concept Review
Questions. Chapter 9 Review Exercises. Chapter
9 Before Moving On. 10. APPLICATIONS OF THE
DERIVATIVE. Applications of the First Derivative.
Using Technology: Using the First Derivative to Analyze
a Function. Applications of the Second Derivative.
Using Technology: Finding the Inflection Points of
a Function. Curve Sketching. Using Technology:
Analyzing the Properties of a Function. Optimization
On. 11. INTEGRATION. Antiderivatives and the Rules
of Integration. Integration by Substitution. Area and
the Definite Integral. The Fundamental Theorem of
Calculus. Portfolio. Using Technology: Evaluating
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11 Before Moving On. 12. CALCULUS OF SEVERAL
Derivatives. Portfolio. Using Technology: Finding Partial
Derivatives at a Given Point. Maxima and Minima of
Functions of Several Variables. Chapter 12 Summary
12 Before Moving On.
© 2013, 976pp, Paperback, 9781133109310
NEW TO THIS EDITION
FEATURES
BRIEF APPLIED CALCULUS,
This text for the applied or business calculus course
students’ interest and show them the practical side of
calculus. The book’s many applications are related to
finance, business, and such general-interest topics as
the growing population of Africa, the composition of
the Supreme Court, water shortage, the fastest pitch
in baseball, and pollution and the depletion of natural
resources. The Sixth Edition maintains the hallmark
features that have made BRIEF APPLIED CALCULUS,
International Edition so popular: contemporary
for APPLIED CALCULUS, 6E, International Edition to
mastery. The pedagogy and exercises in this proven
text become even more effective in Enhanced
WebAssign, supplemented by multimedia tutorial
assistance (e.g., Read It eBook pages, Watch It videos,
and Master It tutorials) and immediate feedback as
students complete their assignments.
further research.
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88
• Optional Graphing Calculator Explorations and
exercises explore new topics, allow students to
easily carry out otherwise messy calculations, or
show the limitations and pitfalls of technology. To
allow for optional use of the graphing calculator,
the Calculator Explorations are boxed, and an icon
identifies exercises that require a graphing calculator.
CONTENTS
Rates and Elasticity of Demand. 5. INTEGRATION AND
Integrals. Integration Using Logarithmic and Exponential
Functions. Definite Integrals and Areas. Further
Applications of Definite Integrals: Average Value and
Area Between Curves. Two Applications to Economics:
Consumers’ Surplus and Income Distribution. Integration
by Substitution. 6. INTEGRATION TECHNIQUES AND
DIFFERENTIAL EQUATIONS. Integration by Parts.
Integration. Differential Equations. Further Applications
of Differential Equations: Three Models of Growth.
of Several Variables. Partial Derivatives. Optimizing
Functions of Several Variables. Least Squares. Lagrange
Multipliers and Constrained Optimization. Total
Differentials and Approximate Changes. Multiple
Integrals.
© 2013, 672pp, Paperback, 9781133103974
BRIEF APPLIED CALCULUS, HYBRID
ONE-TERM MATH AND SCIENCE)
James Stewart, McMaster University; Daniel Clegg, Palomar College
Enhanced WebAssign® . The result—a briefer, less
expensive printed text that engages students online!
New from James Stewart and Dan Clegg, BRIEF
APPLIED CALCULUS, HYBRID takes an intuitive, less
formal approach to calculus without sacrificing the
mathematical integrity. Featuring a wide range of
applications designed to motivate students with a
variety of interests, clear examples detailing important
mathematical processes, and a vast collection of
exercises appropriate for students with disparate skill
sets, this first edition is perfect for students who need
to learn how to apply calculus concepts rather than
replicate the formal proofs behind the techniques.
Early coverage of exponential and logarithmic
functions allows for the inclusion of many interesting
applications throughout the text. Available with a range
of supplements including Enhanced WebAssign®,
BRIEF APPLIED CALCULUS, HYBRID makes calculus
approachable so any student can understand the
concepts and be successful in the course.
FEATURES
• Reflecting Cengage Learning’s commitment to offering
instructors, a hybrid version of the text is offered
that includes all of the instructional presentation
found in the printed text while delivering end-of-
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89
section exercises online in Enhanced WebAssign. The
result—a briefer printed text that engages students
online and saves them money!
• Stewart/Clegg’s writing style speaks clearly and
directly to students, guiding them through key
ideas, theorems, and problem-solving steps, and
encouraging them to think as they read and learn
calculus.
• Prepare Yourself exercises are designed to check
students’ prerequisite skills before they attempt the
core exercise set. These exercises acknowledge the
variety of math abilities, and show students what they
need to work on before they move forward.
• Challenge Yourself exercises are more difficult
problems intended to elicit students’ deeper
understanding of key concepts. These exercises are
designed to be assigned by instructors who wish to
aim at a higher level and keep their more advanced
students interested.
• Projects are included throughout to motivate students
and help them see the relation of calculus to real
life and their intended fields of study. They can be
worked in class, assigned as group projects, or given
as extra credit.
• Tools for Enriching Calculus for Applied Calculus—
an online, interactive resource that allows applied
calculus students to work with animations to deepen
their understanding of key concepts by helping them
visualize the concepts they are learning.
Stewart/Clegg’s Brief Applied Calculus to encourage
the practice that’s so critical for concept mastery. The
meticulously crafted pedagogy and exercises in the
Stewart/Clegg text become even more effective in
Enhanced WebAssign, supplemented by multimedia
tutorial support and immediate feedback as students
complete their assignments. Enhanced WebAssign for
Stewart/Clegg includes opportunities for students to
review prerequisite skills and content throughout.
• Interested in a simple way to complement your
text and course content with study and practice
CONTENTS
1. FUNCTIONS AND MODELS. Functions and their
Representations. Combining and Transforming
Functions. Linear Models and Rates of Change.
Polynomial Models and Power Functions. Exponential
Models. Logarithmic Functions. 2. THE DERIVATIVE.
Measuring Change. Limits. Rates of Change and
Derivatives. The Derivative as a Function. 3.
TECHNIQUES OF DIFFERENTIATION. Short Cuts to
Finding Derivatives. Introduction to Marginal Analysis.
The Product and Quotient Rules. The Chain Rule. Implicit
Differentiation and Logarithms. Exponential Growth
and Decay. 4. APPLICATIONS OF DIFFERENTIATION.
Related Rates. Maximum and Minimum Values.
Derivatives and the Shapes of Curves. Asymptotes.
Curve Sketching. Optimization. Optimization in
Business and Economics. 5. INTEGRALS. Cost, Area,
and the Definite Integral. Fundamental Theorem
of Calculus. The Net Change Theorem and Average
Value. The Substitution Rule. Integration by Parts. 6.
APPLICATIONS OF INTEGRATION. Areas Between
Curves. Applications to Economics. Applications to
Biology. Differential Equations. Improper Integrals.
Probability. 7. FUNCTIONS OF SEVERAL VARIABLES.
Maximum and Minimum Values. LaGrange Multipliers.
© 2012, 400pp, Paperback, 9781111990121
BRIEF APPLIED CALCULUS,
INTERNATIONAL EDITION
James Stewart, McMaster University; Daniel Clegg, Palomar College
New from James Stewart and Dan Clegg, BRIEF APPLIED
CALCULUS, International Edition takes an intuitive,
www.cengageasia.com
90
less formal approach to calculus without sacrificing
the mathematical integrity. Featuring a wide range
of applications designed to motivate students with a
variety of interests, clear examples detailing important
mathematical processes, and a vast collection of
exercises appropriate for students with disparate skill
sets, this first edition is perfect for students who need
to learn how to apply calculus concepts rather than
replicate the formal proofs behind the techniques.
Early coverage of exponential and logarithmic
functions allows for the inclusion of many interesting
applications throughout the text. Available with a range
of supplements including Enhanced WebAssign®,
BRIEF APPLIED CALCULUS, International Edition makes
calculus approachable so any student can understand
the concepts and be successful in the course.
FEATURES
• Stewart/Clegg’s writing style speaks clearly and
directly to students, guiding them through key
ideas, theorems, and problem-solving steps, and
encouraging them to think as they read and learn
calculus.
• Prepare Yourself exercises are designed to check
students’ prerequisite skills before they attempt the
core exercise set. These exercises acknowledge the
variety of math abilities, and show students what they
need to work on before they move forward.
• Challenge Yourself exercises are more difficult
problems intended to elicit students’ deeper
understanding of key concepts. These exercises are
designed to be assigned by instructors who wish to
aim at a higher level and keep their more advanced
students interested.
• Projects are included throughout to motivate students
and help them see the relation of calculus to real
life and their intended fields of study. They can be
worked in class, assigned as group projects, or given
as extra credit.
• Tools for Enriching Calculus for Applied Calculus—
an online, interactive resource that allows applied
calculus students to work with animations to deepen
their understanding of key concepts by helping them
visualize the concepts they are learning.
Stewart/Clegg’s Brief Applied Calculus, International
Edition to encourage the practice that’s so critical
for concept mastery. The meticulously crafted
pedagogy and exercises in the Stewart/Clegg text
assignments. Enhanced WebAssign for Stewart/
Clegg includes opportunities for students to review
prerequisite skills and content throughout.
• Interested in a simple way to complement your
text and course content with study and practice
CONTENTS
1. FUNCTIONS AND MODELS. Functions and their
Representations. Combining and Transforming
Functions. Linear Models and Rates of Change.
Polynomial Models and Power Functions. Exponential
Models. Logarithmic Functions. 2. THE DERIVATIVE.
Measuring Change. Limits. Rates of Change and
Derivatives. The Derivative as a Function. 3.
TECHNIQUES OF DIFFERENTIATION. Short Cuts to
Finding Derivatives. Introduction to Marginal Analysis.
The Product and Quotient Rules. The Chain Rule. Implicit
Differentiation and Logarithms. Exponential Growth
and Decay. 4. APPLICATIONS OF DIFFERENTIATION.
Related Rates. Maximum and Minimum Values.
Derivatives and the Shapes of Curves. Asymptotes.
Curve Sketching. Optimization. Optimization in
Business and Economics. 5. INTEGRALS. Cost, Area,
and the Definite Integral. Fundamental Theorem
of Calculus. The Net Change Theorem and Average
Value. The Substitution Rule. Integration by Parts. 6.
APPLICATIONS OF INTEGRATION. Areas Between
Curves. Applications to Economics. Applications to
Biology. Differential Equations. Improper Integrals.
Probability. 7. FUNCTIONS OF SEVERAL VARIABLES.
Maximum and Minimum Values. LaGrange Multipliers.
© 2012, 528pp, Paperback, 9781111570057
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91
analyze mathematical models from large data sets.
• New! CourseMate brings course concepts to life with
FEATURES
BRIEF CALCULUS, 9E
An Applied Approach, International Edition
Designed specifically for business, economics, or life/
social sciences majors, BRIEF CALCULUS: AN APPLIED
APPROACH, 9E International Edition motivates
students while fostering understanding and mastery.
This brief book emphasizes integrated and engaging
applications that show students the real-world relevance
of topics and concepts. Applied problems drawn from
government sources, industry, current events, and
other disciplines provide well-rounded examples
and appeal to students’ diverse interests. The Ninth
Edition builds upon its applications emphasis through
updated exercises and relevant examples. Pedagogical
features—from algebra review to study tips—continue
to provide extra guidance and practice. In addition,
the BRIEF CALCULUS: AN APPLIED APPROACH, 9E
International Edition program offers a strong support
package—including Enhanced WebAssign® and the
book’s website, CourseMate—that allows students
to review the material independently and retain key
concepts.
NEW TO THIS EDITION
• New! A Summarize feature guides students in creating
section-level concept summaries— helping them
process and organize key concepts while providing a
valuable study tool.
• New! How Do You See It? exercises ask students
to draw conclusions about information presented
visually. Requiring little or no calculation, these
exercises check students’ conceptual understanding
of key concepts.
• New and Updated! Projects, which appear in selected
sections, connect real-life data and applications and
give your students the opportunity to generate and
• Every section begins with a list of objectives that
highlights the learning outcomes of that section and
provides instructors with a tool for lesson planning.
• Appearing in the middle of each chapter, Mid-Chapter
Quizzes are single-page tests that let students
practice skills and concepts learned in the chapter.
This opportunity for self-assessment helps uncover
potential weaknesses that might require further
review of the material.
• Revised! Section-ending Business Capsules and
accompanying exercises address business situations
related to the mathematical concepts covered in the
chapter.
• Revised! At the beginning of each exercise set, Skills
Warm Up exercises give students practice of skills
covered in previous sections that are used in the
exercise set; answers are provided at the back of the
text to reinforce understanding.
• Revised! The Exercise Sets have been revised
based on actual student usage data to improve
student comprehension. More than 3,500 exercises
progress from skill-development problems to more
challenging, real-world applications —all of which can
be customized to the difficulty level of the instructor’s
choice.
• A wide variety of relevant examples—each of which
is titled for easy reference—includes solutions
presented graphically, analytically, and/or numerically
to provide further insight into mathematical concepts.
Examples that illustrate real-life situations are
identified with an icon.
CONTENTS
1. FUNCTIONS, GRAPHS, AND LIMITS. The Cartesian
Plane and the Distance Formula. Graphs of Equations.
Lines in the Plane and Slope. Functions. Limits.
Continuity. 2. DIFFERENTIATION. The Derivative and
the Slope of a Graph. Some Rules for Differentiation.
Rates of Change: Velocity and Marginals. The Product
and Quotient Rules. The Chain Rule. Higher-Order
Derivatives. Implicit Differentiation. Related Rates.
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3. APPLICATIONS OF THE DERIVATIVE. Increasing
and Decreasing Functions. Extrema and the FirstDerivative Test. Concavity and the Second-Derivative
Test. Optimization Problems. Business and Economics
Applications. Asymptotes. Curve Sketching: A
Summary. Differentials and Marginal Analysis. 4.
Exponential Functions. Natural Exponential Functions.
Derivatives of Exponential Functions. Logarithmic
Functions. Derivatives of Logarithmic Functions.
Exponential Growth and Decay. 5. INTEGRATION AND
Integrals. Integration by Substitution and the General
Power Rule. Exponential and Logarithmic Integrals. Area
and the Fundamental Theorem of Calculus. The Area of a
Region Bounded by Two Graphs. The Definite Integral as
the Limit of a Sum. 6. TECHNIQUES OF INTEGRATION.
Integration by Parts and Present Value. Integration
Tables. Numerical Integration. Improper Integrals. 7.
FUNCTIONS OF SEVERAL VARIABLES. The ThreeDimensional Coordinate System. Surfaces in Space.
Extrema of Functions of Two Variables. Lagrange
Multipliers. Least Squares Regression Analysis. Double
Integrals and Area in the Plane. Applications of Double
Integrals. Appendix A. Precalculus Review. The Real
Number Line and Order. Absolute Value and Distance on
the Real Number Line. Exponents and Radicals. Factoring
Polynomials. Fractions and Rationalization. Appendix B.
Alternative Introduction to the Fundamental Theorem
of Calculus. Appendix C. Formulas.
© 2013, 640pp, Paperback, 9781133109785
BRIEF CALCULUS, 9E
An Applied Approach, Hybrid (with Enhanced WebAssign
and Science)
Reflecting Cengage Learning’s commitment to
offering flexible teaching solutions and value for
students and instructors, this new hybrid edition
features the instructional presentation found in the
printed text while delivering end-of-section exercises
online in Enhanced WebAssign. The result—a briefer
printed text that engages students online! Designed
specifically for business, economics, or life/social
sciences majors, BRIEF CALCULUS: AN APPLIED
APPROACH, Ninth Edition, motivates students while
fostering understanding and mastery. This brief book
emphasizes integrated and engaging applications that
show students the real-world relevance of topics and
concepts. Applied problems drawn from government
sources, industry, current events, and other disciplines
provide well-rounded examples and appeal to students’
diverse interests. The Ninth Edition builds upon its
applications emphasis through updated exercises and
relevant examples. Pedagogical features--from algebra
review to study tips--continue to provide extra guidance
and practice. In addition, the BRIEF CALCULUS program
offers a strong support package--including Enhanced
WebAssign® and the book’s website, CourseMate--that
allows students to review the material independently
and retain key concepts.
NEW TO THIS EDITION
section-level concept summaries-- helping them
of key concepts.
www.cengageasia.com
93
FEATURES
chapter.
challenging, real-world applications --all of which can
choice.
Integrals. Appendix A. Precalculus Review. The Real
Number Line and Order. Absolute Value and Distance on
the Real Number Line. Exponents and Radicals. Factoring
© 2013, 544pp, Paperback, 9781133365143
CONTENTS
CALCULUS, 9E
An Applied Approach, Hybrid (with Enhanced WebAssign
and Science)
and instructors, this new hybrid version features
the instructional presentation found in CALCULUS
AN APPLIED APPROACH, Ninth Edition while
delivering end-of-section exercises online in Enhanced
WebAssign®. The result—a briefer printed text that
engages students online! Designed specifically for
www.cengageasia.com
94
business, economics, or life/social sciences majors,
CALCULUS: AN APPLIED APPROACH, Ninth Edition,
motivates students while fostering understanding and
mastery. The book emphasizes integrated and engaging
applications that show students the real-world
relevance of topics and concepts. Applied problems
drawn from government sources, industry, current
events, and other disciplines provide well-rounded
examples and appeal to students’ diverse interests. The
Ninth Edition builds upon its applications emphasis
through updated exercises and relevant examples.
Pedagogical features—from algebra review to study
tips—continue to provide extra guidance and practice.
NEW TO THIS EDITION
• New! Chapter on Differential Equations, includes topics
on solutions of differential equations, separation of
variables, and first-order linear differential equations.
• New! Summarize guides students in creating sectionlevel concept summaries. Summarize is aimed at
helping students process and organize key concepts,
while providing a valuable study tool.
• New and Revised! Based on analyses of actual student
usage data, the Exercise Sets available in both EWA
and the eBook have been revised to improve student
comprehension. Exercises progress from skilldevelopment problems to more challenging, real-life
applications—all of which can be customized to the
difficulty level of the instructor’s choice.
FEATURES
highlight the learning outcomes of that section and
provide instructors a tool for lesson planning.
• A wide variety of relevant examples—each of which is
titled for easy reference—include solutions presented
graphically, analytically, and/or numerically to provide
further insight into mathematical concepts. Examples
that illustrate real-life situations are identified with
an icon.
• Tech Tutor boxes provide guidance on using
technology to ease lengthy calculations, present a
graphical solution, or discuss where using technology
can lead to misleading or wrong solutions. In addition,
exercises requiring technology are identified with a
graphing calculator icon.
CONTENTS
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95
Integrals. 8. TRIGONOMETRIC FUNCTIONS. Radian
Measure of Angles. The Trigonometric Functions. Graphs
of Trigonometric Functions. Derivatives of Trigonometric
Functions. Integrals of Trigonometric Functions. 9.
PROBABILITY AND CALCULUS. Discrete Probability.
Continuous Random Variables. Expected Value and
Variance. 10. SERIES AND TAYLOR POLYNOMIALS.
Sequences. Series and Convergence. p-Series and the
Ratio Test. Power Series and Taylor’s Theorem. Taylor
Polynomials. Newton’s Method. 11. DIFFERENTIAL
EQUATIONS. Solutions of Differential Equations.
Separation of Variables. First-Order Linear Differential
Equations. Applications of Differential Equations.
APPENDIX A: PRECALCULUS REVIEW. The Real
Number Line and Order. Absolute Value and Distance
on the Real Number Line. Exponents and Radicals.
Factoring Polynomials. Fractions and Rationalization.
APPENDIX B: ALTERNATIVE INTRODUCTION TO THE
FUNDAMENTAL THEOREM OF CALCULUS. APPENDIX
C: FORMULAS.
© 2013, 720pp, Paperback, 9781133115007
Coming Soon!
sources, industry, current events, and other disciplines
provide well-rounded examples and appeal to students’
diverse interests. The Ninth Edition builds upon its
applications emphasis through updated exercises and
relevant examples. Pedagogical features--from algebra
review to study tips--continue to provide extra guidance
and practice. In addition, the text offers a strong
support package--including Enhanced WebAssign® and
the book’s website, CourseMate--that allows students
to review the material independently and retain key
concepts.
NEW TO THIS EDITION
• New! A new closing chapter, “Differential Equations,”
includes topics on solutions of differential equations,
separation of variables, and first-order linear
differential equations.
of key concepts.
FEATURES
CALCULUS, 9E
An Applied Approach
Designed specifically for business, economics, or
life/social sciences majors, CALCULUS: AN APPLIED
APPROACH, Ninth Edition, motivates students while
fostering understanding and mastery. The book
emphasizes integrated and engaging applications that
show students the real-world relevance of topics and
concepts. Applied problems drawn from government
www.cengageasia.com
96
chapter.
• Updated! The Exercise Sets have been revised based
on actual student usage data to improve student
comprehension. Approximately 5,000 exercises
challenging, real-world applications--all of which can
choice.
CONTENTS
Integrals. 8. TRIGONOMETRIC FUNCTIONS. Radian
Measure of Angles. The Trigonometric Functions. Graphs
of Trigonometric Functions. Derivatives of Trigonometric
Functions. Integrals of Trigonometric Functions. 9.
PROBABILITY AND CALCULUS. Discrete Probability.
Continuous Random Variables. Expected Value and
Variance. 10. SERIES AND TAYLOR POLYNOMIALS.
Sequences. Series and Convergence. p-Series and the
Ratio Test. Power Series and Taylor’s Theorem. Taylor
Polynomials. Newton’s Method. 11. DIFFERENTIAL
EQUATIONS. Solutions of Differential Equations.
Separation of Variables. First-Order Linear Differential
Appendix A. Precalculus Review. The Real Number
Line and Order. Absolute Value and Distance on the
Real Number Line. Exponents and Radicals. Factoring
© 2013, 864pp, Hardback, 9781133109280
CALCULUS CONCEPTS, 5E
An Informal Approach to the Mathematics of Change,
International Edition
Donald R. LaTorre, Clemson University; John W. Kenelly, Clemson
University; Sherry Biggers, Clemson University; Laurel R. Carpenter,
Designed for a one or two-semester Applied Calculus
course,this innovative text features a graphing
calculator approach, incorporating real-life applications
and such technology as graphing utilities and Excel®
spreadsheets to help students learn mathematical skills
that they will use in their lives and careers. The texts
overall goal is to improve learning of basic calculus
concepts by involving students with new material in
a way that is different from traditional practice. The
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97
development of conceptual understanding coupled
with a commitment to make calculus meaningful to
the student are guiding forces. The material involves
many applications of real situations through its datadriven, technology-based modeling approach. The
ability to correctly interpret the mathematics of reallife situations is considered of equal importance to the
understanding of the concepts of calculus. CALCULUS
CONCEPTS, 5e, International Edition presents concepts
in a variety of forms, including algebraic, graphical,
numeric, and verbal. Targeted toward students majoring
in liberal arts, economics, business, management,
and the life and social sciences, the text’s focus on
technology along with its use of real data and situations
make it a sound choice to help students develop an
intuitive, practical understanding of concepts.
NEW TO THIS EDITION
• Many of the book’s examples and activities are new.
In addition, many data sets have been revised to
incorporate more recent data.
• The concept of limits is introduced early in Chapter
1 and used throughout the discussion of models in
the remainder of that chapter. The concept is also
used to help students understand differentiation and
integration.
• Formerly presented in a self-contained chapter,
coverage of sine models has been incorporated
throughout the text in optional sections and activities.
• Differential equations and slope fields are introduced
in a pair of optional sections located at the end of the
integration chapters.
• The text has been carefully rewritten so that narrative
sections are as clear and concise as possible.
• While a real-world context is still used as the platform
for most of the discussion, some of the less critical
details of these contextual descriptions are now
presented to the side of the primary narrative in
Notes, allowing students to focus on key ideas without
potentially getting distracted.
• Definitions and other important mathematical
elements are highlighted in boxes for easy reference,
and selected mathematical and interpretation skills
are illustrated in Quick Examples.
• Each section’s activity set has been reworked to
incorporate an orderly development of the skills and
concepts presented in that section.
• Many activities have been rewritten to be more
student-friendly, and others have been replaced with
up-to-date applications. Even-numbered activities
are similar to, but not necessarily identical to, oddnumbered activities.
• Many activities have been rewritten to be more
student-friendly, and others have been replaced with
up-to-date applications. Even-numbered activities
are similar to, but not necessarily identical to, oddnumbered activities.
CONTENTS
Table of Contents: Each chapter concludes with a
summary, a concept check, and review activities 1.
INGREDIENTS OF CHANGE: FUNCTIONS AND LIMITS.
Functions—Four Representations. Function Behavior
and End Behavior Limits. Limits and Continuity. Linear
Functions and Models. Exponential Functions and
Models. Models in Finance. Constructed Functions.
Logarithmic Functions and Models. Quadratic Functions
and Models. Logistic Functions and Models. Cubic
Functions and Models. Cyclic Functions and Models.
Representations of a Sine Function. Characteristics
of Sine Functions. 2. DESCRIBING CHANGE: RATES.
Measures of Change over an Interval. Measures of
Change at a Point. Rates of Change—Notation and
Interpretation. Rates of Change—Numerical Limits and
Non-existence. Rates of Change Defined over Intervals.
Sketching Rate-of-Change Graphs. 3. DETERMINING
CHANGE: DERIVATIVES. Simple Rate-of-Change
Formulas. Exponential, Logarithmic, and Cyclic Rateof-Change Formulas. Rates of Change for Functions
That Can Be Composed. Rates of Change of Composite
Functions. Rates of Change for Functions That Can Be
Multiplied. Rates of Change for Product Functions.
Limits of Quotients and L’Hôpital’s Rule. 4. ANALYZING
CHANGE: APPLICATIONS OF DERIVATIVE S.
Linearization. Relative Extreme Points. Relative Extreme
Points. Inflection Points and Second Derivatives.
Marginal Analysis. Optimization of Constructed
Functions. Related Rates. 5. ACCUMULATING CHANGE:
LIMITS OF SUMS AND THE DEFINITE INTEGRAL.
An Introduction to Results of Change. Limit of Sums
and the Definite Integral. Accumulation Functions.
The Fundamental Theorem. Antiderivative Formulas
for Exponential, Natural Log, and Sine Functions.
The Definite Integral—Algebraically. Differences of
Accumulated Change. Average Value and Average
Rate of Change. Integration of Product or Composite
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Functions. 6. ANALYZING ACCUMULATED CHANGE:
INTEGRALS AND ACTION. Perpetual Accumulation and
Improper Integrals. Streams in Business and Biology.
Calculus in Economics—Demand and Elasticity. Calculus
in Economics—Supply and Equilibrium. Calculus in
Probability—Part 1. Calculus in Probability—Part 2.
Differential Equations—Slope Fields and Solutions.
Differential Equations—Proportionality and Common
Forms. 7. INGREDIENTS OF MULTIVARIABLE CHANGE:
FUNCTIONS AND RATES. Multivariable Functions and
Contour Graphs. Cross-Sectional Models and Rates of
Change. Partial Rates of Change. Compensating for
Change. 8. ANALYZING MULTIVARIABLE CHANGE:
OPTIMIZATION. Extreme Points and Saddle Points.
Multivariable Optimization. Optimization Under
Constraints. Least-Squares Optimization. Answers to
Odd Activities. Index of Applications. Subject Index.
FEATURES
© 2012, 744pp, Paperback, 9780538735384
COLLEGE ALGEBRA AND CALCULUS, 2E
Anne V. Hodgkins, Phoenix College
COLLEGE ALGEBRA AND CALCULUS: AN APPLIED
APPROACH, 2E, International Edition provides your
students a comprehensive resource for their college
algebra and applied calculus courses. The mathematical
concepts and applications are consistently presented
in the same tone and pedagogy to promote confidence
and a smooth transition from one course to the next.
The consolidation of content for two courses in a single
text saves you time in your course—and saves your
students the cost of an extra textbook.
NEW TO THIS EDITION
of key concepts.
chapter.
challenging, real-world applications—all of which can
choice.
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CONTENTS
0. FUNDAMENTAL CONCEPTS OF ALGEBRA. Real
Numbers: Order and Absolute Value. The Basic
Rules of Algebra. Integer Exponents. Radicals and
Rational Exponents. Polynomials and Special Products.
Factoring. Fractional Expressions. 1. EQUATIONS
AND INEQUALITIES. Linear Equations. Mathematical
Modeling. Quadratic Equations. The Quadratic Formula.
Other Types of Equations. Linear Inequalities. Other
Types of Inequalities. 2. FUNCTIONS AND GRAPHS.
Graphs of Equations. Lines in the Plane. Linear Modeling
and Direct Variation. Functions. Graphs of Functions.
Transformations of Functions. The Algebra of Functions.
3. POLYNOMIAL AND RATIONAL FUNCTIONS.
Quadratic Functions and Models. Polynomial
Functions of Higher Degree. Polynomial Division. Real
Zeros of Polynomial Functions. Complex Numbers.
The Fundamental Theorem of Algebra. Rational
Functions. 4. EXPONENTIAL AND LOGARITHMIC
FUNCTIONS. Inverse Functions. Exponential Functions.
Logarithmic Functions. Properties of Logarithms.
Solving Exponential and Logarithmic Equations.
Exponential and Logarithmic Models. 5. SYSTEMS
OF EQUATIONS AND INEQUALITIES. Solving Linear
Systems Using Substitution. Solving Linear Systems
Using Elimination. Linear Systems in Three or More
Variables. Systems of Inequalities. Linear Programming.
6. MATRICES AND DETERMINANTS. Matrices and
Linear Systems. Operations with Matrices. The Inverse
of a Square Matrix. The Determinant of a Square Matrix.
Applications of Matrices and Determinants. 7. LIMITS
AND DERIVATIVES. Limits. Continuity. The Derivative
and the Slope of a Graph. Some Rules for Differentiation.
and Quotient Rules. The Chain Rule. 8. APPLICATIONS
OF THE DERIVATIVE. Higher-Order Derivatives.
Implicit Differentiation. Related Rates. Increasing
Test. 9. FURTHER APPLICATIONS OF THE DERIVATIVE.
Optimization Problems. Business and Economics
Applications. Asymptotes. Curve Sketching: A Summary.
Differentials and Marginal Analysis. 10. DERIVATIVES
OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Integrals. Integration by Substitution and The General
Power Rule. Exponential and Logarithmic Integrals.
Area and the Fundamental Theorem of Calculus. The
Area of a Region Bounded by Two Graphs. The Definite
Integral as the Limit of a Sum. 12. TECHNIQUES OF
INTEGRATION. Integration by Parts and Present Value.
Integration Tables. Numerical Integration. Improper
Integrals. 13. FUNCTIONS OF SEVERAL VARIABLES.
The Three-Dimensional Coordinate System. Surfaces
in Space. Functions of Several Variables. Partial
Derivatives. Extrema of Functions of Two Variables.
Lagrange Multipliers. Least Squares Regression Analysis.
Double Integrals and Area in the Plane. Applications of
Double Integrals. 14. TRIGONOMETRIC FUNCTIONS.
Radian Measure of Angles. The Trigonometric Functions.
Graphs of Trigonometric Functions. Derivatives of
Trigonometric Functions. Integrals of Trigonometric
Functions. ONLINE. 15. SERIES AND TAYLOR
POLYNOMIALS. Sequences and Summation Notation.
Arithmetic Sequences and Partial Sums. Geometric
Sequences and Series. Series and Convergence.
p-Series and the Ratio Test. Power Series and Taylor’s
Theorem. Taylor Polynomials. Newton’s Method. 16.
PROBABILITY. Counting Principles. Probability. Discrete
and Continuous Random Variables. Expected Value
and Variance. Mathematical Induction. The Binomial
Theorem. Appendix A: An Introduction to Graphing
Utilities. Appendix B: Conic Sections. Conic Sections.
Conic Sections and Translations. Appendix C: Further
Concepts in Statistics. Data and Linear Modeling.
Measures of Central Tendency and Dispersion.
Appendix D: Precalculus Review. The Real Number
Polynomials. Fractions and Rationalization. Appendix E:
Alternate Introduction to the Fundamental Theorem of
Calculus. Appendix F: Differential Equations. Solutions
of Differential Equations. Separation of Variables.
First-Order Linear Differential Equations. Applications
of Differential Equations. Appendix G: Formulas.
Differentiation and Integration Formulas. Formulas
from Business and Finance. Appendix H: Properties
and Measurement. Review of Algebra, Geometry, and
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100
Trigonometry. Units of Measurements. Appendix I:
Graphing Utility Programs. Appendix J: Mathematical
Induction. Supplements:
© 2013, 1136pp, Paperback, 9781133105183
FINITE (WITH MATHEMATICS
ACCESS CARD)
review process, FINITE is an engaging and accessible
solution to accommodate the diverse lifestyles of
today’s learners at a value-based price. FINITE uses
intriguing, real-world applications to capture the
interest of business, economics, life science, and social
science majors. This practical approach to mathematics,
along with the integration of graphing calculators and
Excel spreadsheet explorations, exposes students to the
tools they will encounter in future careers. An innovative
combination of content delivery both in print and online
provides a core text and a wealth of comprehensive
multimedia teaching and learning assets, including
end-of-chapter review cards, downloadable flashcards
and practice problems, online video tutorials, solutions
to exercises aimed at supplementing learning outside
of the classroom. Also available is Cengage Learning’s
FEATURES
to prepare for class and for tests, including section
summaries and review exercises.
Instructor Editions contain tips for using graphing
calculators and Excel.
make preparation simple by offering chapter
summaries, chapter outlines, and lists of applications.
the purchase of a new book. Interactive quizzes,
videos, extra examples and problems, flashcards,
answers and solutions, and more are only a click away.
Edition, an e-book, an online Instructor’s Manual, and
an online Student’s Solutions Manual.
assignments.
CONTENTS
1. FUNCTIONS. 1.1 Real Numbers, Inequalities, and
Lines. Real Numbers and Inequalities. Sets and Intervals.
The Cartesian Plane. Lines and Slopes. Equations of
Lines. General Linear Equation. 1.2 Exponents. Positive
Integer Exponents. Properties of Exponents. Zero and
Negative Exponents. Roots and Fractional Exponents.
Fractional Exponents. Avoiding Pitfalls in Simplifying.
Learning Curves in Airplane Production. 1.3 Functions.
Functions. Solving Quadratic Equations. Derivation
of the Vertex Formula. Derivation of the Quadratic
Formula. 1.4 More About Functions. Polynomial
Functions. Rational Functions. Piecewise Linear
Functions. Composite Functions. Shifts of Graphs.
1.5 Exponential Functions. Exponential Functions.
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101
Compound Interest. Depreciation by a Fixed Percentage.
The Number e. Continuous Compounding of Interest.
Intuitive Meaning of Continuous Compounding. The
Function y = ex. Exponential Growth. Justification of the
Formula for Continuous Compounding. 1.6 Logarithmic
Functions. Common Logarithms. Properties of Common
Logarithms. Graphs of Logarithmic and Exponential
Functions. Logarithms to Other Bases. Natural
Logarithms. Carbon-14 Dating. 2. MATHEMATICS OF
FINANCE. 2.1 Simple Interest. Simple Interest Formula.
Total Amount Due on a Loan. Discounted Loans and
Effective Interest Rates. 2.2 Compound Interest.
Compound Interest Formula. Growth Times. Rule of 72.
Effective Rates. Recap. 2.3 Annuities. A First Example.
Geometric Series. Accumulated Account Formula.
Sinking Funds. How Long Will It Take?. 2.4 Amortization.
Present Value of an Annuity. Amortization. Unpaid
Balance. Equity. 3. SYSTEMS OF EQUATIONS AND
MATRICES. 3.1 Systems of Two Linear Equations
in Two Variables. Systems of Equations. Graphical
Representations of Equations. Equivalent Systems
of Equations. Elimination Method. 3.2 Matrices and
Linear Equations in Two Variables. Matrices. Augmented
Matrices from Systems of Equations. Row Operations.
Solving Equations by Row Reduction. 3.3 Systems of
Linear Equations and the Gauss–Jordan Method. Names
for Many Variables. Row-Reduced Form. 3.4 Matrix
Arithmetic. Equality of Matrices. Transpose of a Matrix.
Identity Matrix. Scalar Multiplication. Matrix Addition
and Subtraction. Matrix Multiplication as Evaluation.
Identity Matrices. Matrix Multiplication with Systems of
Equations. Matrix Multiplication and Row Operations.
3.5 Inverse Matrices and Systems of Linear Equations.
Inverse Matrices. How to Find Inverse Matrices.
Solving AX = B Using A-1. 3.6 Introduction to Modeling:
Leontief Models. 4. LINEAR PROGRAMMING. 4.1 Linear
Inequalities. Inequalities in Two Variables. Vertices of
Feasible Regions. Bounded and Unbounded Regions.
Applications. 4.2 Two-Variable Linear Programming
Problems. Linear Programming Problems. Fundamental
Theorem of Linear Programming. Extensions to Larger
Problems. 4.3 The Simplex Method for Standard
Maximum Problems. Standard Maximum Problems.
Matrix Form of a Standard Maximum Problem. The
Initial Simplex Tableau. Basic and Nonbasic Variables.
The Pivot Element. The Pivot Operation. The Simplex
Method. 4.4 Standard Minimum Problems and Duality.
Standard Minimum Problems. The Dual of a Standard
Minimum Problem. Matrix Form. Mixed Constraints:
A Transportation Problem. 5. PROBABILITY. 5.1 Sets,
Counting, and Venn Diagrams. Sets and Set Operations.
Addition Principle for Counting. The Multiplication
Principle for Counting. The Number of Subsets of a
Set. 5.2 Permutations and Combinations. Factorials.
Permutations. Combinations. 5.3 Probability Spaces.
Random Experiments and Sample Spaces. Events.
Probabilities of Possible Outcomes. Probabilities of
Events. Probability That an Event Does Not Occur.
Probability Space. Addition Rule for Probability. 5.4
Conditional Probability and Independence. Conditional
Probability. The Product Rule for Probability. Independent
Events. 5.5 Bayes’ Formula. Bayes’ Formula. 5.6 Random
Variables and Distributions. Random Variables. Expected
Value. Binomial Distribution. 6. STATISTICS. 6.1 Random
Samples and Data Organization. Random Samples. Bar
Chart. Histogram. 6.2 Measures of Central Tendency.
Mode. Median. Mean. Mean, Median, and Mode. 6.3
Measures of Variation. Range. Box-and-Whisker Plot.
Interpreting Box-and-Whisker Plots. Sample Standard
Deviation. 6.4 Normal Distributions and Binomial
Approximation. Discrete and Continuous Random
Variables. Normal Distribution. z-Scores.The Normal
and Binomial Distributions. 7. MARKOV CHAINS. 7.1
States and Transitions. States and Transitions. Markov
Chains. Types of Transition Matrices. State Distribution
Vectors. The kth State Distribution Vector. Duration
in a Given State. 7.2 Regular Markov Chains. Regular
Markov Chains. The Fundamental Theorem of Regular
Markov Chains. How to Solve D • T = D. 7.3 Absorbing
Markov Chains. Absorbing Markov Chains. Standard
Form. Transition Times and Absorption Probabilities.
8. GAME THEORY. 8.1 Two-Person Games and Saddle
Points. Payoff Matrix. Optimal Strategy. Finding Saddle
Points. 8.2 Mixed Strategies. Mixed Strategies and
Expected Values. Optimal Mixed Strategies for Games.
Other Interpretations of Mixed Strategies. 8.3 Games
and Linear Programming. Games as Linear Programming
Problems. Every Game Has a Solution. Index.
© 2012, 320pp, Paperback, 9780840065551
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102
FINITE MATH AND APPLIED CALCULUS,
HYBRID, 6E
University
text that engages students online! Full of relevant,
diverse, and current real-world applications, Stefan
Waner and Steven Costenoble’s FINITE MATHEMATICS
AND APPLIED CALCULUS, Sixth Edition helps your
students relate to mathematics. A large number of the
applications are based on real, referenced data from
technology instruction in your courses. Acclaimed for
accuracy and readability, FINITE MATHEMATICS AND
APPLIED CALCULUS appeals to, and is appropriate for,
NEW TO THIS EDITION
• Updated Examples and Exercises: Many examples
and exercises based on dated information have been
replaced by more current versions; those based on
unique or historically interesting data have been
retained.
• Current Topics in Applications: New and updated
real data applications reflect topics that are of
intense current interest or of general interest to
contemporary students. These include Facebook,
the housing crisis, subprime mortgages, travel to
Cancun, the BP 2011 Gulf oil spill, and the U.S. stock
market “flash crash” of May 6, 2010. The inside back
cover lists corporations referenced in the applications.
Chapter 1 now discusses the common practice
of representing functions as equations and vice
versa. The authors encourage students to see this
than as an abstract concept.
• Early Treatment of the Mathematics of Finance:
Formerly Chapter 5, “The Mathematics of Finance” is
now Chapter 2 because many important finance topics
relate directly to the first discussions of compound
interest and other mathematical models in Chapter
1. The discussion of the mathematics of finance does
not require the use of logarithmic functions to solve
for exponents analytically, but instead focuses on
numerical solutions using the technologies discussed.
The use of logarithms is presented as an option for
students and instructors who prefer to use them.
• Chapter 10: The material on limits now discusses
extensively when, and why, substitution can be
used to obtain a limit. The text now also follows the
usual convention of allowing only one-sided limits at
endpoints of domains. This approach also applies to
derivatives, where the book now disallows derivatives
at endpoints of domains, as is the normal convention.
(in Chapter 13).
antiderivative of |x| and well as new exercises
• Chapter 15: The discussion of level curves in Section
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103
15.1 is now more extensive, and includes added
examples and exercises.
• Updated Case Studies: A number of the Case Studies at
the ends of the chapters have been extensively revised
with updated real data. These helpful applications
continue to reflect topics of current interest, such
as subprime mortgages, hybrid car production, the
diet problem (in linear programming), spending on
housing construction, modeling tax revenues, and
pollution control.
CONTENTS
0. PRECALCULUS REVIEW. Real Numbers. Exponents and
Radicals. Multiplying and Factoring Algebraic Equations.
Rational Expressions. Solving Polynomial Equations.
Solving Miscellaneous Equations. The Coordinate Plane.
1. FUNCTIONS AND APPLICATIONS. Functions from
the Numerical, Algebraic, and Graphical Viewpoints.
Functions and Models. Linear Functions and Models.
Linear Regression. 2. THE MATHEMATICS OF FINANCE.
Simple Interest. Compound Interest. Annuities, Loans,
and Bonds. 3. SYSTEMS OF LINEAR EQUATIONS AND
MATRICES. Systems of Two Equations in Two Unknowns.
Using Matrices to Solve Systems of Equations.
Applications of Systems of Linear Equations. 4. MATRIX
ALGEBRA AND APPLICATIONS. Matrix Addition and
Scalar Multiplication. Matrix Multiplication. Matrix
Inversion. Game Theory. Input-Output Models. 5.
LINEAR PROGRAMMING. Graphing Linear Inequalities.
Solving Linear Programming Problems Graphically.
The Simplex Method: Solving Standard Maximization
Problems. The Simplex Method: Solving General
Linear Programming Problems. The Simplex Method
and Duality. 6. SETS AND COUNTING. Sets and Set
Operations. Cardinality. The Addition and Multiplication
Principles. Permutations and Combinations. 7.
PROBABILITY. Sample Spaces and Events. Relative
Frequency. Probability and Probability Models.
Probability and Counting Techniques. Conditional
Probability and Independence. Bayes’ Theorem
and Applications. Markov Systems. 8. RANDOM
VARIABLES AND STATISTICS. Random Variables and
Distributions. Bernoulli Trials and Binomial Random
Variables. Measures of Central Tendency. Measures
of Dispersion. Normal Distributions. 9. NONLINEAR
Algebraic Approach and the Fundamental Theorem
of. 14. FURTHER INTEGRATION TECHNIQUES AND
APPLICATIONS OF THE INTEGRAL. Integration by
Parts. Area Between Two Curves and Applications.
© 2014, 952pp, Paperback, 9781285056364
www.cengageasia.com
104
FINITE MATHEMATICS AND APPLIED
CALCULUS, INTERNATIONAL EDITION,
6E
University
FINITE MATHEMATICS AND APPLIED CALCULUS,
6E, International Edition helps your students relate
to mathematics. A large number of the applications
are based on real, referenced data from business,
economics, the life sciences, and the social sciences.
Thorough, clearly delineated spreadsheet and TI
Graphing Calculator instruction appears throughout
accuracy and readability, FINITE MATHEMATICS AND
APPLIED CALCULUS, 6E, International Edition appeals
to, and is appropriate for, all types of teaching and
learning styles. Resources, such as the accompanying
author website, allow the text to support a range of
course formats, from traditional lectures to strictly
online courses.
NEW TO THIS EDITION
• Updated Examples and Exercises: Many examples
and exercises based on dated information have been
replaced by more current versions; those based on
unique or historically interesting data have been
retained.
• Current Topics in Applications: New and updated
real data applications reflect topics that are of
intense current interest or of general interest to
contemporary students. These include Facebook,
the housing crisis, subprime mortgages, travel to
Cancun, the BP 2011 Gulf oil spill, and the U.S. stock
market “flash crash” of May 6, 2010. The inside back
cover lists corporations referenced in the applications.
Chapter 1 now discusses the common practice
of representing functions as equations and vice
versa. The authors encourage students to see this
than as an abstract concept.
• Chapter 10: The material on limits now discusses
extensively when, and why, substitution can be
used to obtain a limit. The text now also follows the
usual convention of allowing only one-sided limits at
endpoints of domains. This approach also applies to
derivatives, where the book now disallows derivatives
at endpoints of domains, as is the normal convention.
(in Chapter 13).
antiderivative of |x| and well as new exercises
• Chapter 15: The discussion of level curves in Section
15.1 is now more extensive, and includes added
examples and exercises.
www.cengageasia.com
105
continue to reflect topics of current interest, such
as subprime mortgages, hybrid car production, the
diet problem (in linear programming), spending on
housing construction, modeling tax revenues, and
pollution control.
CONTENTS
0. PRECALCULUS REVIEW. Real Numbers. Exponents and
Radicals. Multiplying and Factoring Algebraic Equations.
Rational Expressions. Solving Polynomial Equations.
Solving Miscellaneous Equations. The Coordinate Plane.
1. FUNCTIONS AND APPLICATIONS. Functions from
the Numerical, Algebraic, and Graphical Viewpoints.
Functions and Models. Linear Functions and Models.
Linear Regression. 2. THE MATHEMATICS OF FINANCE.
Simple Interest. Compound Interest. Annuities, Loans,
and Bonds. 3. SYSTEMS OF LINEAR EQUATIONS AND
MATRICES. Systems of Two Equations in Two Unknowns.
Using Matrices to Solve Systems of Equations.
Applications of Systems of Linear Equations. 4. MATRIX
ALGEBRA AND APPLICATIONS. Matrix Addition and
Scalar Multiplication. Matrix Multiplication. Matrix
Inversion. Game Theory. Input-Output Models. 5.
Probability and Independence. Bayes’ Theorem
and Applications. Markov Systems. 8. RANDOM
VARIABLES AND STATISTICS. Random Variables and
Distributions. Bernoulli Trials and Binomial Random
Variables. Measures of Central Tendency. Measures
of Dispersion. Normal Distributions. 9. NONLINEAR
Algebraic Approach and the Fundamental Theorem
of. 14. FURTHER INTEGRATION TECHNIQUES AND
APPLICATIONS OF THE INTEGRAL. Integration by
Parts. Area Between Two Curves and Applications.
© 2014, 1320pp, Paperback, 9781285056357
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106
FINITE MATHEMATICS FOR THE
SCIENCES, 11E
Market-leading FINITE MATHEMATICS FOR THE
MANAGERIAL, LIFE, AND SOCIAL SCIENCES, Eleventh
Edition balances modern applications, solid pedagogy,
and the latest technology to provide students the
context they need to stay motivated in the course
and interested in the material. Suitable for majors and
non-majors alike, the text uses an intuitive approach
that teaches concepts through examples drawn from
real-life—particularly from students’ fields of interest.
In addition, insightful Portfolios highlight the careers of
real people and discuss how they incorporate math into
their daily professional activities. Numerous exercises
ensure that students have a concrete understanding of
concepts before advancing to the next topic. The text’s
pedagogical features coupled with an exciting array of
supplements equip students with the tools they need
to make the most of their study time and to succeed
in the course.
NEW TO THIS EDITION
• New and updated applications.
• New and updated examples.
• New and updated exercises.
• Increased emphasis on prerequisite skills in the
accompanying EnhancedWebAssign course with the
addition of Just-in-Time and Quick Prep Exercises.
FEATURES
• Motivating real-world applications: Included in the
11th edition are more than 150 new and updated
modern applications to motivate students and
to illustrate the relevance of mathematics in
everyday life. Topics include: social media accounts,
corporate fraud, criminal justice, cyber privacy,
brand switching among college students, use of
landlines vs. cellphones, impact of gas prices, credit
card ownership, smartphone ownership, mobile ad
revenues, existing home sales, and hybrid vehicle
mileage.
• Portfolio features illustrate mathematics in the
workplace. Among those interviewed are the City
Manager of Fanfoto and the Technical Director,
Europe, of SpiderCloud Wireless.
exercises.
CONTENTS
PREFACE. 1. STRAIGHT LINES AND LINEAR FUNCTIONS.
The Cartesian Coordinate System. Straight Lines. Using
Technology: Graphing a Straight Line. Linear Functions
and Mathematical Models. Using Technology: Evaluating
a Function. Intersection of Straight Lines. Using
Technology: Finding the Point(s) of Intersection of Two
Graphs. The Method of Least Squares. Portfolio. Using
Technology: Finding an Equation of a Least-Squares Line.
OF LINEAR EQUATIONS AND MATRICES. Systems of
Linear Equations: An Introduction. Systems of Linear
Equations: Unique Solutions. Using Technology: Systems
of Linear Equations: Unique Solutions. Systems of Linear
Equations: Underdetermined and Over-determined
Systems. Using Technology: Systems of Linear Equations:
Underdetermined and Over-determined Systems.
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107
Matrices. Using Technology: Matrix Operations.
Multiplication of Matrices. Using Technology: Matrix
Multiplication. The Inverse of a Square Matrix. Using
Technology: Finding the Inverse of a Square Matrix.
Leontief Input—Output Model. Using Technology: The
Leontief Input—Output Model. Chapter 2 Summary of
Moving On. 3. LINEAR PROGRAMMING: A GEOMETRIC
APPROACH. Graphing Systems of Linear Inequalities in
Two Variables. Linear Programming Problems. Graphical
Solutions of Linear Programming Problems. Sensitivity
Analysis. Chapter 3 Summary of Principal Formulas and
Terms. Chapter 3 Concept Review Questions. Chapter
3 Review Exercises. Chapter 3 Before Moving On. 4.
LINEAR PROGRAMMING: AN ALGEBRAIC APPROACH.
The Simplex Method: Standard Maximization Problems.
Portfolio. Using Technology: The Simplex Method:
Solving Maximization Problems. The Simplex Method:
Standard Minimization Problems. Using Technology:
The Simplex Method: Solving Minimization Problems.
The Simplex Method: Nonstandard Problems. Chapter
4 Summary of Principal Formulas and Terms. Chapter 4
Concept Review Questions. Chapter 4 Review Exercises.
Chapter 4 Before Moving On. 5. MATHEMATICS OF
FINANCE. Compound Interest. Using Technology:
the Effective Rate of Interest, and the Present Value of
an Investment. Annuities. Using Technology: Finding
the Amount of an Annuity. Amortization and Sinking
Funds. Using Technology: Amortizing a Loan. Arithmetic
and Geometric Progressions. Chapter 5 Summary
5 Before Moving On. 5. SETS AND COUNTING. Sets
and Set Operations. The Number of Elements in a
Finite Set. The Multiplication Principle. Permutations
and Combinations. Portfolio. Using Technology:
Evaluating n!, P (n,r) and C (n,r). Chapter 6 Summary
6 Before Moving On. 7. PROBABILITY. Experiments,
Sample Spaces, and Events. Definition of Probability.
Rules of Probability. Use of Counting Techniques in
Probability. Conditional Probability and Independent
Events. Bayes’ Theorem. Chapter 7 Summary of Principal
Questions. Chapter 7 Review Exercises. Chapter 7
Before Moving On. 8. PROBABILITY DISTRIBUTIONS
AND STATISTICS. Distributions of Random Variables.
Using Technology: Graphing a Histogram. Expected
Value. Portfolio. Variance and Standard Deviation.
Using Technology: Finding the Mean and Standard
Deviation. The Binomial Distribution. The Normal
Distribution. Applications of the Normal Distribution.
Exercises. Chapter 8 Before Moving On. 9. MARKOV
CHAINS AND THE THEORY OF GAMES. Markov
Chains. Using Technology: Finding Distribution Vectors.
Regular Markov Chains. Using Technology: Finding
the Long-term Distribution Vector. Absorbing Markov
Chains. Game Theory and Strictly Determined Games.
Portfolio. Games with Mixed Strategies. Chapter 9
Exercises. Chapter 9 Before Moving On. Appendix A:
Introduction to Logic. Propositions and Connectives.
Truth Tables. The Conditional and the Biconditional
Connectives. Laws of Logic. Arguments. Applications of
Logic to Switching Networks. Appendix B: The System
of Real Numbers. Appendix C: A Review of Logarithms.
Appendix D: Tables. Table 1: Binomial Probabilities. Table
2: The Standard Normal Distribution. Answers to OddNumbered Exercises. Index.
© 2015, 704pp, Hardback, 9781285464657
FINITE MATHEMATICS FOR THE
SCIENCES, INTERNATIONAL EDITION,
10E
Market-leading FINITE MATHEMATICS FOR THE
MANAGERIAL, LIFE, AND SOCIAL SCIENCES, 10e,
International Edition educates by application and
real-world examples. A traditional book with a modern
feel, the text pairs pioneering technology with rocksolid theory, offers a vigorous supplement package,
and delivers matchless flexibility to both traditional
www.cengageasia.com
108
and modern practitioners. The Tenth Edition breaks
new ground by dovetailing real-life case studies
into textbook material, creating a volume that is
approachable for both majors and non-majors. This
is achieved through the use of Portfolio features,
which spotlight actual professionals and the usage
of math in their day-to-day business. Furthermore,
the text abounds with helpful exercises, including
Diagnostic Tests, which assure students of a firm grasp
on textbook information before they move on to the
following section. And, by offering a powerful array of
supplements such as Enhanced WebAssign®, the new
Tenth Edition enables students to maximize their study
time and succeed in class.
NEW TO THIS EDITION
• More than 90 new and updated student-friendly
applications. Topics include: health care spending,
global defense spending, box office receipts,
retirement planning, home affordability, tire safety,
alternative fuel vehicles, cost of taking time off, New
York courts total caseload, lightning injuries, and
government debt.
• Five new Portfolio features illustrate mathematics
City Manager of Fanfoto and the Technical Director,
Europe, of SpiderCloud Wireless.
• Updated Excel content enlarges the student
experience.
FEATURES
exercises.
well.
CONTENTS
1. Straight Lines and Linear Functions. The Cartesian
Coordinate System. Straight Lines. Using Technology:
Graphing a Straight Line. Linear Functions and
Mathematical Models. Using Technology: Evaluating
a Function. Intersection of Straight Lines. Using
Technology: Finding the Point(s) of Intersection of Two
Graphs. The Method of Least Squares. Portfolio. Using
Technology: Finding an Equation of a Least-Squares Line.
OF LINEAR EQUATIONS AND MATRICES. Systems of
Linear Equations: An Introduction. Systems of Linear
Equations: Unique Solutions. Using Technology: Systems
of Linear Equations: Unique Solutions. Systems of Linear
Equations: Underdetermined and Overdetermined
Systems. Using Technology: Systems of Linear Equations:
Underdetermined and Overdetermined Systems.
Matrices. Using Technology: Matrix Operations.
Multiplication of Matrices. Using Technology: Matrix
Multiplication. The Inverse of a Square Matrix. Using
Technology: Finding the Inverse of a Square Matrix.
Leontief Input—Output Model. Using Technology: The
Leontief Input—Output Model. Chapter 2 Summary of
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109
Moving On. 3. LINEAR PROGRAMMING: A GEOMETRIC
APPROACH. Graphing Systems of Linear Inequalities in
Two Variables. Linear Programming Problems. Graphical
Solutions of Linear Programming Problems. Sensitivity
Analysis. Chapter 3 Summary of Principal Formulas and
Terms. Chapter 3 Concept Review Questions. Chapter
3 Review Exercises. Chapter 3 Before Moving On. 4.
LINEAR PROGRAMMING: AN ALGEBRAIC APPROACH.
The Simplex Method: Standard Maximization Problems.
Portfolio. Using Technology: The Simplex Method:
Solving Maximization Problems. The Simplex Method:
Standard Minimization Problems. Using Technology:
The Simplex Method: Solving Minimization Problems.
The Simplex Method: Nonstandard Problems. Chapter
4 Summary of Principal Formulas and Terms. Chapter 4
Concept Review Questions. Chapter 4 Review Exercises.
Chapter 4 Before Moving On. 5. MATHEMATICS OF
FINANCE. Compound Interest. Using Technology:
the Effective Rate of Interest, and the Present Value of
an Investment. Annuities. Using Technology: Finding
the Amount of an Annuity. Amortization and Sinking
Funds. Using Technology: Amortizing a Loan. Arithmetic
and Geometric Progressions. Chapter 5 Summary
5 Before Moving On. 5. SETS AND COUNTING. Sets
and Set Operations. The Number of Elements in a
Finite Set. The Multiplication Principle. Permutations
and Combinations. Portfolio. Using Technology:
Evaluating n!, P (n,r) and C (n,r). Chapter 6 Summary
6 Before Moving On. 7. PROBABILITY. Experiments,
Sample Spaces, and Events. Definition of Probability.
Rules of Probability. Use of Counting Techniques in
Probability. Conditional Probability and Independent
Events. Bayes’ Theorem. Chapter 7 Summary of Principal
Questions. Chapter 7 Review Exercises. Chapter 7
Before Moving On. 8. PROBABILITY DISTRIBUTIONS
AND STATISTICS. Distributions of Random Variables.
Using Technology: Graphing a Histogram. Expected
Value. Portfolio. Variance and Standard Deviation.
Using Technology: Finding the Mean and Standard
Deviation. The Binomial Distribution. The Normal
Distribution. Applications of the Normal Distribution.
Exercises. Chapter 8 Before Moving On. 9. MARKOV
CHAINS AND THE THEORY OF GAMES. Markov
Chains. Using Technology: Finding Distribution Vectors.
Regular Markov Chains. Using Technology: Finding
the Long-term Distribution Vector. Absorbing Markov
Chains. Game Theory and Strictly Determined Games.
Portfolio. Games with Mixed Strategies. Chapter 9
Exercises. Chapter 9 Before Moving On. Appendix A:
Introduction to Logic. Propositions and Connectives.
Truth Tables. The Conditional and the Biconditional
Connectives. Laws of Logic. Arguments. Applications of
Logic to Switching Networks. Appendix B: The System
of Real Numbers. Appendix C: A Review of Logarithms.
Appendix D: Tables. Table 1: Binomial Probabilities. Table
2: The Standard Normal Distribution. Answers to OddNumbered Exercises. Index.
© 2012, 656pp, Paperback, 9780840049070
FINITE MATHEMATICS, ENHANCED
EDITION (WITH ENHANCED WEBASSIGN
WITH EBOOK FOR ONE TERM MATH AND
SCIENCE PRINTED ACCESS CARD), 7E
Howard L. Rolf, Baylor University
Instructors are loyal to Howard Rolf’s text because
teaching from it is easy. Why? Exercises at a variety
of levels, flexible technology integration, and many
interesting business applications make concepts
relevant, clear, and easier to understand for students.
The new edition of FINITE MATHEMATICS continues to
rely on a rich array of examples and a student-friendly
www.cengageasia.com
110
approach to illustrate the utility of mathematical
concepts in analyzing and solving problems. Optional
graphing calculator problems and Microsoft® Excel®
applications are available for instructors who wish to
bring technology into the course. This Enhanced Edition
includes instant access to Enhanced WebAssign®,
the most widely-used and reliable homework system.
Enhanced WebAssign® presents over a thousand
problems, links to relevant textbook sections, video
examples, problem-specific tutorials, and more, that
help students grasp the concepts needed to succeed in
this course. As an added bonus, the Start Smart Guide
has been bound into this text. This guide contains
instructions to help students learn the basics of
WebAssign quickly.
NEW TO THIS EDITION
• Enhanced WebAssign®, the most widely-used and
reliable homework system, presents over a thousand
problems, links to relevant textbook sections, video
examples, problem-specific tutorials, and more, that
help students grasp the concepts needed to succeed
in this course. As an added bonus, the Start Smart
Guide has been bound into this text. This guide
contains instructions to help students learn the basics
of WebAssign quickly.
• This edition includes many new exercises that use
real data with modern business applications, further
reinforcing the relevance of this material to applied
math students.
• CengageNOW saves you time and provides students
with an efficient way to study. Based on answers to
chapter pre-tests, Personalized Study plans direct
students to interactive tutorials and videos that they
need to review. Results flow directly to the instructor
gradebook. CengageNOW is also ideal for self-study,
with no setup required by you.
• Videos of the author working through text examples,
previously located on a CD, are now available on the
book companion website.
• Many new exercises use real data with modern
business applications, further reinforcing the
relevance of the material to applied math students.
• Expanded Microsoft Excel guidance includes more
real-life material and larger scale projects in the
accompanying technology exercises.
• Videos of the author working through text examples,
previously located on a CD, are now available on the
book companion website.
CONTENTS
1. FUNCTIONS AND LINES. Functions. Graphs and
Lines. Mathematical Models and Applications of
Linear Functions. 2. LINEAR SYSTEMS. Systems of
Two Equations. Systems with Three Variables: An
Introduction to a Matrix Representation of a Linear
System of Equations. Gauss-Jordan Method for
General Systems of Equations. Matrix Operations.
Multiplication of Matrices. The Inverse of a Matrix.
Leontief Input-Output Model in Economics. Linear
Regression. 3. LINEAR PROGRAMMING. Linear
Inequalities in Two Variables. Solutions of Systems of
Inequalities: A Geometric Picture. Linear Programming:
A Geometric Approach. Applications. 4. LINEAR
PROGRAMMING: THE SIMPLEX METHOD. Setting
Up the Simplex Methods. The Simplex Method. The
Standard Minimum Problem: Duality. Mixed Constraints.
Multiple Solutions, Unbounded Solutions, and No
Solutions. What’’s Happening in the Simplex Method?
(Optional). 5. MATHEMATICS OF FINANCE. Simple
Interest. Compound Interest. Annuities and Sinking
Funds. Present Value of an Annuity and Amortization.
6. SETS AND COUNTING. Sets. Counting Elements
in a Subset Using a Venn Diagram. Basic Counting
Principles. Permutations. Combinations. A Mixture
of Counting Problems. Partitions (Optional). 7.
PROBABILITY. Introduction to Probability. Equally
Likely Events. Compound Events: Union, Intersection,
and Complement. Conditional Probability. Independent
Events. Bayes’’ Rule. Markov Chains. 8. STATISTICS.
Frequency Distributions. Measures of Central Tendency.
Measures of Dispersion: Range, Variance, and
Standard Deviation. Random Variables and Probability
Distributions of Discrete Random Variables. Expected
Value of a Random Variable. Binomial Experiments and
Binomial Distribution. Normal Distribution. Estimating
Bounds on a Proportion. 9. GAME THEORY. Two-Person
Games. Mixed Strategy Games. 10. LOGIC. Statements.
Conditional Statements. Equivalent Statements. Valid
Arguments. APPENDIX A: REVIEW TOPICS. Properties
of Real Numbers. Solving Linear Equations. Coordinate
Systems. Linear Inequalities and Interval Notation.
APPENDIX B: USING A TI-83 GRAPHING CALCULATOR.
Notation. Arithmetic Operations. Graphing. Evaluating
A Function. Finding the Intersection of Two Graphs.
Constructing a Table. Matrices. Statistics. APPENDIX
C: USING EXCEL.
© 2011, 920pp, Hardback, 9780538497329
www.cengageasia.com
111
offering more options to meet the expectations and
needs of today’s instructors and students. Enhanced
WebAssign®, available with the text, includes an
increased number of problems and supporting
assets. In addition, the Rolf package now includes
YouBook (an interactive eBook version of the text
that instructors can customize), CourseMate, and a
hybrid version of the text.
• Discussions and keystroke instructions in Using Excel
have been updated to Excel 2007 and Excel 2010.
FINITE MATHEMATICS, HYBRID (WITH
LOE PRINTED ACCESS CARD FOR ONETERM MATH AND SCIENCE), 8E
that engages students online! Instructors are loyal to
Howard Rolf’s text because teaching from it is easy.
Why? Exercises at a variety of levels, flexible technology
integration, and many interesting business applications
make concepts relevant, clear, and easier to understand
for students. The new edition of FINITE MATHEMATICS
continues to rely on a rich array of examples and
exercises and a student-friendly approach to illustrate
the applications of mathematical concepts in analyzing
and solving problems. Optional graphing calculator
problems and Microsoft® Excel® applications are
available for instructors who wish to bring technology
into the course.
NEW TO THIS EDITION
• The end-of-chapter review has been expanded
to include Important Concepts. This new feature
summarizes the key theorems, formulas, and
equations from the chapter. Important Concepts
together with Important Terms provides students with
a comprehensive and useful tool for study and review.
• Updated problem sets include many new exercises
that use real data with modern business applications,
further reinforcing the relevance of this material to
applied math students.
• The book’s technology program has been expanded,
FEATURES
• Detailed computations enable students to easily
follow successive steps in the problem-solving
process.
• More than 3,200 exercises and 500 examples offer
instructors and students with an abundance of
homework and practice problems. Examples and
exercises are cross-referenced, identifying for
students a corresponding exercise to check their
understanding after they read through an example
and solution.
• Exercises are graded by level of difficulty: level 1
for routine problems, level 2 for elementary word
problems, and level 3 for more thought-provoking
problems.
• Discussion questions provide the option of using the
graphing calculator or spreadsheet technology to
solve the problem. “Explorations” encourage students
to think more deeply about mathematical concepts,
often providing an opportunity to use the graphing
calculator. Many of these exercises may be used for
group projects or writing assignments.
• References to technology keep the text current with
new applications. “Using Your TI Graphing Calculator”
and “Using Excel” boxes walk students through the
steps necessary to apply the technology to selected
exercises. Additional guidance on how to use the
graphing calculator is found in an appendix.
CONTENTS
www.cengageasia.com
112
Solutions. What’s Happening in the Simplex Method?
Events. Bayes’ Rule. Markov Chains. 8. STATISTICS.
Bounds on a Proportion. 9. GAME THEORY. TwoPerson Games. Mixed Strategy Games. 10. LOGIC.
Statements. Conditional Statements. Equivalent
Statements. Valid Arguments. APPENDIX A: REVIEW
TOPICS. Properties of Real Numbers. Solving Linear
Equations. Coordinate Systems. Linear Inequalities
and Interval Notation. APPENDIX B: USING A TI-83/84
GRAPHING CALCULATOR. Notation. Arithmetic
Operations. Graphing. Evaluating A Function. Finding
the Intersection of Two Graphs. Constructing a Table.
Matrices. Statistics. APPENDIX C: USING EXCEL.
© 2014, 640pp, Paperback, 9781285084640
FINITE MATHEMATICS, HYBRID (WITH
University
that engages students online! Full of relevant, diverse,
and current real-world applications, Stefan Waner and
Steven Costenoble’s FINITE MATHEMATICS, Sixth
Edition helps your students relate to mathematics.
A large number of the applications are based on
real, referenced data from business, economics,
the life sciences, and the social sciences. Thorough,
clearly delineated spreadsheet and TI Graphing
Calculator instruction appears throughout the text. The
Technology Notes and Technology Guides are optional,
allowing you to include any amount of technology
instruction in your courses. Acclaimed for accuracy and
readability, FINITE MATHEMATICS appeals to, and is
appropriate for, all types of teaching and learning styles.
Resources, such as the accompanying author website,
allow the text to support a range of course formats,
from traditional lectures to strictly online courses.
NEW TO THIS EDITION
based on dated information have been replaced by
more current versions; those based on unique or
historically interesting data have been retained. New
and updated real data applications reflect topics that
are of intense current interest or of general interest
www.cengageasia.com
113
to contemporary students. These include Facebook,
XBoxes, iPhones, iPads, foreclosure rates, the housing
crisis, subprime mortgages, stock market gyrations,
shorting the stock market, and travel to Cancun. The
inside back cover lists corporations referenced in the
applications.
continue to reflect topics of current interest, such as
subprime mortgages, hybrid car production, and the
diet problem (in linear programming).
exclusively on Microsoft® Excel®. This enables
readers to use any of the several alternatives now
available, such as Google’s online Google Sheets®,
Open Office®, and Apple’s Numbers®.
FEATURES
• Case Studies: Each chapter ends with a Case Study,
an extended application that uses and illustrates
the central ideas of the chapter, focusing on the
development of mathematical models appropriate
to the topics. Ideal for assignment as projects, these
applications conclude with groups of exercises.
• Before We Go On: Most examples are followed by
supplementary discussions, which may include a
check on the answer, a discussion of the feasibility
and significance of a solution, or an in-depth look at
what the solution means.
• Quick Examples: Most definition boxes include quick,
straightforward examples that students can use to
solidify their understanding of each new concept.
CONTENTS
and Models. Linear Regression. 2. THE MATHEMATICS
OF FINANCE. Simple Interest. Compound Interest.
Annuities, Loans, and Bonds. 3. SYSTEMS OF LINEAR
EQUATIONS AND MATRICES. Systems of Two Equations
in Two Unknowns. Using Matrices to Solve Systems of
Equations. Applications of Systems of Linear Equations.
4. MATRIX ALGEBRA AND APPLICATIONS. Matrix
Addition and Scalar Multiplication. Matrix Multiplication.
Matrix Inversion. Game Theory. Input-Output Models. 5.
www.cengageasia.com
114
Probability and Independence. Bayes’ Theorem and
Applications. Markov Systems. 8. RANDOM VARIABLES
AND STATISTICS. Random Variables and Distributions.
Bernoulli Trials and Binomial Random Variables.
Measures of Central Tendency. Measures of Dispersion.
Normal Distributions.
© 2014, 520pp, Bundled Package, 9781285056319
FINITE MATHEMATICS, INTERNATIONAL
EDITION, 6E
University
FINITE MATHEMATICS, 6E, International Edition helps
your students relate to mathematics. A large number of
the applications are based on real, referenced data from
accuracy and readability, FINITE MATHEMATICS, 6E,
International Edition appeals to, and is appropriate for,
NEW TO THIS EDITION
based on dated information have been replaced by
more current versions; those based on unique or
historically interesting data have been retained. New
and updated real data applications reflect topics that
are of intense current interest or of general interest
to contemporary students. These include Facebook,
XBoxes, iPhones, iPads, foreclosure rates, the housing
crisis, subprime mortgages, stock market gyrations,
shorting the stock market, and travel to Cancun. The
inside back cover lists corporations referenced in the
applications.
continue to reflect topics of current interest, such as
subprime mortgages, hybrid car production, and the
diet problem (in linear programming).
www.cengageasia.com
115
exclusively on Microsoft® Excel®. This enables
readers to use any of the several alternatives now
available, such as Google’s online Google Sheets®,
Open Office®, and Apple’s Numbers®.
FEATURES
• Case Studies: Each chapter ends with a Case Study,
an extended application that uses and illustrates
the central ideas of the chapter, focusing on the
development of mathematical models appropriate
to the topics. Ideal for assignment as projects, these
applications conclude with groups of exercises.
• Before We Go On: Most examples are followed by
supplementary discussions, which may include a
check on the answer, a discussion of the feasibility
and significance of a solution, or an in-depth look at
what the solution means.
• Quick Examples: Most definition boxes include quick,
straightforward examples that students can use to
solidify their understanding of each new concept.
CONTENTS
and Models. Linear Regression. 2. THE MATHEMATICS
OF FINANCE. Simple Interest. Compound Interest.
Annuities, Loans, and Bonds. 3. SYSTEMS OF LINEAR
EQUATIONS AND MATRICES. Systems of Two Equations
in Two Unknowns. Using Matrices to Solve Systems of
Equations. Applications of Systems of Linear Equations.
4. MATRIX ALGEBRA AND APPLICATIONS. Matrix
Addition and Scalar Multiplication. Matrix Multiplication.
Matrix Inversion. Game Theory. Input-Output Models. 5.
Probability and Independence. Bayes’ Theorem and
Applications. Markov Systems. 8. RANDOM VARIABLES
AND STATISTICS. Random Variables and Distributions.
Bernoulli Trials and Binomial Random Variables.
Measures of Central Tendency. Measures of Dispersion.
Normal Distributions.
© 2014, 696pp, Paperback, 9781285056272
FINITE MATHEMATICS, INTERNATIONAL
EDITION, 8E
Instructors are loyal to Howard Rolf’s text because
teaching from it is easy. Why? Exercises at a variety
of levels, flexible technology integration, and many
interesting business applications make concepts
relevant, clear, and easier to understand for students.
FINITE MATHEMATICS, 8E, International Edition
continues to rely on a rich array of examples and
exercises and a student-friendly approach to illustrate
the applications of mathematical concepts in analyzing
and solving problems. Optional graphing calculator
www.cengageasia.com
116
problems and Microsoft® Excel® applications are
available for instructors who wish to bring technology
into the course.
NEW TO THIS EDITION
• The end-of-chapter review has been expanded
to include “Important Concepts”—a new feature
that summarizes the key theorems, formulas, and
equations from the chapter. “Important Concepts”
together with “Important Terms” provides students
with a comprehensive and useful tool for study and
review.
• Updated problem sets include many new exercises
that use real data with modern business applications,
further reinforcing the relevance of this material to
applied math students.
• The book’s technology program has been expanded,
offering more options to meet the expectations and
needs of today’s instructors and students. Enhanced
WebAssign®, available with the text, includes an
increased number of problems and supporting
assets. In addition, the Rolf package now includes
YouBook (an interactive eBook version of the text
that instructors can customize), CourseMate, and a
hybrid version of the text.
• Discussions and keystroke instructions in “Using
Excel” boxes have been updated to Excel 2007 and
Excel 2010.
FEATURES
• Detailed computations enable students to easily
follow successive steps in the problem-solving
process.
• More than 3,200 exercises and 500 examples offer
instructors and students with an abundance of
homework and practice problems. Examples and
exercises are cross-referenced, identifying for
students a corresponding exercise to check their
understanding after they read through an example
and solution.
• Exercises are graded by level of difficulty: level 1
for routine problems, level 2 for elementary word
problems, and level 3 for more thought-provoking
problems.
• Discussion questions provide the option of using the
graphing calculator or spreadsheet technology to
solve the problem. “Explorations” encourage students
to think more deeply about mathematical concepts,
often providing an opportunity to use the graphing
calculator. Many of these exercises may be used for
group projects or writing assignments.
• References to technology keep the text current with
new applications. “Using Your TI Graphing Calculator”
and “Using Excel” boxes walk students through the
steps necessary to apply the technology to selected
exercises. Additional guidance on how to use the
graphing calculator is found in an appendix.
CONTENTS
Solutions. What’s Happening in the Simplex Method?
Events. Bayes’ Rule. Markov Chains. 8. STATISTICS.
Bounds on a Proportion. 9. GAME THEORY. TwoPerson Games. Mixed Strategy Games. 10. LOGIC.
www.cengageasia.com
117
Statements. Conditional Statements. Equivalent
Statements. Valid Arguments. APPENDIX A: REVIEW
TOPICS. Properties of Real Numbers. Solving Linear
Equations. Coordinate Systems. Linear Inequalities
and Interval Notation. APPENDIX B: USING A TI-83/84
GRAPHING CALCULATOR. Notation. Arithmetic
Operations. Graphing. Evaluating A Function. Finding
the Intersection of Two Graphs. Constructing a Table.
Matrices. Statistics. APPENDIX C: USING EXCEL.
© 2014, 912pp, Paperback, 9781285084688
MATH APPS (WITH MATH COURSEMATE
WITH EBOOK PRINTED ACCESS CARD)
Ronald J. Harshbarger, University of South Carolina
review process, MATH APPS is an engaging and
accessible solution to accommodate the diverse
lifestyles of today’s learners at a value-based price. The
book’s concept-based approach, multiple presentation
methods, and interesting and relevant applications
keep students who typically take the course—business,
economics, life sciences, and social sciences majors—
engaged in the material. An innovative combination
of content delivery both in print and online provides a
core text and a wealth of comprehensive multimedia
FEATURES
to prepare for class and for tests, including objectives,
keywords, formulas, and practice tests.
Instructor Editions contain tips for using graphing
calculators and Excel.
make preparation simple by offering a chapter
preview, chapter and section objectives, a section on
applications, and a section on problem classification.
different learning styles is available to students at
CourseMate for MATH APPS. Log in at cengagebrain.
com. Interactive Quizzes, videos, extra examples and
problems, flashcards, answers and solutions, and more
are only a click away.
Edition, an interactive e-Book, an online Instructor’s
Manual and Student’s Solutions Manual.
assignments.
CONTENTS
1. Linear Equations and Functions. 1.1. Solutions of
Linear Equations and Inequalities in One Variable.
Equations. Linear Inequalities. 1.2. Functions. Relations
and Functions. Graphs of Functions. Function Notation.
Domains and Ranges. Operations with Functions. 1.3.
Linear Functions. Intercepts. Rate of Change; Slope of a
Line. Writing Equations of Lines. 1.4. Solutions of Systems
of Linear Equations. Graphical Solution. Solution by
Substitution. Solution by Elimination. Three Equations
in Three Variables. 1.5. Applications of Functions in
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118
Business and Economics. Total Cost, Total Revenue, and
Profit. Break-Even Analysis. Supply, Demand, and Market
Equilibrium. Supply, Demand, and Taxation. Chapter
Exercises. 2. Quadratic and Other Special Functions.
2.1. Quadratic Equations. Factoring Methods. The
Quadratic Formula. 2.2 Q u a d r a t i c F u n c t i o n s :
Parabolas. Parabolas. 2.3. Business Applications of
Quadratic Functions. Supply, Demand, and Market
Equilibrium. Break-Even Points and Maximization. 2.4.
Special Functions and Their Graphs. Basic Functions.
Polynomial and Rational Functions. Piecewise Defined
Functions. 2.5. Modeling Data with Graphing Utilities
(optional). Chapter Exercises. Chapter 3
Matrices.
3.1. Operations with Matrices. Addition and Subtraction
of Matrices. Scalar Multiplication. 3.2. Multiplication of
Matrices. Product of Two Matrices. 3.3. Gauss-Jordan
Elimination: Solving Systems of Equations. Systems with
Unique Solutions. Systems with Nonunique Solutions.
Nonsquare Systems. 3.4. Inverse of a Square Matrix.
Matrix Equations. Determinants. Chapter Exercises.
4. Inequalities and Linear Programming. 4.1 Linear
Inequalities in Two Variables. One Linear Inequality in
Two Variables. Systems of Linear Inequalities. 4.2. Linear
Programming: Graphical Methods. Solving Graphically.
4.3. The Simplex Method: Maximization. The Simplex
Method. Tasks and Procedure. Nonunique Solutions:
Multiple Solutions and No Solution. 4.4. The Simplex
Method: Duality and Minimization. Dual Problems.
Duality and Solving. 4.5. The Simplex Method with Mixed
Constraints. Mixed Constraints and Maximization. Mixed
Constraints and Minimization. Chapter Exercises. 5.
Exponential and Logarithmic Functions. 5.1. Exponential
Functions. Modeling with Exponential Functions.
5.2. Logarithmic Functions and Their Properties.
Logarithmic Functions and Graphs. Modeling with
Change of Base. 5.3. Applications of Exponential and
Logarithmic Functions. Solving Exponential Equations
Using Logarithmic. Properties. Growth and Decay.
Economic and Management Applications. Chapter
Exercises. 6. Mathematics of Finance. 6.1. Simple Interest
and Arithmetic Sequences. Future Value. Arithmetic
Sequences. 6.2 Compound Interest and Geometric
Sequences. Compound Interest. Geometric Sequences.
6.3. Future Values of Annuities. Ordinary Annuities.
Annuities Due. 6.4. Present Values of Annuities.
Ordinary Annuities. Annuities Due. Deferred Annuities.
6.5. Loans and Amortization. Amortization. Unpaid
Balance of a Loan. Chapter Exercises. 7. Introduction to
Probability. 7.1. Probability and Odds. Sample Spaces and
Single Events. Empirical Probability. Odds. 7.2. Unions,
Intersections, and Complements of Events. Inclusion
Exclusion Principle. 7.3. Conditional Probability: The
Product Rule. 7.4. Probability Trees and Bayes’ Formula.
Probability Trees. Bayes’ Formula. 7.5. Counting:
Permutations and Combinations. Permutations.
Combinations. 7.6. Permutations, Combinations,
and Probability. Chapter Exercises. 8. Probability
and Data Description. 8.1. Binomial Probability
Experiments. 8.2. Describing Data. Statistical Graphs.
Types of Averages. Variance and Standard Deviation.
8.3. Discrete Probability Distributions. Discrete
Probability Distributions. Measures of Dispersion. The
Binomial Distribution. Binomial Formula. 8.4. Normal
Probability Distribution. z-Scores. Chapter Exercises. 9.
Derivatives. 9.1. Limits. Notion of a Limit. Properties of
Limits, Algebraic Evaluation. Limits of Piecewise Defined
Functions. 9.2. Continuous Functions; Limits at Infinity.
Continuous Functions. Limits at Infinity. 9.3. Average
and Instantaneous Rates of Change: The Derivative.
Instantaneous Rates of Change: Velocity. Tangent to a
Curve. Differentiability and Continuity. 9.4. Derivative
Formulas. Additional Formulas. Marginal Revenue.
9.5. The Product Rule and the Quotient Rule. Product
Rule. Quotient Rule. 9.6. The Chain Rule and the Power
Rule. Chain Rule. Power Rule. 9.7. Using Derivative
Formulas. 9.8. Higher-Order Derivatives. Second
Derivatives. Higher-Order Derivatives. 9.9. Derivatives
in Business and Economics. Marginal Revenue.
Marginal Cost. Marginal Profit. Chapter Exercises.
10. Applications of Derivatives. 10.1. Relative Maxima
and Minima: Curve Sketching. 10.2. Concavity: Points
of Inflection. Points of Inflection. Second-Derivative
Test. 10.3. Optimization in Business and Economics.
Absolute Extrema. Maximizing Revenue. Minimizing
Average Cost. Maximizing Profit. 10.4. Applications of
Maxima and Minima. 10.5. Rational Functions: More
Curve Sketching. Asymptotes. More Curve Sketching.
Chapter Exercises. 11. Derivatives Continued. 11.1.
Derivatives of Logarithmic Functions. Using Properties
of Logarithms. 11.2. Derivatives of Exponential Functions.
11.3. Implicit Differentiation. 11.4. Related Rates. Percent
Rates of Change. Solving Related-Rates Problems. 11.5.
Applications in Business and Economics. Elasticity of
Demand. Taxation in a Competitive Market. Chapter
Exercises. 12. Indefinite Integrals. 12.1. The Indefinite
Integral. 12.2. The Power Rule. 12.3. Integrals Involving
Exponential and Logarithmic Functions. Integrals
Involving Exponential Functions. Integrals Involving
Logarithmic Functions. 12.4. The Indefinite Integral in
Business and Economics. Total Cost and Profit. National
Consumption and Savings. 12.5. Differential Equations.
Solution of Differential Equations. Separable Differential
www.cengageasia.com
119
Chapter Exercises. 13. Definite Integrals: Techniques of
Integration. 13.1. The Definite Integral: The Fundamental
Theorem of Calculus. Estimating the Area under a Curve.
13.2. Area between Two Curves. 13.3. Definite Integrals in
Business and Economics. Continuous Income Streams.
Consumer’s Surplus. Producer’s Surplus. 13.4. Using
Tables of Integrals. 13.5. Integration by Parts. 13.6.
Improper Integrals and Their Applications. Chapter
Exercises. 14. Functions of Two or More Variables.
14.1. Functions of Two or More Variables. 14.2. Partial
Differentiation. First-Order Partial Derivatives.
Higher-Order Partial Derivatives. 14.3. Functions of
Two Variables in Business and Economics. Joint Cost
and Marginal Cost. Production Functions. Demand
Functions. 14.4. Maxima and Minima. 14.5. Constrained
Optimization and Lagrange Multipliers. Chapter
Exercises. Answers to Odd-Numbered Exercises. Index.
© 2012, 368pp, Paperback, 9780840058225
MATHEMATICAL APPLICATIONS FOR
THE MANAGEMENT, LIFE, AND SOCIAL
SCIENCES, HYBRID (WITH ENHANCED
WEBASSIGN WITH EBOOK LOE PRINTED
ACCESS CARD FOR ONE-TERM MATH
AND SCIENCE), 10E
Ronald J. Harshbarger, University of South Carolina; James J. Reynolds,
Clarion University
text that engages students online! MATHEMATICAL
APPLICATIONS FOR THE MANAGEMENT, LIFE, AND
SOCIAL SCIENCES, 10th Edition, is intended for a
two-semester applied calculus or combined finite
mathematics and applied calculus course. The book’s
concept-based approach, multiple presentation
methods, and interesting and relevant applications
keep students who typically take the course--business,
economics, life sciences, and social sciences majors-engaged in the material. This edition broadens
the book’s real-life context by adding a number of
environmental science and economic applications. The
use of modeling has been expanded, with modeling
problems now clearly labeled in the examples. Also
included in the Tenth Edition is a brief review of algebra
to prepare students with different backgrounds for the
material in later chapters.
NEW TO THIS EDITION
WebAssign.
• Updated Exercise Sets: Drill exercises throughout the
text have been revised and reorganized to improve
grading and pairing. In addition, multi-step problems
have been revised to give students additional
opportunities to interpret results.
• New Applications: Interesting applications
illustrate the relevance of mathematics in business,
management, and the life and social sciences. Datadriven applications have been updated or replaced
with contemporary applications that address social,
environmental, and economic issues. The variety of
the application examples and exercises is one of the
most appreciated features of this book.
• Technology: The Technology Notes, Calculator Notes,
and Spreadsheet Notes throughout the text have
been streamlined. Specific step-by-step instructions
for using the various features of a graphing calculator
or Microsoft® Excel are now included in two new
appendices--Graphing Calculator Guide and Excel
Guide. Excel information has been updated to include
Excel 2007 and Excel 2010. Technology material
remains optional, so instructors and students may
skip it without loss of continuity.
• CourseMate: CourseMate brings course concepts
to life with interactive learning, study, and exam
preparation tools that support the printed textbook.
Watch student comprehension soar as your class
works with the printed textbook and the textbook-
www.cengageasia.com
120
specific website. CourseMate goes beyond the book
to deliver what you need!
FEATURES
• Comprehensive Exercise Sets: While the overall
variety and grading of drill and application exercises
offer problems for different skill levels, there are
enough challenging problems to stimulate students in
thoughtful investigations. Many sets contain critical
thinking and thought-provoking multi-step problems
that extend students’ knowledge and skills.
• Flexibility: To accommodate alternate teaching
approaches, the text offers a great deal of flexibility
in the order in which topics may be presented and
the degree to which they may be emphasized.
Consequently, the book can be adapted to variations
in coverage and sequencing of topics at different
colleges and universities, depending upon the
purpose of the course and the nature of the student
audience.
• Technology: An icon throughout the text denotes
Technology Notes, Calculator Notes and Spreadsheet
Notes. Step-by-step instructions for using the various
features of a graphing calculator or Microsoft® Excel
are included in two new appendices.
• Objective Lists: Every section begins with a brief list
of objectives that outline the goals of that section
and aid instructors in lesson planning/preparation.
CONTENTS
0. ALGEBRAIC CONCEPTS. Sets. The Real Numbers.
Integral Exponents. Radicals and Rational Exponents.
Operations with Algebraic Expressions. Factoring.
Algebraic Fractions. 1. LINEAR EQUATIONS AND
FUNCTIONS. Solutions of Linear Equations and
Inequalities in One Variable. Functions. Linear
Functions. Graphs and Graphing Utilities. Solution of
Systems of Linear Equations. Applications of Functions
in Business and Economics. 2. QUADRATIC AND
OTHER SPECIAL FUNCTIONS. Quadratic Equations.
Quadratic Functions: Parabolas. Business Applications
Using Quadratics. Special Functions and Their Graphs.
Modeling; Fitting Curves to Data with Graphing Utilities
(optional). 3. MATRICES. Matrices. Multiplication of
Matrices. Gauss-Jordan Elimination: Solving Systems
of Equations. Inverse of a Square Matrix; Matrix
Equations. Applications of Matrices: Leontief InputOutput Models. 4. INEQUALITIES AND LINEAR
PROGRAMMING. Linear Inequalities in Two Variables.
Linear Programming: Graphical Methods. The Simplex
Method: Maximization. The Simplex Method: Duality
and Minimization. The Simplex Method with Mixed
Constraints. 5. EXPONENTIAL AND LOGARITHMIC
Functions and Their Properties. Solution of Exponential
Equations: Applications of Exponential and Logarithmic
Functions. 6. MATHEMATICS OF FINANCE. Simple
Interest; Sequences. Compound Interest; Geometric
Sequences. Future Value of Annuities. Present Value of
Annuities. Loans and Amortization. 7. INTRODUCTION
TO PROBABILITY. Probability; Odds. Unions and
Intersections of Events: One-Trial Experiments.
Conditional Probability: The Product Rule. Probability
Trees and Bayes’ Formula. Counting: Permutations
and Combinations. Permutations, Combinations,
and Probability. Markov Chains. 8. FURTHER TOPICS
IN PROBABILITY; DATA DESCRIPTION. Binomial
Probability Experiments. Data Descriptions. Discrete
Probability Distributions; The Binomial Distribution.
Normal Probability Distribution. The Normal Curve
Approximation to the Binomial Distribution. 9.
DERIVATIVES. Limits. Continuous Functions; Limits at
Infinity. Rates of Change and Derivatives. Derivative
Formulas. The Product Rule and the Quotient Rule.
The Chain Rule and the Power Rule. Using Derivative
Formulas. Higher-Order Derivatives. Applications:
Marginals and Derivatives. 10. APPLICATIONS OF
DERIVATIVES. Relative Maxima and Minima: Curve
Sketching. Concavity: Points of Inflection. Optimization
in Business and Economics. Applications of Maxima and
Minima. Rational Functions: More Curve Sketching. 11.
DERIVATIVES CONTINUED. Derivatives of Logarithmic
Functions. Derivatives of Exponential Functions. Implicit
Differentiation. Related Rates. Applications in Business
and Economics. 12. INDEFINITE INTEGRALS. The
Indefinite Integral. The Power Rule. Integrals Involving
Exponential and Logarithmic Functions. Applications
of the Indefinite Integral in Business and Economics.
Differential Equations. 13. DEFINITE INTEGRALS:
TECHNIQUES OF INTEGRATION. Area Under a Curve.
The Definite Integral: The Fundamental Theorem of
Calculus. Area Between Two Curves. Applications of
Definite Integrals in Business and Economics. Using
Tables of Integrals. Integration by Parts. Improper
Integrals and Their Applications. Numerical Integration
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121
Methods: Trapezoidal Rule and Simpson’s Rule. 14.
FUNCTIONS OF TWO OR MORE VARIABLES. Functions
of Two or More Variables. Partial Differentiation.
Applications of Functions of Two Variables in Business
and Economics. Maxima and Minima. Maxima and
Minima of Functions Subject to Constraints: Lagrange
Multipliers. Appendix A: Financial Tables. Appendix B:
Areas Under the Standard Normal Curve. Appendix C:
Calculator Guide. Appendix D: Guide to Excel.
© 2013, 832pp, Paperback, 9781133364832
MATHEMATICAL APPLICATIONS FOR
THE MANAGEMENT, LIFE, AND SOCIAL
SCIENCES, INTERNATIONAL EDITION,
10E
Ronald J. Harshbarger, University of South Carolina; James J. Reynolds,
Clarion University
M AT H E M AT I C A L A P P L I C AT I O N S F O R T H E
MANAGEMENT, LIFE, AND SOCIAL SCIENCES, 10E,
International Edition is intended for a two-semester
applied calculus or combined finite mathematics
and applied calculus course. The book’s conceptbased approach, multiple presentation methods, and
interesting and relevant applications keep students
who typically take the course—business, economics,
life sciences, and social sciences majors—engaged in
the material. This edition broadens the book’s real-life
context by adding a number of environmental science
and economic applications. The use of modeling has
been expanded, with modeling problems now clearly
labeled in the examples. Also included in the Tenth
Edition is a brief review of algebra to prepare students
with different backgrounds for the material in later
chapters.
NEW TO THIS EDITION
• Updated Exercise Sets: Drill exercises throughout the
text have been revised and reorganized to improve
grading and pairing. In addition, multi-step problems
have been revised to give students additional
opportunities to interpret results.
• New Applications: Interesting applications
illustrate the relevance of mathematics in business,
management, and the life and social sciences. Datadriven applications have been updated or replaced
with contemporary applications that address social,
environmental, and economic issues. The variety of
the application examples and exercises is one of the
most appreciated features of this book.
• Technology: The Technology Notes, Calculator Notes,
and Spreadsheet Notes throughout the text have
been streamlined. Specific step-by-step instructions
for using the various features of a graphing calculator
or Microsoft® Excel are now included in two new
appendices—Graphing Calculator Guide and Excel
Guide. Excel information has been updated to include
Excel 2007 and Excel 2010. Technology material
remains optional, so instructors and students may
skip it without loss of continuity.
works with the printed textbook and the textbookspecific website. CourseMate goes beyond the book
FEATURES
works with the printed textbook and the textbookspecific website. CourseMate goes beyond the book
• Flexibility: To accommodate alternate teaching
approaches, the text offers a great deal of flexibility
in the order in which topics may be presented and
the degree to which they may be emphasized.
Consequently, the book can be adapted to variations
in coverage and sequencing of topics at different
colleges and universities, depending upon the
purpose of the course and the nature of the student
www.cengageasia.com
122
audience.
• Technology: An icon throughout the text denotes
Technology Notes, Calculator Notes and Spreadsheet
Notes. Step-by-step instructions for using the various
features of a graphing calculator or Microsoft® Excel
are included in two new appendices.
• Objective Lists: Every section begins with a brief list
of objectives that outline the goals of that section
and aid instructors in lesson planning/preparation.
CONTENTS
0. ALGEBRAIC CONCEPTS. Sets. The Real Numbers.
Integral Exponents. Radicals and Rational Exponents.
Operations with Algebraic Expressions. Factoring.
Algebraic Fractions. 1. LINEAR EQUATIONS AND
FUNCTIONS. Solutions of Linear Equations and
Inequalities in One Variable. Functions. Linear
Functions. Graphs and Graphing Utilities. Solution of
Systems of Linear Equations. Applications of Functions
in Business and Economics. 2. QUADRATIC AND
OTHER SPECIAL FUNCTIONS. Quadratic Equations.
Quadratic Functions: Parabolas. Business Applications
Using Quadratics. Special Functions and Their Graphs.
Modeling; Fitting Curves to Data with Graphing Utilities
(optional). 3. MATRICES. Matrices. Multiplication of
Matrices. Gauss-Jordan Elimination: Solving Systems
of Equations. Inverse of a Square Matrix; Matrix
Equations. Applications of Matrices: Leontief InputOutput Models. 4. INEQUALITIES AND LINEAR
PROGRAMMING. Linear Inequalities in Two Variables.
Linear Programming: Graphical Methods. The Simplex
Method: Maximization. The Simplex Method: Duality
and Minimization. The Simplex Method with Mixed
Constraints. 5. EXPONENTIAL AND LOGARITHMIC
Functions and Their Properties. Solution of Exponential
Equations: Applications of Exponential and Logarithmic
Functions. 6. MATHEMATICS OF FINANCE. Simple
Interest; Sequences. Compound Interest; Geometric
Sequences. Future Value of Annuities. Present Value of
Annuities. Loans and Amortization. 7. INTRODUCTION
TO PROBABILITY. Probability; Odds. Unions and
Intersections of Events: One-Trial Experiments.
Conditional Probability: The Product Rule. Probability
Trees and Bayes’ Formula. Counting: Permutations
and Combinations. Permutations, Combinations,
and Probability. Markov Chains. 8. FURTHER TOPICS
IN PROBABILITY; DATA DESCRIPTION. Binomial
Probability Experiments. Data Descriptions. Discrete
Probability Distributions; The Binomial Distribution.
Normal Probability Distribution. The Normal Curve
Approximation to the Binomial Distribution. 9.
DERIVATIVES. Limits. Continuous Functions; Limits at
Infinity. Rates of Change and Derivatives. Derivative
Formulas. The Product Rule and the Quotient Rule.
The Chain Rule and the Power Rule. Using Derivative
Formulas. Higher-Order Derivatives. Applications:
Marginals and Derivatives. 10. APPLICATIONS OF
DERIVATIVES. Relative Maxima and Minima: Curve
Sketching. Concavity: Points of Inflection. Optimization
in Business and Economics. Applications of Maxima and
Minima. Rational Functions: More Curve Sketching. 11.
DERIVATIVES CONTINUED. Derivatives of Logarithmic
Functions. Derivatives of Exponential Functions. Implicit
Differentiation. Related Rates. Applications in Business
and Economics. 12. INDEFINITE INTEGRALS. The
Indefinite Integral. The Power Rule. Integrals Involving
Exponential and Logarithmic Functions. Applications
of the Indefinite Integral in Business and Economics.
Differential Equations. 13. DEFINITE INTEGRALS:
TECHNIQUES OF INTEGRATION. Area Under a Curve.
The Definite Integral: The Fundamental Theorem of
Calculus. Area Between Two Curves. Applications of
Definite Integrals in Business and Economics. Using
Tables of Integrals. Integration by Parts. Improper
Integrals and Their Applications. Numerical Integration
Methods: Trapezoidal Rule and Simpson’s Rule. 14.
FUNCTIONS OF TWO OR MORE VARIABLES. Functions
of Two or More Variables. Partial Differentiation.
Applications of Functions of Two Variables in Business
and Economics. Maxima and Minima. Maxima and
Minima of Functions Subject to Constraints: Lagrange
Multipliers. Appendix A: Financial Tables. Appendix B:
Areas Under the Standard Normal Curve. Appendix C:
Calculator Guide. Appendix D: Guide to Excel.
© 2013, 1088pp, Paperback, 9781133108481
www.cengageasia.com
123
BERRESFORD/ROCKETT’S APPLIED
CALCULUS, 6TH, 6E
Contains fully worked-out solutions to all of the oddnumbered exercises in the text, giving students a way
to check their answers and ensure that they took the
correct steps to arrive at an answer.
© 2013, 384pp, Paperback, 9781133104018
TAN’S APPLIED CALCULUS FOR THE
SCIENCES, 9TH, 9E
Check your work and reinforce your understanding with
this manual, which contains complete solutions for all
odd-numbered exercises in the text. You will also find
problem-solving tips plus additional algebra steps and
review for selected problems.
© 2014, 320pp, Paperback, 9781133960928
ROLF’S FINITE MATHEMATICS, 8TH, 8E
Check your work--and your understanding--with this
manual, which provides worked-out solutions to the
odd-numbered problems in the text.
© 2014, 256pp, Paperback, 9781285084695
WANER/COSTENOBLE’S FINITE MATH, 6E
University
Check your work and reinforce your understanding with
this manual, which contains complete solutions for all
odd-numbered exercises in the text. You will also find
problem-solving strategies plus additional algebra steps
and review for selected problems.
© 2014, 320pp, Paperback, 9781285085586
www.cengageasia.com
124
Liberal Arts Mathematics
FUNDAMENTALS OF ALGEBRAIC
MODELING, INTERNATIONAL EDITION,
6E
Daniel L. Timmons, Alamance Community College; Catherine W.
Johnson, Alamance Community College; Sonya McCook, Alamance
Community College
FUNDAMENTALS OF ALGEBRAIC MODELING, 6E,
International Edition strives to show the student
connections between math and their daily lives.
Algebraic modeling concepts and solutions are
presented in non-threatening, easy-to-understand
language with numerous step-by-step examples to
illustrate ideas. Whether they are going on to study
early childhood education, graphic arts, automotive
technologies, criminal justice, or something else,
students will discover that the practical applications
of mathematical modeling will continue to be useful
well after they have finished this course.
NEW TO THIS EDITION
• A new four-color design helps further distinguish the
features of the text.
• Examples and exercises have been updated.
• A brand new Chapter R A Review of Algebra
Fundamentals has been added and it gives students
an opportunity to review the algebra skills needed to
be successful in a modeling course.
• A section on scientific notation has been added.
• Chapter 1 Mathematical Model Fundamentals has
been reorganized.
• Geometric models has been moved from chapter 5
to chapter 2.
• Chapter 7 Probability Models has been reorganized
creating additional sections.
• Chapter 8 Modeling with Statistics now includes
a section on reading and interpreting graphical
information.
• Exclusively from Cengage Learning®, Enhanced
WebAssign is now available with FUNDAMENTALS
OF ALGEBRAIC MODELING, 6E, International Edition.
Enhanced WebAssign combines the exceptional
mathematics content that you know and love with
the most powerful online homework solution,
WebAssign. Enhanced WebAssign engages students
with immediate feedback, rich tutorial content,
and interactive e-books that help students to
develop a deeper conceptual understanding of their
subject matter. Online assignments can be built by
selecting from thousands of text-specific problems
or supplemented with problems from any Cengage
Learning textbook.
FEATURES
• Laboratory Exercises at the end of each chapter get
students involved in guided hands-on activities.
Some are designed to be completed as individual
assignments and others require group work.
CONTENTS
A REVIEW OF ALGEBRA FUNDAMENTALS. Real
Numbers and Mathematical Operations. Solving
Linear Equations. Percents. Scientific Notation.
1. MATHEMATICAL MODEL FUNDAMENTALS.
Mathematical Models. Formulas. Ratio and Proportion.
Word Problem Strategies. 2. GEOMETRIC MODELS.
Models and Patterns in Plane Geometry. Models and
Patterns in Triangles. Models and Patterns in Art and
Architecture: Perspective and Symmetry. Models and
Patterns in Art and Architecture and Nature: Scale
and Proportion. Models and Patterns in Music. 3.
GRAPHING. Rectangular Coordinate System. Graphing
Linear Equations. Slope. Writing Equations of Lines.
Applications and Uses of Graphs. 4. FUNCTIONS.
Functions. Using Function Notation. Linear Functions
as Models. Direct and Inverse Variation. Quadratic
Functions as Models. Exponential Functions as
Models. 5. MATHEMATICAL MODELS IN CONSUMER
MATH. Mathematical Models in the Business World.
Mathematical Models in Banking. Mathematical Models
in Consumer Credit. Mathematical Models in Purchasing
an Automobile. Mathematical Models in Purchasing a
Home. Mathematical Models in Insurance Options and
Rates. Mathematical Models in Stocks, Mutual Funds,
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125
and Bonds. Mathematical Models in Personal Income.
6. MODELING WITH SYSTEMS OF EQUATIONS. Solving
Systems by Graphing. Solving Systems Algebraically.
Applications of Linear Systems. Systems of Non-Linear
Functions. 7. PROBABILITY MODELS. Sets and Set
Theory. What is Probability? Theoretical Probability.
Odds. Tree Diagrams and the Counting Principle.
Probabilities Involving “Or”. Probabilities Involving
“And”. Permutations and Combinations. 8. MODELING
WITH STATISTICS. Introduction to Statistics and
Surveys. Frequency Tables and Histograms. Reading
and Interpreting Graphical Information. Descriptive
Statistics. Variation. Normal Curve. Scatter Diagrams
and Linear Regression.
© 2014, 464pp, Paperback, 9781133365839
FEATURES
• An innovative combination of content delivery both
assets based on input from student focus groups and
surveys, and from interviews with nearly 120 faculty
and students.
• Chapter in Review cards at the back of the Student
Editions provide students a portable study tool
containing all of the pertinent information for class
preparation.
• Your Instructor’s Edition will include one Prep Card
per chapter, perforated so you can slide it into your
briefcase or leave it on the podium while you lecture.
These cards include Topics, a chapter outline, key
terms, and various activities both for in-class exercises
and take-home assignments.
the purchase of a new book. Downloadable flash cards,
practice problems, video tutorials, exercise solutions
and more are only a click away.
CONTENTS
MATH FOR LIBERAL ARTS (WITH ARTS
ACCESS CARD)
Karl Smith, Santa Rosa Junior College
review process, involving over 120 students and faculty
members, MATH is an engaging and accessible solution
that accommodates the busy lifestyles of today’s
learners at a value-based price. This paperback text
offers a full suite of learning aids, including end-ofchapter review cards, downloadable flashcards and
exercises and practice quizzes aimed at supplementing
learning outside of the classroom. MATH presents
concepts in a visual and approachable way, ideal for
combating the math anxiety often found in Liberal Arts
Math students. Also available is Cengage Learning’s
1. THE NATURE OF NUMERATION. Math Anxiety Source.
What’s the Problem? Early Numeration Systems. HinduArabic Numeration Systems. Different Numeration
Systems. Binary Numeration Systems. History of
Calculating Devices. 2. THE NATURE OF NUMBERS. It’s
Natural. Prime Numbers. Numbers — Up and Down. It’s
a Long Way From Zero to One. It’s Irrational. Be Real.
Mathematical Modeling. 3. THE NATURE OF ALGEBRA.
Polynomials. Factoring. Evaluation, Application, and
Spreadsheets. Equations. Inequalities. Algebra in
Problem Solving. Ratios, Proportions, and Problem
Solving. Percents. Modeling Uncategorized Problems. 4.
THE NATURE OF GEOMETRY. Geometry. Polygons and
Angles. Triangles. Mathematics, Art, and Non-Euclidean
Geometries. Perimeter and Area. Surface Area, Volume
and Capacity. 5. THE NATURE OF NETWORKS. Euler
Circuits and Hamiltonian Cycles. Trees and Minimum
Spanning Trees. Topology and Fractals. 6. THE NATURE
OF GROWTH. Exponential Equations. Logarithmic
Equations. Applications of Growth and Decay. 7. THE
NATURE OF MONEY. It’s Simple. Buying on Credit.
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126
Credit Card Interest. Compound Interest. Buying
a Home. 8. THE NATURE OF SETS AND LOGIC.
Introduction to Sets. Set Relationships. Operations
with Sets. Venn Diagrams. Survey Problems Using
Sets. Inductive and Deductive Reasoning. 9. THE
NATURE OF COUNTING. Permutations. Combinations.
Counting Without Counting. Rubik’s Cube and Instant
Insanity. 10. THE NATURE OF CHANCE. It’s Not Certain.
Probability Models. Odds and Conditional Probability.
Mathematical Expectation. Frequency Distributions
and Graphs. Descriptive Statistics. It’s Normal. 11.
THE NATURE OF GRAPHS – THE MARRIAGE OF
ALGEBRA AND GEOMETRY. Cartesian Coordinate
System. Functions. Lines. Systems and Inequalities.
Graphing Curves. 12. THE NATURE OF VOTING
AND APPORTIONMENT. Voting. Voting Dilemmas.
Apportionment. Apportionment Paradoxes.
NEW TO THIS EDITION
• New! Interactive Excursions are now available through
Enhanced WebAssign. These activities with assignable
questions are based on the Excursions found in the
textbook. Through these activities, students can
become more openly engaged as they explore the
Excursions in a newly enriched, media-enhanced
environment.
• New! A comprehensive skills-review is now available
through Enhanced WebAssign. This preloaded and
assignable review presents students with questions
that focus on prerequisite skills. The review will help
students refresh their knowledge and fill in any gaps
so they may advance more smoothly through new
concepts or topics.
FEATURES
© 2011, 272pp, Paperback, 9781439047026
MATHEMATICAL EXCURSIONS,
ENHANCED EDITION, 3RD, 3E
Richard N. Aufmann, Palomar College; Joanne S. Lockwood, Nashua
Community College; Richard D. Nation, Palomar College; Daniel K.
Clegg, Palomar College
MATHEMATICAL EXCURSIONS, Third Edition, teaches
you that mathematics is a system of knowing and
understanding our surroundings. For example, sending
information across the Internet is better understood
when you understand prime numbers; the perils of
radioactive waste take on new meaning when you
understand exponential functions; and the efficiency
of the flow of traffic through an intersection is more
interesting after seeing the system of traffic lights
represented in a mathematical form. You will learn
those facets of mathematics that strengthen your
quantitative understanding and expand the way you
know, perceive, and comprehend your world. We hope
you enjoy the journey.
• The Third Edition’s table of contents has been
reorganized and rearranged to group the chapters by
broad topics that you can cover sequentially.
• In the News exercises, based on media sources, have
been added to this edition, providing another way to
engage students by demonstrating the contemporary
use of mathematics.
• Chapter Summaries now appear in an easy-to-use grid
format organized by section. Each summary point is
now paired with the page numbers of an example
that illustrates the concept, and exercises that allow
students to practice the relevant skill or technique.
• All application Examples, Exercises, and Excursions
have been updated to reflect the most recent data
and trends.
• Definitions are now boxed and highlighted for greater
prominence throughout the text, facilitating study
and review.
• All graphing calculator notes have been updated to
refer to the TI-84 Plus.
• In the Answer Section, answers to Chapter Test
exercises now include a reference to a similar example
in the text, making it easy for students to review
relevant material for exercises that they answer
incorrectly.
• Content includes a subsection on Reading and
Interpreting Graphs, a section on Right Triangle
Trigonometry, and a section on Stocks, Bonds, and
Mutual Funds.
www.cengageasia.com
127
CONTENTS
1. PROBLEM SOLVING. Inductive and Deductive
Reasoning. Excursion: KenKen Puzzles: An Introduction.
Problem Solving with Patterns. Excursion: Polygonal
Numbers. Problem-Solving Strategies. Excursion: Routes
on a Probability Demonstrator. Chapter 1 Summary.
Chapter 1 Review. Chapter 1 Test. 2. SETS. Basic
Properties of Sets. Excursion: Fuzzy Sets. Complements,
Subsets, and Venn Diagrams. Excursion: Subsets and
Complements of Fuzzy Sets. Set Operations. Excursion:
Union and Intersection of Fuzzy Sets. Applications of
Sets. Excursion: Voting Systems. Infinite Sets. Excursion:
Transfinite Arithmetic. Chapter 2 Summary. Chapter
2 Review Exercises. Chapter 2 Test. 3. LOGIC. Logic
Statements and Quantifiers. Excursion: Switching
Networks. Truth Tables, Equivalent Statements, and
Tautologies. Excursion: Switching Networks-Part II.
The Conditional and the Biconditional. Excursion:
Logic Gates. The Conditional and Related Statements.
Excursion: Sheffer’s Stroke and the NAND Gate.
Symbolic Arguments. Excursion: Fallacies. Arguments
and Euler Diagrams. Excursion: Using Logic to Solve
Crypterithms. Chapter 3 Summary. Chapter 3 Review
Exercises. Chapter 3 Test. 4. APPORTIONMENT AND
VOTING. Introduction to Apportionment. Excursion:
Apportioning the 1790 House of Representatives.
Introduction to Voting. Excursion: Variations of the
Borda Count Method. Weighted Voting Systems.
Excursion: Blocking Coalitions and the Banzhaf
Power Index. Chapter 4 Summary. Chapter 4 Review
Exercises. Chapter 4 Test. 5. THE MATHEMATICS
OF GRAPHS. Graphs and Euler Circuits. Excursion:
Pen-Tracing Puzzles. Weighted Graphs. Excursion:
Extending the Greedy Algorithm. Planarity and Euler’s
Formula. Excursion: The Five Regular Convex Polyhedra.
Graph Coloring. Excursion: Modeling Traffic Lights
with Graphs. Chapter 5 Summary. Chapter 5 Review
Exercises. Chapter 5 Test. 6. NUMERATION SYSTEMS
AND NUMBER THEORY. Early Numeration Systems.
Excursion: A Rosetta Tablet for the Traditional Chinese
Numeration System. Place-Value Systems. Excursion:
Subtraction via the Nines Complement and the EndAround Carry. Different Base Systems. Excursion:
Information Retrieval via a Binary Search. Arithmetic
in Different Bases. Excursion: Subtraction in Base Two
via the Ones Complement and the End-Around Carry.
Prime Numbers. Excursion: The Distribution of the
Primes. Topics from Number Theory. Excursion: A Sum
of the Divisors Formula. Chapter 6 Summary. Chapter
6 Review Exercises. Chapter 6 Test. 7. GEOMETRY.
Basic Concepts of Euclidean Geometry. Excursion:
Preparing a Circle Graph. Perimeter and Area of Plane
Figures. Excursion: Perimeter and Area of a Rectangle
with Changing Dimensions. Properties of Triangles.
Excursion: Topology: A Brief Introduction. Volume and
Surface Area. Excursion: Water Displacement. Right
Triangle Trigonometry. Excursion: Approximating the
Value of Trigonometric Ratios. Non-Euclidean Geometry.
Excursion: Finding Geodesics. Fractals. Excursion: The
Heighway Dragon Fractal. Chapter 7 Summary. Chapter
7 Review Exercises. Chapter 7 Test. 8. MATHEMATICAL
SYSTEMS. Modular Arithmetic. Excursion: Computing
the Day of the Week. Applications of Modular Arithmetic.
Excursion: Public Key Cryptography. Introduction to
Group Theory. Excursion: Wallpaper Groups. Chapter
8 Summary. Chapter 8 Review Exercises. Chapter 8
Test. 9. APPLICATIONS OF EQUATIONS. First-Degree
Equations and Formulas. Excursion: Body Mass Index.
Rate, Ratio, and Proportion. Excursion: Earned Run
Average. Percent. Excursion: Federal Income Tax.
Second-Degree Equations. Excursion: The Sum and
Product of the Solutions of a Quadratic Equation.
Chapter 9 Summary. Chapter 9 Review Exercises.
Chapter 9 Test. 10. APPLICATIONS OF FUNCTIONS.
Rectangular Coordinates and Functions. Excursion:
Dilations of a Geometric Figure. Properties of Linear
Functions. Excursion: Negative Velocity. Finding Linear
Models. Excursion: A Linear Business Model. Quadratic
Functions. Excursion: Reflective Properties of a Parabola.
Exponential Functions. Excursion: Chess and Exponential
Functions. Logarithmic Functions. Excursion: Benford’s
Law. Chapter 10 Summary. Chapter 10 Review Exercises.
Chapter 10 Test. 11. THE MATHEMATICS OF FINANCE.
Simple Interest. Excursion: Day-of-the-Year Table.
Compound Interest. Excursion: Consumer Price Index.
Credit Cards and Consumer Loans. Excursion: Car
Leases. Stocks, Bonds, and Mutual Funds. Excursion:
Treasury Bills. Home Ownership. Excursion: Home
Ownership Issues. Chapter 11 Summary. Chapter 11
Review Exercises. Chapter 11 Test. 12. COMBINATORICS
AND PROBABILITY. The Counting Principle. Excursion:
Decision Trees. Permutations and Combinations.
Excursion: Choosing Numbers in Keno. Probability and
Odds. Excursion: The Value of Pi by Simulation. Addition
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128
and Complement Rules. Excursion: Keno Revisited.
Conditional Probability. Excursion: Sharing Birthdays.
12.6 Expectation. Excursion: Chuck-a-luck. Chapter
Test. 13. STATISTICS. Measures of Central Tendency.
Excursion: Linear Interpolation and Animation.
Measures of Dispersion. Excursion: Geometric View
of Variance and Standard Deviation. Measures of
Relative Position. Excursion: Stem-and-Leaf Diagrams.
Normal Distribution. Excursion: Cut-Off Scores. Linear
Regression and Correlation. Excursion: An Application
of Linear Regression. Chapter 13 Summary. Chapter 13
Review Exercises. Chapter 13 Test.
© 2015, 1008pp, Hardback, 9781285454221
MATHEMATICAL EXCURSIONS,
• Mathematical Excursions, 3E, International Edition’s
table of contents has been reorganized and rearranged
to group the chapters by broad topics that you can
cover sequentially.
• In the News exercises, based on media sources, have
been added to this edition, providing another way to
engage students by demonstrating the contemporary
use of mathematics.
• Chapter Summaries now appear in an easy-to-use grid
format organized by section. Each summary point is
now paired with the page numbers of an example
that illustrates the concept, and exercises that allow
students to practice the relevant skill or technique.
• All application Examples, Exercises, and Excursions
have been updated to reflect the most recent data
and trends.
• Definitions are now boxed and highlighted for greater
prominence throughout the text, facilitating study
and review.
• All graphing calculator notes have been updated to
refer to the TI-84 Plus.
• In the Answer Section, answers to Chapter Test
exercises now include a reference to a similar example
in the text, making it easy for students to review
relevant material for exercises that they answer
incorrectly.
FEATURES
MATHEMATICAL EXCURSIONS, 3E, International
Edition teaches students that mathematics is a system
of knowing and understanding our surroundings. For
example, sending information across the Internet
is better understood when one understands prime
numbers; the perils of radioactive waste take on new
meaning when one understands exponential functions;
and the efficiency of the flow of traffic through an
intersection is more interesting after seeing the
system of traffic lights represented in a mathematical
form. Students will learn those facets of mathematics
that strengthen their quantitative understanding and
expand the way they know, perceive, and comprehend
their world. We hope you enjoy the journey.
NEW TO THIS EDITION
• Content includes a subsection on Reading and
Interpreting Graphs, a section on Right Triangle
Trigonometry, and a section on Stocks, Bonds, and
Mutual Funds.
• An online algebra review appendix helps students
review prerequisite algebra concepts.
• An Excursion activity and corresponding Excursion
Exercises conclude each section, providing
concept reinforcement and opportunities for inclass cooperative work, hands-on learning, and
development of critical-thinking skills.
CONTENTS
Reasoning. Excursion: KenKen Puzzles: An Introduction.
Problem Solving with Patterns. Excursion: Polygonal
Numbers. Problem-Solving Strategies. Excursion: Routes
on a Probability Demonstrator. Chapter 1 Summary.
Chapter 1 Review. Chapter 1 Test. 2. SETS. Basic
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Properties of Sets. Excursion: Fuzzy Sets. Complements,
Subsets, and Venn Diagrams. Excursion: Subsets and
Complements of Fuzzy Sets. Set Operations. Excursion:
Union and Intersection of Fuzzy Sets. Applications of
Sets. Excursion: Voting Systems. Infinite Sets. Excursion:
Transfinite Arithmetic. Chapter 2 Summary. Chapter
2 Review Exercises. Chapter 2 Test. 3. LOGIC. Logic
Statements and Quantifiers. Excursion: Switching
Networks. Truth Tables, Equivalent Statements, and
Tautologies. Excursion: Switching Networks—Part
II. The Conditional and the Biconditional. Excursion:
Logic Gates. The Conditional and Related Statements.
Excursion: Sheffer’s Stroke and the NAND Gate.
Symbolic Arguments. Excursion: Fallacies. Arguments
and Euler Diagrams. Excursion: Using Logic to Solve
Crypterithms. Chapter 3 Summary. Chapter 3 Review
Exercises. Chapter 3 Test. 4. APPORTIONMENT AND
VOTING. Introduction to Apportionment. Excursion:
Apportioning the 1790 House of Representatives.
Introduction to Voting. Excursion: Variations of the
Borda Count Method. Weighted Voting Systems.
Excursion: Blocking Coalitions and the Banzhaf
Power Index. Chapter 4 Summary. Chapter 4 Review
Exercises. Chapter 4 Test. 5. THE MATHEMATICS
OF GRAPHS. Graphs and Euler Circuits. Excursion:
Pen-Tracing Puzzles. Weighted Graphs. Excursion:
Extending the Greedy Algorithm. Planarity and Euler’s
Formula. Excursion: The Five Regular Convex Polyhedra.
Graph Coloring. Excursion: Modeling Traffic Lights
with Graphs. Chapter 5 Summary. Chapter 5 Review
Exercises. Chapter 5 Test. 6. NUMERATION SYSTEMS
AND NUMBER THEORY. Early Numeration Systems.
Excursion: A Rosetta Tablet for the Traditional Chinese
Numeration System. Place-Value Systems. Excursion:
Subtraction via the Nines Complement and the EndAround Carry. Different Base Systems. Excursion:
Information Retrieval via a Binary Search. Arithmetic
in Different Bases. Excursion: Subtraction in Base Two
via the Ones Complement and the End-Around Carry.
Prime Numbers. Excursion: The Distribution of the
Primes. Topics from Number Theory. Excursion: A Sum
of the Divisors Formula. Chapter 6 Summary. Chapter
6 Review Exercises. Chapter 6 Test. 7. GEOMETRY.
Basic Concepts of Euclidean Geometry. Excursion:
Preparing a Circle Graph. Perimeter and Area of Plane
Figures. Excursion: Perimeter and Area of a Rectangle
with Changing Dimensions. Properties of Triangles.
Excursion: Topology: A Brief Introduction. Volume and
Surface Area. Excursion: Water Displacement. Right
Triangle Trigonometry. Excursion: Approximating the
Value of Trigonometric Ratios. Non-Euclidean Geometry.
Excursion: Finding Geodesics. Fractals. Excursion: The
Heighway Dragon Fractal. Chapter 7 Summary. Chapter
7 Review Exercises. Chapter 7 Test. 8. MATHEMATICAL
SYSTEMS. Modular Arithmetic. Excursion: Computing
the Day of the Week. Applications of Modular Arithmetic.
Excursion: Public Key Cryptography. Introduction to
Group Theory. Excursion: Wallpaper Groups. Chapter
Test. 9. APPLICATIONS OF EQUATIONS. First-Degree
Equations and Formulas. Excursion: Body Mass Index.
Rate, Ratio, and Proportion. Excursion: Earned Run
Average. Percent. Excursion: Federal Income Tax.
Second-Degree Equations. Excursion: The Sum and
Product of the Solutions of a Quadratic Equation.
Chapter 9 Summary. Chapter 9 Review Exercises.
Chapter 9 Test. 10. APPLICATIONS OF FUNCTIONS.
Rectangular Coordinates and Functions. Excursion:
Dilations of a Geometric Figure. Properties of Linear
Functions. Excursion: Negative Velocity. Finding Linear
Models. Excursion: A Linear Business Model. Quadratic
Functions. Excursion: Reflective Properties of a Parabola.
Exponential Functions. Excursion: Chess and Exponential
Functions. Logarithmic Functions. Excursion: Benford’s
Law. Chapter 10 Summary. Chapter 10 Review Exercises.
Chapter 10 Test. 11. THE MATHEMATICS OF FINANCE.
Simple Interest. Excursion: Day-of-the-Year Table.
Compound Interest. Excursion: Consumer Price Index.
Credit Cards and Consumer Loans. Excursion: Car
Leases. Stocks, Bonds, and Mutual Funds. Excursion:
Treasury Bills. Home Ownership. Excursion: Home
Ownership Issues. Chapter 11 Summary. Chapter 11
Review Exercises. Chapter 11 Test. 12. COMBINATORICS
AND PROBABILITY. The Counting Principle. Excursion:
Decision Trees. Permutations and Combinations.
Excursion: Choosing Numbers in Keno. Probability and
Odds. Excursion: The Value of Pi by Simulation. Addition
and Complement Rules. Excursion: Keno Revisited.
Conditional Probability. Excursion: Sharing Birthdays.
12.6 Expectation. Excursion: Chuck-a-luck. Chapter
Test. 13. STATISTICS. Measures of Central Tendency.
Excursion: Linear Interpolation and Animation.
Measures of Dispersion. Excursion: Geometric View
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of Variance and Standard Deviation. Measures of
Relative Position. Excursion: Stem-and-Leaf Diagrams.
Normal Distribution. Excursion: Cut-Off Scores. Linear
Regression and Correlation. Excursion: An Application
of Linear Regression. Chapter 13 Summary. Chapter 13
Review Exercises. Chapter 13 Test.
© 2013, 1008pp, Paperback, 9781111579081
MATHEMATICS, 7E
A Practical Odyssey, International Edition
David B. Johnson, Diablo Valley College; Thomas A. Mowry
MATHEMATICS: A PRACTICAL ODYSSEY, 7E,
International Edition demonstrates mathematics’
usefulness and relevance to students’ daily lives through
topics such as calculating interest and understanding
voting systems. Well known for its clear writing and
unique variety of topics, the text emphasizes problemsolving skills, practical applications, and the history of
mathematics, and unveils the relevance of mathematics
and its human aspect to students. To offer flexibility
in content, the book contains more information than
might be covered in a one-term course. The chapters
are independent of each other so instructors can select
the ideal topics for their courses.
NEW TO THIS EDITION
• New! New section on Fair Division in Chapter 6 has
been added.
• New! Lecture Videos by Dana Mosley ideal for
promoting individual study and review and help
support students in online courses.
• Updated! Examples, exercises, and articles have been
updated and added with current real-world data and
issues.
• New material has been added connecting math and
art.
• Chapter openers have been updated.
FEATURES
• Accessibility: Emphasizing problem-solving skills,
the variety of applications-oriented examples and
exercises connect the material to students’ lives. “…in
the Real World” feature incorporates specific chapter
material into a real-world context. The authors have
an accessible writing style that engages students and
retains their interest.
• Usability: This book is user friendly. The examples do
not skip steps; key points are boxed for emphasis;
procedures are given step-by-step, making them
easier to follow and understand; and an abundance
of exposition is provided.
• History: Students see the human side of mathematics
as the history of the subject matter is interwoven
throughout most chapters. In addition, “Historical
Notes” give in-depth biographies of the prominent
people involved.
• Flexibility: The text offers an assortment of content
to choose from. The chapters are independent of
each other so instructors can select the ideal topics
for their courses.
• Topic X Real World Connections: The “Topic X . . .”
feature incorporates specific chapter material into a
real-world context.
CONTENTS
Preface. 1. LOGIC. Deductive Logic versus Inductive
Logic. Symbolic Logic. Truth Tables. More on
Conditionals. Analyzing Arguments. Chapter 1 Review.
2. SETS AND COUNTING. Sets and Set Operations.
Applications of Venn Diagrams. Introduction to
Combinatorics. Permutations and Combinations.
Infinite Sets. Chapter 2 Review. 3. PROBABILITY. History
of Probability. Basic Terms of Probability. Basic Rules of
Probability. Combinatorics and Probability. Expected
Value. Conditional Probability. Independence; Trees in
Genetics. Chapter 3 Review. 4. STATISTICS. Population,
Sample, and Data. Measures of Central Tendency.
Measures of Dispersion. The Normal Distribution.
Polls and Margin of Error. Linear Regression. Chapter
4 Review. 5. FINANCE. Simple Interest. Compound
Interest. Annuities. Amortized Loans. Annual Percentage
Rate with a TI’s TVM Application. Payout Annuities.
Chapter 5 Review. 6. VOTING AND APPORTIONMENT.
Voting Systems. Methods of Apportionment. Flaws of
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Apportionment. Chapter 6 Review. 7. NUMBER SYSTEMS
AND NUMBER THEORY. Place Systems. Addition and
Subtraction in Different Bases. Multiplication and
Division in Different Bases. Prime Numbers and Perfect
Numbers. Fibonacci Numbers and the Golden Ratio.
Chapter 7 Review. 8. GEOMETRY Perimeter and Area.
Volume and Surface Area. Egyptian Geometry. The
Greeks. Right Triangle Trigonometry. Linear Perspective.
Conic Sections and Analytic Geometry. Non-Euclidean
Geometry. Fractal Geometry. The Perimeter and Area of
a Fractal. Chapter 8 Review. 9. GRAPH THEORY. A Walk
through Königsberg. Graphs and Euler Trails. Hamilton
Circuits. Networks. Scheduling. Chapter 9 Review. 10.
Review of Exponentials and Logarithms. Review
of Properties of Logarithms. Exponential Growth.
Exponential Decay. Logarithmic Scales. Chapter 10
Review. 11. MATRICES AND MARKOV CHAINS. Review
of Matrices. Introduction to Markov Chains. Systems
of Linear Equations. Long-Range Predictions with
Markov Chains. Solving Larger Systems of Equations.
More on Markov Chains. Chapter 11 Review. 12. LINEAR
PROGRAMMING. Review of Linear Inequalities. The
Geometry of Linear Programming. Chapter 12 Review.
12. LINEAR PROGRAMMING (ONLINE). Introduction to
the Simplex Method. The Simplex Method: Complete
Problems. Chapter 12 Review. 13. THE CONCEPTS AND
HISTORY OF CALCULUS (ONLINE). Review of Rations,
Parabolas, and Functions. The Antecedents of Calculus.
Four Problems. Newton and Tangent Lines. Newton on
Falling Objects and the Derivative. The Trajectory of a
Cannonball. Newton and Areas. Conclusion. Chapter 13
Review. APPENDIXES. Appendix A. Appendix B Using
a Graphing Calculator. Appendix C Graphing with a
Graphing Calculator. Appendix D Finding Points of
Intersection with a Graphing Calculator. Appendix E
Dimensional Analysis. Appendix F Body Table for the
Standard Normal Distribution. Index.
© 2012, 1024pp, Paperback, 9780840048363
MATHEMATICS, 10E
Its Power and Utility, International Edition
MATHEMATICS: ITS POWER AND UTILITY, 10E,
International Edition combines a unique and practical
focus on real-world problem solving allowing even
the least-interested or worst-prepared student
to appreciate the beauty and value of math while
mastering basic concepts and skills they will apply
to their daily lives. The first half of the book explores
the POWER and historic impact of mathematics and
helps students harness that POWER by developing an
effective approach to problem solving. The second half
builds upon this foundation by exploring the UTLITY
and application of math concepts to a wide variety of
real-life situations: money management; handling of
credit cards; inflation; purchase of a car or home; the
effective use of probability, statistics, and surveys;
and many other topics of life interest. Unlike many
mathematics texts, MATHEMATICS: ITS POWER AND
UTILITY, 10E, International Edition assumes a basic
working knowledge of arithmetic, making it effective
even for students with no exposure to algebra.
Completely self-contained chapters make it easy to
teach to a customized syllabus or support the precise
pace and emphasis that students require.
NEW TO THIS EDITION
• The “Power/Utility of Math” section openers (formerly
called “In This World: The Power/Utility of Math”)
have been rewritten. These introductory boxes are
designed to engage students by encouraging them
to think about how the material in the section relates
to their life.
• The “Problem of the Day” feature in the end-of-section
exercise sets is now called “The Power/Utility of Math”
to better reflect its direct connection to the section
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132
opener with the same name. These exercises, now
boxed and prominently titled, can be found at the
beginning of each end-of-section exercise set.
• An outline of “Essential Ideas,” together with
problems that correspond with these ideas, has been
moved from the end-of-chapter review material to
each chapter opener.
• Over 300 new problems have been included.
• The Chapter Summary and Review sections have been
reorganized and redesigned, making them easier for
students to use in identifying their strengths and
weaknesses.
• Section 7.5, which is included in the chapter on
applications of percent, now includes information on
401(K) and retirement.
• Section 7.6, which is included in the chapter on
applications of percent, now contains information on
amortization, including an amortization table.
• A new section called “Connectives and Truth Tables”
has been added to chapter 8, sets and logic.
FEATURES
• The first half of the book, “The Power of Math,”
develops some ideas in arithmetic, algebra, and
geometry. The second half of the book, “The Utility of
Math,” develops the ideas around mathematics that
students will use outside of the classroom.
• Each chapter opener helps students anticipate
upcoming topics. Topics included in “The Power of
Math” or “The Utility of Math” section openers are
identified. A list of essential ideas tells students what
they need to know after they have worked through
the chapter.
Algebra. Inequalities. Summary and Review. 4. Percents
and Problem Solving. Ratio and Proportion. Problem
Solving with Proportions. Percent. Problem Solving
with Percents. Summary and Review. 5. Introduction
to Geometry. Euclidean Geometry. Angles and
Polynomials. Triangles. Similar Triangles. Summary
and Review. 6. Measurement and Problem Solving.
Precision, Accuracy, and Estimation. Perimeter. Area.
Volume and Capacity. Miscellaneous Measurements.
Converting Units. Summary and Review. Part II:
APPLICATIONS: THE UTILITY OF MATHEMATICS.
7. Applications of Percent. Discount, Sale Price, and
Sales Tax. Simple Interest. Buying on Credit. Credit
Card Interest. Compound Interest. Buying a Home.
Summary and Review. 8. Sets and Logic. Introduction
to Sets. Set Relationship. Operations with Sets. Venn
Diagrams. Survey Problems Using Sets. Inductive and
Deductive Reasoning. Connectives and Truth Tables.
Summary and Review. 9. Probability. Introduction to
Probability. Probability Models. Odds and Conditional
Probability. Mathematical Expectation. Summary and
Review. 10 Statistics. Frequency Distribution and
Graphs. Measures of Central Tendency. Measures of
Position. Measures of Dispersion. The Normal Curve and
Sampling. Summary and Review. 11. Graphs. Cartesian
Coordinate System. Functions. Lines. Systems and
Inequalities. Graphing Curves. Summary and Review.
© 2013, 624pp, Paperback, 9781111579104
CONTENTS
Part I: FOUNDATIONS: THE POWER OF MATHEMATICS.
1. Arithmetic, Calculators, and Problem Solving. Math
Anxiety. Formulating the Problem. Fractions and
Decimals. Rounding and Estimation. Exponents and
Prime Factorization. Common Fractions. Adding and
Subtracting Fractions. Hindu-Arabic Numeration
System. Different Numeration System. Summary and
Review. 2. Sets of Numbers. Symbol Shock. Addition
of Integers. Subtraction of Integers. Multiplication of
Integers. Division of Integers. Rational and Irrational
Numbers. Summary and Review. 3. Introduction to
Algebra. Polynomials. Similar Terms. Simplification.
Equations. Solving Equations. Problem Solving with
MATHEMATICS FOR ELEMENTARY
TEACHERS
A Process Approach, International Edition
Mark A. Freitag
Freitag’s MATHEMATICS FOR ELEMENTARY SCHOOL
TEACHERS: A PROCESS APPROACH, International
Edition was developed using the five Content
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133
Standards from the NCTM Principles and Standards
for School Mathematics, and the Common Core State
Standards for Mathematics. Traditionally, textbooks
for pre-service elementary teachers have focused on
problem solving. However, problem solving is not the
only process through which mathematics is learned.
It is also learned through mathematical reasoning,
communication, representation, and connections.
Recent trends in mathematics education now advocate
implementing all five processes as a vital part of
learning and doing mathematics. Consequently, preserve teachers need to have concrete experiences with
these processes that they will be required to teach. The
goal of this textbook is to treat each of the processes
equitably by using an approach in which the five
processes serve as the central pedagogical theme. Most
of the examples, exercises, and activities are designed
to either model the processes or to have students
become directly engaged in working with them. By
doing so, pre-service teachers will not only come to
understand the different processes, but also appreciate
them as an integral to learning and doing mathematics.
If this broader view can be instilled in pre-service
teachers, they are more likely to give their students a
more well-rounded and holistic view of mathematics
once they enter the classroom. The content of the
book is directly related to the mathematics that is
taught in grades K – 8. The purpose is not to reteach
elementary mathematics. Rather, the intent is to look
at the content from a theoretical or generalized point
of view, so that elementary and middle-grades teachers
can better understand the concepts and processes
behind the mathematics they will teach. In short, the
book focuses on the “why” behind the mathematics in
addition to the “how.”
FEATURES
• The FIVE MATHEMATICAL PROCESSES identified
in the NCTM Principles and Standards are used as
a framework for this textbook through which the
content is stated, explained, demonstrated, and
engaged. This “process approach” can be seen in
the EXAMPLES and each process is identified by the
appropriate icon.
• An OPENING PROBLEM appears on the first page
of each chapter and provides an application of the
upcoming content. The problems can be answered by
using specific content contained within the chapter.
Answers are given directly before the Chapter Review.
• GETTING STARTED introduces each chapter and
relates the mathematical content of the chapter
to how the concepts are used in an elementary
classroom.
• CLASSROOM LEARNING OBJECTIVES are tables that
feature specific learning outcomes from the K – 8
classroom and are adapted from the Common Core
State Standards for Mathematics. Each table lists the
learning objectives that are relevant to the content
of the chapter and then indicates the grade level at
which the objective is most likely to be taught.
• DEFINITIONS and THEOREMS are clearly identified.
• STUDENT PAGES from elementary textbooks provide
further connections to the elementary classroom by
demonstrating how concepts are often presented to
elementary students.
• HISTORICAL NOTES provide a context for the content
by identifying historical figures or occurrences
relevant to the content of the section.
• CHECK YOUR UNDERSTANDING in-text quizzes
provide an opportunity for students to monitor their
understanding of the content through quick skillcheck exercises. Answers to all items are given after
the chapter review exercises.
• TALK ABOUT IT questions are included in Check Your
Understanding and give students the opportunity to
discuss the content they have just learned. You can
use these questions to start a lecture or give them to
small groups of students to respond to.
• ACTIVITIES provide students with an opportunity to
engage the material of each subsection by solving
a problem often using a hands-on manipulative.
Activities in the book are designed to take up minimal
classroom time usually taking only five to ten minutes.
Answers to all items are given after the chapter review
exercises.
CONTENTS
1. MATHEMATICAL PROCESSES. Getting Started:
The NCTM Process Standards. Communication
Through Mathematical Representations. Inductive
Reasoning and Patterns. Deductive Reasoning and
Proof. Mathematical Problem Solving. Problem Solving
with Different Strategies. Chapter 1 Review. Answers
to Check Your Understandings and Activities. 2.
SETS. Getting Started: Sets in the Classroom. Set
Basics. Set Operations. Chapter 2 Review. Answers to
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Chapter 2 Check Your Understandings and Activities.
3. NUMBERS AND NUMERATION. Getting Started:
Numbers and Numeration in the Classroom. A
Brief History of Numeration. The Hindu-Arabic or
Decimal System. Other Base Numeration Systems.
Chapter 3 Review. Answers to Chapter 3 Check Your
Understandings and Activities. Reviewing the Big Ideas
Chapters 1-3. 4. WHOLE-NUMBER COMPUTATION.
Getting Started: Whole-Number Computation in the
Classroom. Understanding Whole-Number Addition and
Subtraction. Adding and Subtracting Large Numbers.
Understanding Whole-Number Multiplication and
Division. Multiplying and Dividing Large Numbers.
Computation in Base b. Chapter 4 Review. Answers to
5. BASIC NUMBER THEORY. Getting Started: Number
Theory in the Classroom. Divisibility, Primes, and
Composites. Greatest Common Factors and Least
Common Multiples. Modular and Clock Arithmetic.
Understandings and Activities. 6. THE INTEGERS.
Getting Started: Integers in the Classroom. Integer
Basics, Addition, and Subtraction. Integer Multiplication
and Division. Chapter 6 Review. Answers to Chapter 6
Check Your Understandings and Activities. Reviewing
the Big Ideas Chapters 4-6. 7. FRACTIONS AND THE
RATIONAL NUMBERS. Getting Started: Fractions and
the Rational Numbers in the Classroom. Fractions and
the Set of Rational Numbers. Adding and Subtracting
Rational Numbers. Multiplying and Dividing Rational
Numbers. Chapter 7 Review. Answers to Check Your
Understandings and Activities. 8. DECIMALS, REAL
NUMBERS, AND PROPORTIONAL REASONING.
Getting Started: Decimals and Proportional Reasoning in
the Classroom. Decimals and the Real Numbers. Decimal
and Real Number Operations. Proportional Reasoning.
Percents. Chapter 8 Review. Answers to Chapter 8 Check
Your Understandings and Activities. 9. ALGEBRAIC
THINKING. Getting Started: Algebraic Thinking in the
Classroom. Numerical Sequences. Functions and Their
Representations. Linear Functions and Constant Change.
Solving Equations and Inequalities. Algebraic Thinking
and Mathematical Modeling. Chapter 9 Review. Answers
to Chapter 9 Check You Understandings and Activities.
Reviewing the Big Ideas Chapters 7-9. 10. GEOMETRICAL
SHAPES. Getting Started: Geometrical Shapes in
the Classroom. Lines, Planes, and Angles. Triangles.
Quadrilaterals, Polynomials, and Circles. Geometric
Surfaces and Solids. Chapter 10 Review. Answers to
Chapter 10 Check Your Understandings and Activities. 11.
CONGRUENCE, SIMILARITY, AND CONSTRUCTIONS.
Getting Started: Congruence, Constructions, and
Similarity in the Classroom. Congruent Shapes. Similar
Shapes. Basic Geometrical Constructions. Constructing
Shapes. Chapter 11 Review. Answers to Chapter
11 Check Your Understandings and Activities. 12.
COORDINATE AND TRANSFORMATION GEOMETRY
IN THE CLASSROOM. Getting Started: Coordinate and
Transformation Geometry in the Classroom. Coordinate
Geometry. Transformations. Congruence, Similarity, and
Symmetry with Transformations. Geometric Patterns.
Understandings and Activities. Reviewing the Big
Ideas Chapters 10-12. 13. MEASUREMENT. Getting
Started: Measurement in the Classroom. Length and
the Measurement Process. Perimeter and Area. Surface
Area. Volume. Other Measures. Chapter 13 Review.
Answers to Chapter 13 Check Your Understandings and
Activities. 14. STATISTICAL THINKING. Getting Started:
Statistical Thinking in the Classroom. Formulating
Questions and Collecting Data. Representing and
Analyzing Data with Statistical Graphs. Representing
and Analyzing Data with Descriptive Statistics.
Abuse of Statistics. Chapter 14 Review. Answers
to Chapter 14 Check Your Understandings and
Activities. 15. PROBABILITY. Getting Started: Probability
in the Classroom. Experimental Probability and
Making Predictions from Data. Theoretical Probability.
Conditional and Geometric Probability, Odds, and
Expected Value. Counting Techniques and Probability.
Chapters 13-15.
© 2014, 1104pp, Paperback, 9781133109976
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135
NATURE OF MATHEMATICS, 12E
Written for liberal arts students and based on the
belief that learning to solve problems is the principal
reason for studying mathematics, Karl Smith introduces
students to Polya’s problem-solving techniques and
shows them how to use these techniques to solve
unfamiliar problems that they encounter in their
own lives. Through the emphasis on problem solving
and estimation, along with numerous in-text study
aids, students are assisted in understanding the
concepts and mastering the techniques. In addition
to the problem-solving emphasis, THE NATURE OF
MATHEMATICS is renowned for its clear writing,
coverage of historical topics, selection of topics, level,
and excellent applications problems. Smith includes
material on such practical real-world topics as finances
(e.g. amortization, installment buying, annuities) and
voting and apportionment. With the help of this text,
thousands of students have “experienced” mathematics
rather than just do problems--and benefited from a
writing style that boosts their confidence and fosters
their ability to use mathematics effectively in their
everyday lives.
NEW TO THIS EDITION
• The examples throughout the book have been
redesigned to more effectively engage students.
Each now includes a title and is presented in a fresh,
easy-to-read format.
• A “Chapter Challenge” problem appears in each
chapter, providing additional problem-solving
practice. To encourage students to stretch their
problem-solving skills, these new types of problems
present contexts other than those presented in the
chapter.
• “Historical Quest” problems, an overwhelming success
in the previous edition, appear more frequently in
the Twelfth Edition. These problems are designed to
involve students in the historical development of the
great ideas in mathematical history.
• Expanded and updated chapter openers include “What
in the World?” introductions, which draw students into
the material by relating the mathematics to common
scenarios they may encounter in their everyday lives.
• The prologue--updated for this edition--asks the
all-important question, “Why Math?”. The prologue
puts mathematics into a historical perspective for
students, and is also designed to encourage them to
begin thinking about problem solving.
• Updated for this edition, the problems accompanying
the “Why Not Math?” epilogue show students how
mathematics touches just about every course of study.
FEATURES
• Real-World Problem-Solving Emphasis: Polya’s method
of problem solving is used throughout the text.
Students learn how to apply these techniques to solve
problems they encounter in their everyday lives in such
areas as finance (installment buying, amortization,
annuities) and voting and apportionment.
• Flexibility: The chapters are independent of one
another and allow maximum teaching flexibility.
• Learning Aids: The book offers a variety of interesting
and helpful learning aids. Icons like “Caution” and
“Stop” guide students through concepts. “Historical
Notes” place students’ view of mathematics in a
historical perspective and include a category of
related problems entitled “Historical Quest”. “Chapter
Summaries” include chapter review exercises, group
research projects, and individual research projects.
Additionally, a list of important terms and types of
problems, including section references, is available
to students at www.mathnature.com.
• Exercise Sets: Problems range from easy to challenging
and are clearly marked by type. “Level 1” problems are
mechanical or drill. “Level 2” problems require the
understanding of concepts. “Level 3” problems require
problem-solving skills or original thinking.
CONTENTS
Prologue: Why Math? A Historical Overview. 1.
THE NATURE OF PROBLEM SOLVING. The Nature
of Problem Solving. Problem Solving. Inductive
and Deductive Reasoning. Scientific Notation and
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Estimation. Summary. 2. THE NATURE OF SETS. Sets,
Subsets, and Venn Diagrams. Operations with Sets.
Applications of Sets. Finite and Infinite Sets. Summary.
3. THE NATURE OF LOGIC. Deductive Reasoning.
Truth Tables and the Conditional. Operators and
Laws of Logic. The Nature of Proof. Problem Solving
Using Logic. Logic Circuits (Optional). Summary. 4.
THE NATURE OF NUMERATION SYSTEMS. Early
Numeration Systems. Hindu-Arabic Numeration System.
Different Numeration Systems. Binary Numeration
System. History of Calculating Devices (Optional).
Summary. 5. THE NATURE OF NUMBERS. Natural
Numbers. Prime Numbers. Integers. Rational Numbers.
Irrational Numbers. Groups, Fields, and Real Numbers.
Discrete Mathematics. Cryptography (Optional).
Summary. 6. THE NATURE OF ALGEBRA. Polynomials.
Factoring. Evaluation, Applications, and Spreadsheets.
Equations. GUEST ESSAY: “CHAOS”. Inequalities.
Algebra in Problem Solving. Ratios, Proportions, and
Problem Solving. Percents. Modeling Uncategorized
Problems. Summary. 7. THE NATURE OF GEOMETRY.
Geometry. Polygons and Angles. Triangles. Similar
Triangles. Right Triangle Trigonometry (Optional).
Mathematics, Art, and Non-Euclidean Geometries
(Optional Sections). Summary. 8. THE NATURE OF
NETWORKS AND GRAPH THEORY. Euler Circuits and
Hamiltonian Cycles. Trees and Minimum Spanning
Trees. Topology and Fractals. GUEST ESSAY: “WHAT
GOOD ARE FRACTALS?”. Summary. 9. THE NATURE
OF MEASUREMENT. Perimeter. Area. Surface Area,
Volume and Capacity. Miscellaneous Measurements
(Optional). U.S.-Metric Conversions. Summary. 10.
THE NATURE OF GROWTH. Exponential Equations.
Logarithmic Equations. Applications of Growth and
Decay. Summary. 11. THE NATURE OF SEQUENCES,
SERIES, AND FINANCIAL MANAGEMENT. Interest.
Installment Buying. Sequences. Series. Annuities.
Amortization. Summary of Financial Formulas. Summary.
12. THE NATURE OF COUNTING. Permutations.
Combinations. Counting without Counting. Rubik’s
Cube and Instant Insanity (Optional). Summary. 13.
THE NATURE OF PROBABILITY. Introduction to
Probability. Mathematical Expectation. Probability
Models. Calculated Probabilities. The Binomial
Distribution (Optional). GUEST ESSAY: “EXTRASENSORY
PERCEPTION”. Summary. 14. THE NATURE OF
STATISTICS. Frequency Distributions and Graphs.
Descriptive Statistics. The Normal Curve. Correlation
and Regression. Sampling (Optional). Summary. 15. THE
NATURE OF GRAPHS AND FUNCTIONS. Cartesian
Coordinates and Graphing Lines. Graphing Half-Planes.
Graphing Curves. Conic Sections. Functions. Summary.
16. THE NATURE OF MATHEMATICAL SYSTEMS.
Systems of Linear Equations. Problem Solving with
Systems. Matrix Solution of a System of Equations.
Inverse Matrices. Modeling with Linear Programming
(Optional). Summary. 17. THE NATURE OF VOTING
Apportionment. Apportionment Flaws. Summary.
18. THE NATURE OF CALCULUS (OPTIONAL). What
Is Calculus? Limits. Derivatives. Integrals. Summary.
Epilogue: Why Not Math? Mathematics in the Natural
Sciences, Social Sciences, and in the Humanities.
Appendices. A. Glossary. B. Selected Answers. C. Index.
© 2012, 1024pp, Hardback, 9780538737586
AUFMANN/LOCKWOOD/NATION/
CLEGG’S MATHEMATICAL EXCURSIONS,
3RD, 3E
© 2013, 256pp, Paperback, 9781133112211
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BELLO/KAUL/BRITTON’S TOPICS IN
CONTEMPORARY MATHEMATICS, 10TH,
10E
TIMMONS/JOHNSON/MCCOOK’S
FUNDAMENTALS OF ALGEBRAIC
MODELING, 6E, 6E
Ignacio Bello, University of South Florida; Anton Kaul, California
Polytechnic State University; Jack R. Britton, Late of University of
South Florida
Daniel L. Timmons, Alamance Community College; Catherine W.
Johnson, Alamance Community College; Sonya McCook, Alamance
Community College
Prepare for exams and succeed in your mathematics
course with this comprehensive solutions manual!
Featuring worked out-solutions to the problems in
TOPICS IN CONTEMPORARY MATHEMATICS, 10th
Edition, this manual shows you how to approach
and solve problems using the same step-by-step
explanations found in your textbook examples.
FUNDAMENTALS OF ALGEBRAIC MODELING, 6th
Edition, this manual shows you how to approach
and solve problems using the same step-by-step
explanations found in your textbook examples.
© 2014, 288pp, Paperback, 9781285420745
© 2014, 176pp, Paperback, 9781285420424
FOR FREITAG’S MATHEMATICS FOR
ELEMENTARY SCHOOL TEACHERS: A
PROCESS APPROACH
TOPICS IN CONTEMPORARY
MATHEMATICS, INTERNATIONAL
EDITION, 10E
Mark A. Freitag
© 2014, 400pp, Paperback, 9781285420233
Ignacio Bello, University of South Florida; Anton Kaul, California
Polytechnic State University; Jack R. Britton, Late of University of
South Florida
Written for the Math for Liberal Arts course, TOPICS IN
CONTEMPORARY MATHEMATICS, 10e, International
Edition helps students see math at work in the world
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138
by presenting problem solving in purposeful and
meaningful contexts. Many of the problems in the text
demonstrate how math relates to subjects—such as
sociology, psychology, business, and technology—that
generally interest students.
NEW TO THIS EDITION
• A Getting Started outline of objectives that
corresponds to the objective heads in the exposition
and in the end-of-section exercise sets has been added
to the beginning of each section to provide students
with a map to navigate each chapter.
• In response to feedback from reviewers, Chapter 5
on Number Theory and the Real Numbers has been
extensively revised and condensed creating a more
comprehensive chapter.
• Throughout the text, applications have been replaced
and revised for currency and student interest.
Exercises now include diverse topics such as the
garbage pizza, gadgets owned by Americans, hacked
passwords, the correlation of healthcare to life
expectancy, the total cost of college, and many more.
• The following topics are now more easily accessible
in the printed book rather than being available
online only: the section on linear programming, right
triangle trigonometry, chaos and fractals, as well as
the chapters on voting and apportionment, and graph
theory.
• Exclusively from Cengage Learning®, Enhanced
WebAssign combines the exceptional mathematics
content that you know and love with the most powerful
online homework solution, WebAssign. Enhanced
WebAssign engages students with immediate
feedback, rich tutorial content, and interactive
e-books that help students to develop a deeper
conceptual understanding of their subject matter.
Online assignments can be built by selecting from
thousands of text-specific problems or supplemented
with problems from any Cengage Learning textbook.
• An Instructor’s Edition is available for the tenth
edition providing instructors with an appendix in the
book that contains answers to all exercises and an
appendix that outlines the exercises that are available
through Enhanced WebAssign.
FEATURES
• Motivational chapter and section opening vignettes
contain applications drawn from a broad range of
fields and introduce students to the techniques and
ideas covered. Applications are further integrated
throughout the text, examples and in the exercise sets
to help students develop the skills to apply problemsolving techniques in the real-world.
• The text incorporates suggestions of AMATYC’s
Standards for Introductory College Mathematics. For
instance, the authors de-emphasize the more abstract
and theoretical aspects of the subject matter, placing
emphasis on promoting the understanding and use of
concepts introduced.
• A unique problem-solving approach emphasized
throughout the text helps students learn the
mathematical skills that will benefit them in their lives
and careers. Using the RSTUV method (Read, Select,
Think, Use, and Verify), this approach guides students
through problems and includes references to similar
problems in the exercise set.
• A strong technology focus motivates students and
shows them different ways in which mathematics can
be applied. Web references and Web It exercises in the
text offer students ways to utilize the Internet as an
educational and creative tool to study mathematical
concepts. Graph It, a feature found in the book
margins, provides step-by-step directions for solving
specific examples using the TI-83 graphing calculator.
CONTENTS
Reasoning. Estimation: A Problem-Solving Tool. Graph
Interpretation: A Problem-Solving Tool. 2. SETS. Sets: A
Problem-Solving Tool. Set Operations. Venn Diagrams.
The Number of Elements in a Set: A Problem-Solving
Tool. Infinite Sets. 3. LOGIC. Statements. Truth
Tables: A Problem-Solving Tool. The Conditional and
the Biconditional. Variations of the Conditional and
Implications. Euler Diagrams: A Problem-Solving
Tool. Truth Tables and Validity of Arguments. 4.
NUMERATION SYSTEMS. Egyptian, Babylonian,
and Roman Numeration Systems. The Hindu-Arabic
(Decimal System). Number Systems with Bases Other
Than 10. Binary Octal, and Hexadecimal Arithmetic. 5.
NUMBER THEORY AND THE REAL NUMBERS. Number
Theory: Primes and Composites. Whole Numbers,
Integers, and Order of Operations. Operations with
Rational Numbers, Expanded and Scientific Notation.
Rationals and Irrationals as Decimals: Percents. Radicals
and Real Numbers. Number Sequences. 6. EQUATIONS,
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INEQUALITIES, AND PROBLEM SOLVING. Solutions
of First-Degree (linear) Sentences. Graphs of Algebraic
Sentences. Sentences Involving Absolute Values.
Quadratic Equations. Modeling and Problem Solving.
Ratio, Proportion, and Variation. 7. FUNCTIONS AND
GRAPHS. Graphing Relations and Functions. Linear
Functions, Relations, and Applications. Slopes and
Equations of a Line. Quadratic Functions and Their
Graphs. Exponential and Logarithmic Functions. Two
Linear Equations in Two Variables. Linear Inequalities.
Linear Programming. 8. GEOMETRY. Points, Lines, Planes,
and Angles. Triangles and Other Polygons. Perimeter and
Circumference. Area Measure and the Pythagorean
Theorem. Volume and Surface Area. Networks, NonEuclidean Geometry, and Topology. Right Triangle
Trigonometry. Chaos and Fractals. 9. MATHEMATICAL
SYSTEMS. Clock and Modular Arithmetic. Abstract
Mathematical Systems: Groups and Fields. Game Theory.
10. COUNTING TECHNIQUES. The Sequential Counting
Principle (SCP): A Problem-Solving Tool. Permutations.
Combinations. Miscellaneous Counting Methods.
11. PROBABILITY. Sample Spaces and Probability.
Counting Techniques and Probability. Computations
of Probabilities. Conditional Probability. Independent
Events. Odds and Mathematical Expectation. 12.
STATISTICS. Sampling, Frequency Distributions, and
Graphs. Measures of Central Tendency: The Mean,
Median, and Mode. Measures of Dispersion: The Range
and Standard Deviation. The Normal Distribution: A
Problem-Solving Tool. Statistical Graphs: A ProblemSolving Tool. Making Predictions: Linear Regression.
Scattergrams and Correlation. 13. YOUR MONEY AND
YOUR MATH. Interest, Taxes, and Discounts. Credit
Cards and Consumer Credit. Annual Percentage Rate
(APR) and the Rule of 78. Buying a House. Investing in
Stocks, Bonds, and Mutual Funds. 14. VOTING AND
APPORTIONMENT. Voting Systems. Voting Objections.
Apportionment Methods. Apportionment Objections.
15. GRAPH THEORY. Introduction to Graph Theory.
Euler Paths and Euler Circuits. Hamilton Paths and
Hamilton Circuits. Trees.
© 2014, 992pp, Paperback, 9781133365808
Mathematics
MULTIVARIABLE CALCULUS, HYBRID
(WITH ENHANCED WEBASSIGN
AND SCIENCE), 7E
Stewart’s CALCULUS texts are widely renowned for
their mathematical precision and accuracy, clarity of
exposition, and outstanding examples and problem
sets. Millions of students worldwide have explored
calculus through Stewart’s trademark style, while
instructors have turned to his approach time and
time again. In the Seventh Edition of MULTIVARIABLE
CALCULUS, Stewart continues to set the standard
com/instructors.
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140
NEW TO THIS EDITION
• TOC change: Chapters 1 and 2 have been combined –
and some material has been moved to an appendix—to
streamline the presentation of these early topics.
problem.
students.
CONTENTS
1 0 . PA R A M E T R I C E Q UAT I O N S A N D P O L A R
COORDINATES. Curves Defined by Parametric
Bézier Curves. Polar Coordinates. Laboratory Project:
Families of Polar Curves. Areas and Lengths in Polar
Coordinates. Conic Sections. Conic Sections in Polar
Coordinates. Review. 11. INFINITE SEQUENCES AND
SERIES. Sequences. Laboratory Project: Logistic
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The Intersection of Three Cylinders . Triple Integrals in
Change of Variables in Multiple Integrals. Review.
16. ECTOR CALCULUS. Vector Fields. Line Integrals.
Divergence Theorem. Summary. Review. 17. SECONDORDER DIFFERENTIAL EQUATIONS. Second-Order
Series Solutions. Review. APPENDIXES. F. Proofs of
Theorems. G. Graphing Calculators and Computers .
H. Complex Numbers. I. Answers to Odd-Numbered
Exercises.
© 2012, 480pp, Paperback, 9781133110835
Early Transcendentals, Hybrid Edition (with Enhanced
WebAssign with eBook Printed Access Card for Multi
Term Math and Science)
Stewart’s CALCULUS: EARLY TRANSCENDENTALS
com/instructors.
NEW TO THIS EDITION
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problem.
students.
CONTENTS
Inverse Functions and Logarithms. Review. 2. LIMITS
AND DERIVATIVES. The Tangent and Velocity Problems.
The Limit of a Function. Calculating Limits Using the
Limit Laws. The Precise Definition of a Limit. Continuity.
Limits at Infinity; Horizontal Asymptotes. Derivatives
and Rates of Change. Writing Project: Early Methods for
3. DIFFERENTIATION RULES. Derivatives of Polynomials
and Exponential Functions. Applied Project: Building a
Better Roller Coaster. The Product and Quotient Rules.
Derivatives of Trigonometric Functions. The Chain Rule.
Applied Project: Where Should a Pilot Start Descent?
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Implicit Differentiation. Derivatives of Logarithmic
Functions. Rates of Change in the Natural and Social
Sciences. Exponential Growth and Decay. Related Rates.
Project: Taylor Polynomials. Hyperbolic Functions.
Derivatives Affect the Shape of a Graph. Indeterminate
Forms and L’Hospital’s Rule. Writing Project: The Origins
Method. Antiderivatives. Review. 5. INTEGRALS.
6. APPLICATIONS OF INTEGRATION. Areas between
Curves. Volume. Volumes by Cylindrical Shells. Work.
Average Value of a Function. Applied Project: Where
to Sit at the Movies. Review. 7. TECHNIQUES OF
INTEGRATION. Integration by Parts. Trigonometric
Integrals. Trigonometric Substitution. Integration of
Rational Functions by Partial Fractions. Strategy for
Project: Which is Faster, Going Up or Coming Down?
Models for Population Growth. Applied Project:
Calculus and Baseball. Linear Equations. Predator-Prey
Systems. Review. 10. PARAMETRIC EQUATIONS AND
POLAR COORDINATES. Curves Defined by Parametric
Bezier Curves. Polar Coordinates. Areas and Lengths
in Polar Coordinates. Conic Sections. Conic Sections in
Polar Coordinates. Review. 11. INFINITE SEQUENCES
AND SERIES. Sequences. Laboratory Project: Logistic
. Binomial Series. Applications of Taylor Polynomials.
APPENDIXES. A. Numbers, Inequalities, and Absolute
of Second-Degree Equations. D. Trigonometry. E. Sigma
Notation. F. Proofs of Theorems. G. The Logarithm
© 2012, 720pp, Paperback, 9781111426705
1, 7E
www.cengageasia.com
144
NEW TO THIS EDITION
problem.
students.
FEATURES
CONTENTS
Tangents.The Derivative as a Function. Differentiation
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the Natural and Social Sciences. Related Rates.
Project: Taylor Polynomials. Review. Problems Plus. 3.
APPLICATIONS OF DIFFERENTIATION.
Maximum and Minimum Values. Applied Project:
The Calculus of Rainbows. The Mean Value Theorem.
How Derivatives Affect the Shape of a Graph. Limits
at Infinity; Horizontal Asymptotes. Summary of Curve
Optimization Problems. Applied Project: The Shape
of a Can. Newton’s Method. Antiderivatives. Review.
Problems Plus. 4. INTEGRALS. Areas and Distances. The
The Gini Index. Volumes. Volumes by Cylindrical Shells.
Work. Average Value of a Function. Applied Project:
Calculus and Baseball. Review. Problems Plus. Appendix
A: Intervals, Inequalities, and Absolute Values.
Appendix B: Coordinate Geometry and Lines. Appendix
C: Graphs of Second-Degree Equations. Appendix D:
Trigonometry. Appendix E: Sigma Notation. Appendix F:
Proofs of Theorems. Appendix G: Graphing Calculators
and Computers. Appendix H: Complex Numbers.
Appendix I: Answers to Odd-Numbered Exercises.
© 2012, 504pp, Hardback, 9780538497848
2, 7E
NEW TO THIS EDITION
problem.
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146
students.
FEATURES
CONTENTS
4. INTEGRALS. Areas and Distances. The Definite
Integral. Discovery Project: Area Functions. The
The Gini Index. Volume. Volumes by Cylindrical Shells.
Work. Average Value of a Function. Review. Problems
Plus. 6. INVERSE FUNCTIONS: Exponential, Logarithmic,
and Inverse Trigonometric Functions. Inverse Functions.
Problems Plus. 7. TECHNIQUES OF INTEGRATION.
Integration by Parts. Trigonometric Integrals.
Trigonometric Substitution. Integration of Rational
Functions by Partial Fractions. Strategy for Integration.
Applied Project: Calculus and Baseball. Integration
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© 2012, 648pp, Hardback, 9780538497855
Mathematics for Education
MATHEMATICAL PRACTICES,
MATHEMATICS FOR TEACHERS
Activities, Models, and Real-Life Examples
To become a successful mathematics teacher, you
must first become a successful mathematics student.
Ron Larson and Robyn Silbey’s first edition of
MATHEMATICAL PRACTICES, MATHEMATICS FOR
TEACHERS: ACTIVITIES, MODELS, AND REAL-LIFE
EXAMPLES helps students aspire to be the best
educators they can be. Peruse the book and you’ll find
Classroom Activities integrated into each section;
modeling Examples that ask students how to model
math concepts in the classroom; real-life Examples
that model math concepts students will encounter
in their everyday lives; and finally, to frame Ron and
Robyn’s approach, Common Core State Standards
relevant to each lesson to provide future teachers with
the knowledge of what their students should know at
various grade levels.
FEATURES
• An Activity, similar to what can be found in an
elementary mathematics textbook, appears before
every lesson. These can be completed as part of the
coursework or simply used as a motivational tool
for the lesson because they cover topics within the
lessons but are not prerequisites of the lessons.
• Featured in the margin, Standards are grouped
by grade levels (K-2, 3-5, and 6-8) and appear at
the beginning of each lesson. Domain and cluster
statements indicate the area of the Common Core
State Standards that pertain to the lesson.
• Learning Objectives appear at the beginning of each
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148
lesson and identify the concepts taught in the lesson.
• Real-Life Examples show the math concepts in a reallife situation and are indicated by the green example
head graphic.
• Modeling Examples show how to use manipulatives,
fraction strips, number line models, area models, set
models, and so on, to model math concepts in the
classroom. These are indicated by the orange example
head graphic.
• Mathematical Practices appear throughout each
lesson and highlight the connection between the
Examples and the processes and proficiencies
identified in the Common Core Math Practices.
• Classroom Tips appear in the margin throughout
each lesson, and they provide additional information
for a teacher to use in the elementary/middle school
classroom such as teaching suggestions, problemsolving methods, classroom motivators (activities),
what students learn in doing the example, additional
information about the example, or differing definitions
(e.g., U.S. versus European).
• Writing a Solution Key Exercises develops the
elementary/middle school teacher’s ability to write a
rubric for grading students’ work and appear in every
lesson exercise set.
• A Grading the Activity Exercise appears in every lesson
exercise set and provides the elementary/middle
school teacher practice in grading an assignment.
• In Your Classroom Exercises are application/concept
exercises similar to the ones found in classroom
textbooks. These appear in every lesson exercise set
and include connections on how to teach the concept
in the classroom.
CONTENTS
1. PROBLEM SOLVING. Problem-Solving Strategies.
More Problem-Solving Strategies. Reasoning and
Logic. Chapter Summary, Review Exercises, and
Chapter Test. 2. SETS AND NUMERAL SYSTEMS. Sets.
Whole Numbers. Number Lines and Numeral Systems.
Chapter Summary, Review Exercises, and Chapter
Test. 3. OPERATIONS WITH WHOLE NUMBERS.
Adding Whole Numbers. Subtracting Whole Numbers.
Multiplying Whole Numbers. Dividing Whole Numbers.
Test. 4. EXPONENTS AND ESTIMATION. Mental
Math and Estimation. Exponents. Order of Operations.
Test. 5. NUMBER THEORY. Divisibility Tests. Primes
and Composites. Greatest Common Factor and Least
Common Multiple. Chapter Summary, Review Exercises,
and Chapter Test. 6. FRACTIONS. Fractions. Adding
and Subtracting Fractions. Multiplying and Dividing
Fractions. Ratio and Proportion. Chapter Summary,
Review Exercises, and Chapter Test. 7. DECIMALS
AND PERCENTS. Decimals. Adding and Subtracting
Decimals. Multiplying and Dividing Decimals. Percents.
Test. 8. INTEGERS. Integers. Adding and Subtracting
Integers. Multiplying and Dividing Integers. Chapter
Summary, Review Exercises, and Chapter Test. 9.
RATIONAL NUMBERS AND REAL NUMBERS. Rational
Numbers. Solving Equations Using Rational Numbers.
Real Numbers. Chapter Summary, Review Exercises,
and Chapter Test. 10. POLYGONS AND POLYHEDRA.
Triangles. Quadrilaterals. Polygons and Tessellations.
Polyhedra. Chapter Summary, Review Exercises, and
Chapter Test. 11. MEASUREMENT. Standard and
Nonstandard Units. Perimeter and Area of Polygons.
Surface Area of a Polyhedron. Volume of a Polyhedron.
Chapter Summary, Review Exercises, and Chapter Test.
12. CIRCLES AND CIRCULAR SOLIDS. Circumference
and Area of Circles. Surface Area of Circular Solids.
Volume of Circular Solids. Chapter Summary, Review
Exercises, and Chapter Test. 13. CONGRUENCE AND
SIMILARITY. Congruence of Triangles. Similarity.
Construction Techniques. Chapter Summary, Review
Exercises, and Chapter Test. 14. TRANSFORMATIONS.
Translations and Rotations. Reflections. Dilations and
Scale Drawings. Chapter Summary, Review Exercises,
and Chapter Test. 15. COORDINATE GEOMETRY.
The Coordinate Plane and Distance. Slope of a Line.
Equations in Two Variables. Functions. Chapter
Summary, Review Exercises, and Chapter Test. 16.
PROBABILITY. Introduction to Probability. Counting
Techniques. Independent and Dependent Events.
Expected Value. Chapter Summary, Review Exercises,
and Chapter Test. 17. STATISTICS. Graphs of Data.
Measure of Central Tendency. Variation. Other Types
of Graphs. Chapter Summary, Review Exercises, and
Chapter Test. Answers. Index.
© 2015, 784pp, Hardback, 9781285447100
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elementary and middle-grades teachers can better
understand the concepts and processes behind the
mathematics they will teach. In short, the book focuses
on the “why” behind the mathematics in addition to
the “how.”
FEATURES
SCHOOL TEACHERS
A Process Approach
Mark A. Freitag
Freitag’s MATHEMATICS FOR ELEMENTARY SCHOOL
TEACHERS: A PROCESS APPROACH was developed
using the five Content Standards from the NCTM
Principles and Standards for School Mathematics, and
the Common Core State Standards for Mathematics.
Traditionally, textbooks for pre-service elementary
teachers have focused on problem solving. However,
problem solving is not the only process through
which mathematics is learned. It is also learned
through mathematical reasoning, communication,
representation, and connections. Recent trends in
mathematics education now advocate implementing
all five processes as a vital part of learning and doing
mathematics. Consequently, pre-serve teachers need
to have concrete experiences with these processes
that they will be required to teach. The goal of this
textbook is to treat each of the processes equitably
by using an approach in which the five processes
serve as the central pedagogical theme. Most of the
examples, exercises, and activities are designed to
either model the processes or to have students become
directly engaged in working with them. By doing so,
pre-service teachers will not only come to understand
the different processes, but also appreciate them as
an integral to learning and doing mathematics. If this
broader view can be instilled in pre-service teachers,
they are more likely to give their students a more
well-rounded and holistic view of mathematics once
they enter the classroom. The content of the book is
directly related to the mathematics that is taught in
grades K – 8. The purpose is not to reteach elementary
mathematics. Rather, the intent is to look at the content
from a theoretical or generalized point of view, so that
• The FIVE MATHEMATICAL PROCESSES identified
in the NCTM Principles and Standards are used as
a framework for this textbook through which the
content is stated, explained, demonstrated, and
engaged. This “process approach” can be seen in
the EXAMPLES and each process is identified by the
appropriate icon.
• An OPENING PROBLEM appears on the first page
of each chapter and provides an application of the
upcoming content. The problems can be answered by
using specific content contained within the chapter.
Answers are given directly before the Chapter Review.
• GETTING STARTED introduces each chapter and
relates the mathematical content of the chapter
to how the concepts are used in an elementary
classroom.
• CLASSROOM LEARNING OBJECTIVES are tables
that feature specific learning outcomes from the K - 8
classroom and are adapted from the Common Core
State Standards for Mathematics. Each table lists the
learning objectives that are relevant to the content
of the chapter and then indicates the grade level at
which the objective is most likely to be taught.
• DEFINITIONS and THEOREMS are clearly identified.
• STUDENT PAGES from elementary textbooks provide
further connections to the elementary classroom by
demonstrating how concepts are often presented to
elementary students.
• HISTORICAL NOTES provide a context for the content
by identifying historical figures or occurrences
relevant to the content of the section.
• CHECK YOUR UNDERSTANDING in-text quizzes
provide an opportunity for students to monitor their
understanding of the content through quick skillcheck exercises. Answers to all items are given after
the chapter review exercises.
• TALK ABOUT IT questions are included in Check Your
Understanding and give students the opportunity to
discuss the content they have just learned. You can
use these questions to start a lecture or give them to
small groups of students to respond to.
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• ACTIVITIES provide students with an opportunity to
engage the material of each subsection by solving
a problem often using a hands-on manipulative.
Activities in the book are designed to take up minimal
classroom time usually taking only five to ten minutes.
Answers to all items are given after the chapter review
exercises.
CONTENTS
1. MATHEMATICAL PROCESSES. Getting Started:
The NCTM Process Standards. Communication
Through Mathematical Representations. Inductive
Reasoning and Patterns. Deductive Reasoning and
Proof. Mathematical Problem Solving. Problem Solving
with Different Strategies. Chapter 1 Review. Answers
to Check Your Understandings and Activities. 2.
SETS. Getting Started: Sets in the Classroom. Set
Basics. Set Operations. Chapter 2 Review. Answers to
3. NUMBERS AND NUMERATION. Getting Started:
Numbers and Numeration in the Classroom. A
Brief History of Numeration. The Hindu-Arabic or
Decimal System. Other Base Numeration Systems.
Chapters 1-3. 4. WHOLE-NUMBER COMPUTATION.
Getting Started: Whole-Number Computation in the
Classroom. Understanding Whole-Number Addition and
Subtraction. Adding and Subtracting Large Numbers.
Understanding Whole-Number Multiplication and
Division. Multiplying and Dividing Large Numbers.
Computation in Base b. Chapter 4 Review. Answers to
5. BASIC NUMBER THEORY. Getting Started: Number
Theory in the Classroom. Divisibility, Primes, and
Composites. Greatest Common Factors and Least
Common Multiples. Modular and Clock Arithmetic.
Understandings and Activities. 6. THE INTEGERS.
Getting Started: Integers in the Classroom. Integer
Basics, Addition, and Subtraction. Integer Multiplication
and Division. Chapter 6 Review. Answers to Chapter 6
Check Your Understandings and Activities. Reviewing
the Big Ideas Chapters 4-6. 7. FRACTIONS AND THE
RATIONAL NUMBERS. Getting Started: Fractions and
the Rational Numbers in the Classroom. Fractions and
the Set of Rational Numbers. Adding and Subtracting
Rational Numbers. Multiplying and Dividing Rational
Numbers. Chapter 7 Review. Answers to Check Your
Understandings and Activities. 8. DECIMALS, REAL
NUMBERS, AND PROPORTIONAL REASONING.
Getting Started: Decimals and Proportional Reasoning in
the Classroom. Decimals and the Real Numbers. Decimal
and Real Number Operations. Proportional Reasoning.
Percents. Chapter 8 Review. Answers to Chapter 8 Check
Your Understandings and Activities. 9. ALGEBRAIC
THINKING. Getting Started: Algebraic Thinking in the
Classroom. Numerical Sequences. Functions and Their
Representations. Linear Functions and Constant Change.
Solving Equations and Inequalities. Algebraic Thinking
and Mathematical Modeling. Chapter 9 Review. Answers
to Chapter 9 Check You Understandings and Activities.
Reviewing the Big Ideas Chapters 7-9. 10. GEOMETRICAL
SHAPES. Getting Started: Geometrical Shapes in
the Classroom. Lines, Planes, and Angles. Triangles.
Quadrilaterals, Polynomials, and Circles. Geometric
Surfaces and Solids. Chapter 10 Review. Answers to
Chapter 10 Check Your Understandings and Activities. 11.
CONGRUENCE, SIMILARITY, AND CONSTRUCTIONS.
Getting Started: Congruence, Constructions, and
Similarity in the Classroom. Congruent Shapes. Similar
Shapes. Basic Geometrical Constructions. Constructing
Shapes. Chapter 11 Review. Answers to Chapter
11 Check Your Understandings and Activities. 12.
COORDINATE AND TRANSFORMATION GEOMETRY
IN THE CLASSROOM. Getting Started: Coordinate and
Transformation Geometry in the Classroom. Coordinate
Geometry. Transformations. Congruence, Similarity, and
Symmetry with Transformations. Geometric Patterns.
Understandings and Activities. Reviewing the Big
Ideas Chapters 10-12. 13. MEASUREMENT. Getting
Started: Measurement in the Classroom. Length and
the Measurement Process. Perimeter and Area. Surface
Area. Volume. Other Measures. Chapter 13 Review.
Answers to Chapter 13 Check Your Understandings and
Activities. 14. STATISTICAL THINKING. Getting Started:
Statistical Thinking in the Classroom. Formulating
Questions and Collecting Data. Representing and
Analyzing Data with Statistical Graphs. Representing
and Analyzing Data with Descriptive Statistics.
Abuse of Statistics. Chapter 14 Review. Answers
to Chapter 14 Check Your Understandings and
Activities. 15. PROBABILITY. Getting Started: Probability
in the Classroom. Experimental Probability and
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Making Predictions from Data. Theoretical Probability.
Conditional and Geometric Probability, Odds, and
Expected Value. Counting Techniques and Probability.
Chapters 13-15.
© 2014, 1104pp, Hardback, 9780618610082
SCHOOL TEACHERS, INTERNATIONAL
EDITION, 5E
Tom Bassarear, Keene State College
MATHEMATICS FOR ELEMENTARY SCHOOL
TEACHERS, 5E, International Edition offers future
teachers a comprehensive mathematics course
designed to foster concept development through
examples, investigations, and explorations. In this
text, intended for the one- or two-semester course
required of Education majors, Bassarear demonstrates
that there are many paths to solving a problem, and
sometimes problems have more than one solution.
The author presents real-world problems—problems
that require active learning in a method similar to how
archaeologists explore an archaeological find: they
carefully uncover the site, slowly revealing more and
more of the structure. Visual icons throughout the main
text allow instructors to easily connect content to the
hands-on activities in the corresponding Explorations
Manual. With this exposure, future teachers will be
better able to assess student needs using diverse
approaches.
NEW TO THIS EDITION
• The new edition features improved visual
representations of concepts, adding diagrams and
illustrations.
• Updated Instructor Resource Manual! Now with
additional answers to the exercises in the Explorations
Manual.
• NEW 4-color design. 2-color design upgraded to
4-color to better present the author’s approach to
teaching.
• NEW chapter openers outline the sections within the
chapter and the Investigations that appear within
the section.
• NEW Looking Back feature appears before the
Chapter Summary in each chapter and includes a
brief discussion about problem solving, reasoning,
connections and relationships, unit, and equivalence
as it applies to each chapter.
• Updated! The 4e content for chapter 1 has been
rearranged to reflect 4 sections instead of the 7 found
in the 4e.
• NEW component has been added to the Classroom
Connection feature in which examples of actual
assignments appropriate for elementary math
students are illustrated. In addition to this, questions
in the exercise sets have been identified as a part
of Classroom Connection, along with margin boxes
throughout the text. An apple icon identifies and ties
in all three parts of this feature.
• NEW exercises have been added to most chapters.
NEW sub-categories have been added to the exercises
and they have been rearranged breaking these
down into these three topics for most chapters:
Basic, Deepening Your Understanding, and From
Standardized Assessments.
• NEW From Standardized Assessments exercises
appear as a subset in the exercise sets in most
chapters. Since they are actual questions that appear
on standardized assessments, these give students
a sense of the high-cognitive level of questions to
expect on national assessments.
• NEW Investigations have been added to most chapters
and have been renumbered to increase accessibility.
Multiple strategies occur after many Investigations
allowing students to analyze numerous approaches
to solving problems.
CONTENTS
1. FOUNDATIONS FOR LEARNING MATHEMATICS. 1.1
Getting Started and Problem Solving. Investigation 1.1a
Pigs and Chickens. Investigation 1.1b A Coin Problem.
1.2 Patterns and Communication. Investigation 1.2a
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Sequences and Patterns. Investigation 1.2b Patterns in
Multiplying by 11. Investigation 1.2c Pascal’s Triangle.
Investigation 1.2d Communicating Patterns in a Magic
Square. 1.3 Reasoning and Proof. Investigation 1.3a Does
Your Answer Make Sense? Investigation 1.3b Inductive
Thinking With Fractions. Investigation 1.3c Deductive
Reasoning and Venn Diagrams. Investigation 1.3d Why
is the Sum of Two Even Numbers an Even Number.
Investigation 1.3e Darts, Proof, and Communication.
Investigation 1.3f The Nine Dots Problem. Investigation
1.3g How Many Games in the Tournament?. 1.4
Representation and Connections. Investigation 1.4a
How Long Will it Take the Frog to Get Out of the Well?.
Investigation 1.4b How Many Pieces of Wire?. Looking
Back on Chapter 1. Chapter 1 Summary. Chapter 1
Review Exercises. 2. FUNDAMENTAL CONCEPTS. 2.1
Sets. Investigation 2.1a Classifying Quadrilaterals.
Investigation 2.1b Describing Sets. Investigation 2.1c
How Many Subsets?. Investigation 2.1d Translating
Among Representations. Investigation 2.1e Finding
Information from Venn Diagrams. 2.2 Algebraic
Thinking. Investigation 2.2a A Variable by Any Other
Name is Still a Variable. Investigation 2.2b Baby-sitting.
Investigation 2.2c Choosing Between Functions.
Investigation 2.2d Matching Graphs to Situations.
Investigation 2.2e Developing “Graph Sense.” .
Investigation 2.2f Looking for Generalizations.
Investigation 2.2g How Many Dots?. 2.3 Numeration.
Investigation 2.3a Relative Magnitude of Numbers.
Investigation 2.3b What if Our System was Based on
One Hand?. Investigation 2.3c How Well do you
Understand Base Five?. Investigation 2.3d Base Sixteen.
Looking Back on Chapter 2. Chapter 2 Summary.
Chapter 2 Review Exercises. 3. THE FOUR
FUNDAMENTAL OPERATIONS OF ARITHMETIC. 3.1
Understanding Addition. Investigation 3.1a Pattern in
the Addition Table. Investigation 3.1b Mental Addition.
3.1c Children’s Strategirs for Adding Large Numbers.
Investigations 3.1d An Alternative Algorithm.
Investigation 3.1e Addition in Base Five. Investigation
3.1f Children’s Mistakes. Investigation 3.1g What Was
the Total Attendance?. Investigation 3.1h Estimating by
Making Compatible Numbers. Investigation 3.1i Number
Sense with Addition. 3.2 Understanding Subtraction.
Investigation 3.2a Mental Subtraction. Investigation
3.2b Children’s Strategies for Subtraction with Large
Numbers. Investigation 3.2c An Alternative Algorithm.
Investigation 3.2d Children’s Mistakes in Subtraction.
Investigation 3.2e Rough and Best Estimations with
Subtraction. Investigation 3.2f Number Sense with
Subtraction. 3.3 Understanding Multiplication.
Investigation 3.3a A Pattern in the Multiplication Table.
Investigation 3.3b Mental Multiplication. Investigation
3.3c An Alternative Algorithm. Investigation 3.3d Why
Does the Trick for Multiplying by 11 Work?. Investigation
3.3e Multiplication in Base Five. Investigation 3.3f
Children’s Mistakes in Multiplication. Investigation 3.3g
Developing Estimation Strategies for Multiplication.
Investigation 3.3h Using Various Strategies in a Real-life
Multiplication Situation. Investigation 3.3i Number
Sense with Multiplication. 3.4 Understanding Division.
Investigation 3.4a Mental Division. Investigation 3.4b
Understanding Division Algorithms. Investigation 3.4c
The Scaffolding Algorithm. Investigation 3.4d Children’s
Mistakes in Division. Investigation 3.4e Estimates with
Division. Investigation 3.4f Number Sense with Division.
Investigation 3.4g Applying Models to a Real-life
Situation. Investigation 3.4h Operation Sense. Looking
Review Exercises. 4. NUMBER THEORY. 4.1 Divisibility
and Related Concepts. Investigation 4.1a Interesting
Dates. Investigation 4.1b Patterns in Odd and Even
Numbers. Investigation 4.1c Understanding Divisibility
Relationships. Investigation 4.1d Determining the Truth
of an Inverse Statement. Investigation 4.1e
Understanding Why the Divisibility Rule for 3 Works.
Investigation 4.1f Divisibility by 4 and 8. Investigation
4.1g Creating a Divisibility Rule for 12. 4.2 Prime and
Composite Numbers. Investigation 4.2a The Sieve of
Eratosthenes. Investigation 4.2b Numbers with
Personalities: Perfect and Other Numbers. 4.3 Greatest
Common Factor and Least Common Multiple.
Investigation 4.3a Cutting Squares Using Number
Theory Concepts. Investigation 4.3b Methods for
Finding the GCF. Investigation 4.3c Relationships
Between the GCF and the LCM. Investigation 4.3d
Going Deeper into the GCF and LCM. Looking Back on
Chapter 4. Chapter 4 Summary. Chapter 4 Review
Exercises. 5. EXTENDING THE NUMBER SYSTEM. 5.1
Integers. Investigation 5.1a Subtraction with Integers.
Investigation 5.1b The Product of a Positive and a
Negative Number. 5.2 Fractions and Rational Numbers.
Investigation 5.2a Rational Number Contexts: What
Does 3/4 Mean?. Investigation 5.2b Wholes and Units:
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Sharing Brownies. Investigation 5.2c Unitizing.
Investigation 5.2d Fund-Raising and Thermometers.
Investigation 5.2e Partitioning with Number Line
Models. Investigation 5.2f Partitioning with Area
Models. Investigation 5.2g Partitioning with Discrete
Models. Investigation 5.2h Determining an Appropriate
Representation. Investigation 5.2i Sharing Cooking.
Investigation 5.2j Ordering Rational Numbers.
Investigation 5.2k Estimating with Fractions. 5.3
Understanding Operations with Fractions. Investigation
5.3a Using Fraction Models to Understand Addition of
Fractions. Investigation 5.3b Connecting Improper
Fractions and Mixed Numbers. Investigation 5.3c
Estimation and Mental Arithmetic: Sums and Differences
of Fractions. Investigation 5.3d Estimating sums and
Differences with Fractions. Investigation 5.3e
Understanding Multiplication of Rational Numbers.
Investigation 5.3f Division of Rational Numbers.
Investigation 5.3g Estimating Products and Quotients.
Investigation 5.3h When Did He Run Out of Gas?.
Investigation 5.3i They’ve Lost Their Faculty!. 5.4 Beyond
Integers and Fractions: Decimals, Exponents, and Real
Numbers. Investigation 5.4a Base 10 Blocks and
Decimals. Investigation 5.4b When Two Decimals Are
Equal. Investigation 5.4c When is the Zero Necessary
and When is it Optional?. Investigation 5.4d Connecting
Decimals and Fractions. Investigation 5.4e Ordering
Decimals. Investigation 5.4f Rounding with Decimals.
Investigation 5.4g Decimals and Language. Investigation
5.4h Decimal Sense: Grocery Store Estimates.
Investigation 5.4i Decimal Sense: How Much Will the
Project Cost?. Investigation 5.4j How Long Will She
Run?. Investigation 5.4k Exponents and Bacteria.
Investigation 5.4l Scientific Notation: How Far is a LightYear?. Investigation 5.4m Square Roots. Looking Back
on Chapter 5. Chapter 5 Summary. Chapter 5 Review
Exercises. 6. PROPORTIONAL REASONING. 6.1 Ratio
and Proportion. Investigation 6.1a Unit Pricing—Is
Bigger Always Cheaper?. Investigation 6.1b How Many
Trees Will be Saved?. Investigation 6.1c How Much
Money Will the Trip Cost?. Investigation 6.1d
Reinterpreting Old Problems. Investigation 6.1e Using
Estimation with Ratios. Investigation 6.1f Comparing
Rates. Investigation 6.1g Is the School on Target?.
Investigation 6.1h Finding Information from Maps.
Investigation 6.1i From Raw Numbers to Rates.
Investigation 6.1j How Much Does That Extra Light
Cost?. 6.2 Percents. Investigation 6.2a Who’s the Better
Free-Throw Shooter?. Investigation 6.2b Understanding
a Newspaper Article. Investigation 6.2c Buying a House.
Investigation 6.2d Sale?. Investigation 6.2e What is a
Fair Reason?. Investigation 6.2f How Much Money Did
the Bookstore Pay for the Textbook?. Investigation 6.2g
The Copying Machine. Investigation 6.2h 132% Increase.
Investigation 6.2i Saving for College. Investigation 6.2j
How Much Does that Credit Card Cost You?. Looking
Review Exercises. 7. UNCERTAINTY: DATA AND
CHANCE. 7.1 The Process of Collecting and Analyzing
Data. Investigation 7.1a What is Your Favorite Sport?.
Investigation 7.1b How Many Siblings do you Have?.
Investigation 7.1c Going Beyond a Computational Sense
of Average. Investigation 7.1d How Many Peanuts Can
You Hold in One Hand?. Investigation 7.1e How Long
Does it Take Students to Finish the Final Exam?
Investigation 7.1f Videocassette Recorders. Investigation
7.1g Fatal Crashes. Investigation 7.1h Hitting the Books.
7.2 Going Beyond the Basics. Investigation 7.2a How
Many More Peanuts Can Adults Hold Than Children?.
Investigation 7.2b Scores on a Test. Investigation 7.2c
Which Battery do You Buy?. Investigation 7.2d
Understanding Standard Deviation. Investigation 7.2e
Analyzing Standardized Test Scores. Investigation 7.2f
How Long Should the Tire be Guaranteed?. Investigation
7.2g Comparing Students in Three Countries.
Investigation 7.2h Grade Point Average. Investigation
7.2i What Does Amy Need to Bring Her GPA up to 2.5?.
7.3 Concepts Related to Chance. Investigation 7.3a
Probability of Having 2 Boys and 2 Girls. Investigation
7.3b Probability of Having 3 Boys and 2 Girls. Investigation
7.3c Probability of Having at Least 1 Girl. Investigation
7.3d 50-50 Chance of Passing. Investigation 7.3e What
is the Probability of Rolling a 7?. Investigation 7.3f What
is the Probability of Rolling a 13 with 3 Dice?. Investigation
7.3g “The Lady of the Tiger. Investigation 7.3h Gumballs.
Investigation 7.3i Is this a Fair Game?. Investigation 7.3j
What about this Game?. Investigation 7.3k Insurance
Rates. 7.4 Counting and Chance. Investigation 7.4a How
Many Ways to Take the Picture?. Investigation 7.4b How
Many Different Election Outcomes?. Investigation 7.4c
How Many Outcomes this Time?. Investigation 7.4d
Pick a Card, Any Card!. Investigation 7.4e So You Think
You’re Going to Win the Lottery?. Looking Back on
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Exercises. 8. GEOMETRY AS SHAPE. 8.1 Basic Ideas and
Building Blocks. Investigation 8.1a Playing Tetris.
Investigation 8.1b Different Objects and Their Functions.
Investigation 8.1c Point, Line, and Plane. Investigation
8.1d Measuring Angles. 8.2 Two-Dimensional Figures.
Investigation 8.2a Recreating Shapes from Memory.
Investigation 8.2b All the Attributes. Investigation 8.2c
Classifying Figures. Investigations 8.2d Why Triangles
are so Important. Investigation 8.2e Classifying
Triangles. Investigation 8.2f Triangles and Venn
Diagrams. Investigation 8.2g Congruence with Triangles.
Investigation 8.2h Quadrilaterals and Attributes.
Investigation 8.2i Challenges. Investigation 8.2j
Relationships Among Quadrilaterals. Investigation 8.2k
Sum of Interior Angles of a Polygon. Investigation 8.2l
What are my Coordinates?. Investigation 8.2m
Understanding the Distance Formula. Investigation 8.2n
The Opposite Sides of a Parallelogram are Congruent.
Investigation 8.2o Midpoints of any Quadrilateral. 8.3
Three-Dimensional Figures. Investigation 8.3a What do
you See?. Investigation 8.3b Connecting Polygons to
Polyhedra. Investigation 8.3c Features of ThreeDimensional Objects. Investigation 8.3d Prisms and
Pyramids. Investigation 8.3e Different Views of a
Building. Investigation 8.3f Isometric Drawings.
Investigation 8.3g Cross Sections. Investigation 8.3h
Nets. Looking Back on Chapter 8. Chapter 8 Summary.
Chapter 8 Review Exercises. 9. GEOMETRY AS
T R A N S FO R M I N G S H A P E S . 9 . 1 Co n g r u e n c e
Transformations. Investigation 9.1a Understanding
Translations. Investigation 9.1b Understanding
Reflections. Investigation 9.1c Understanding Rotations.
Investigation 9.1d Understanding Translations,
Reflections, and Rotations. Investigation 9.1e Connecting
Transformations. Investigation 9.1f Transformations and
Art. 9.2 Symmetry and Tessellations. Investigation 9.2a
Reflection and Rotation Symmetry in Triangles.
Investigation 9.2b Reflection and Rotation Symmetry in
Quadrilaterals. Investigation 9.2c Reflection and
Rotation Symmetry in Other Figures. Investigation 9.2d
Letters of the Alphabet and Symmetry. Investigation
9.2e Patterns. Investigation 9.2f Symmetries of Strip
Patterns. Investigation 9.2g Analyzing Brick Patterns.
Investigation 9.2h Which Triangles Tessellate?.
Investigation 9.2i Which Regular Polygons Tessellate?.
Investigation 9.2j Tessellating Trapezoids. Investigation
9.2k More Tessellating Polygons. Investigation 9.2l
Generating Pictures Through Transformations. 9.3
Similarity. Investigation 9.3a Understanding Similarity.
Investigation 9.3b Similarity Using an Artistic
Perspective. Investigation 9.3c Using Coordinate
Geometry to Understand Similarity. Looking Back on
Exercises. 10. GEOMETRY AS MEASUREMENT. 10.1
Systems of Measurement. Investigation 10.1a Developing
Metric Sense. Investigation 10.1b Converting Among
Units in the Metric System. 10.2 Perimeter and Area.
Investigation 10.2a What is the Length of the Arc?.
Investigation 10.2b Converting Units of Area.
Investigation 10.2c Using the Pythagorean Theorem.
Investigation 10.2d Understanding the Area Formulas
for Circles. Investigation 10.2e A 16-Inch Pizza Versus
an 8-Inch Pizza. Investigation 10.2f How Big in the
Footprint?. Investigation 10.2g Making a Fence with
Maximum Area. 10.3 Surface Area and Volume.
Investigation 10.3a Are Their Picture Misleading?.
Investigation 10.3b Finding the Volume of a Hollow Box.
Investigation 10.3c Surface Area and Volume. Looking
Review Exercises.
© 2012, 784pp, Paperback, 9781111578657
SCHOOL TEACHERS, INTERNATIONAL
EDITION
Ricardo Fierro, California State University, San Marcos
MATHEMATICS FOR ELEMENTARY SCHOOL
TEACHERS, International Edition is designed to give
prospective elementary school teachers a profound
understanding of the mathematical content they are
expected to know and be able to teach. Chapters
integrate and are built around the NCTM Standards and
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155
Expectations, the new Common Core Standards and
highlights from research literature. As a result students
follow a precise learning path that begins with the
“Where Are We Going?” Chapter Openers to the Yellow
Markers showing the process standards throughout the
context, to the Concept Maps, to the Section Problem
Sets with their “refreshers” of process standards as
directions, to the Chapter Organizer with Learning
Outcomes, and finally, conclude at the Chapter Test
with their overarching Learning Outcomes. The author
steadfastly guides the student through the course and
the many concepts from the content standards using
the process standards and Learning Outcomes to teach
students to become better students and hence better
prospective teachers.
FEATURES
• The relevant NATIONAL COUNCIL OF TEACHERS
OF MATHEMATICS (NCTM) PRINCIPLES AND
STANDARDS OF MATHEMATICS (2000) appear in the
exposition. These Principles and Standards that are
adopted by the NCTM represent the most significant
and influential collaboration among educators to
improve mathematics education at a national level.
It is the gold standard used by many states to meet
the No Child Left Behind Act of 2001 that requires
challenging standards for grades 3-8 mathematics
and annual assessment.
• COMMON CORE STATE STANDARDS (CCSS) are
also referenced in the text. The CCSS are “aligned
with college and work expectations; build upon
strengths and lessons of current state standards;
and include rigorous content and application of
knowledge through high-order skills.” The idea behind
CCSS is that “Common standards will help ensure
that students are receiving a high quality education
consistently, from school to school and state to state.
Common standards will provide a greater opportunity
to share experiences and best practices within and
across states that will improve our ability to best
serve the needs of students.” States that voluntarily
accept the Common Core standards would eliminate
their own state standards.
• In addition to the NCTM Content Standards, there
are five NCTM PROCESS STANDARDS: Problem
Solving, Reasoning and Proof, Communication,
Connections, and Representation. The Process
Standards are integrated by an icon throughout the
text that highlights where the standard appears and
specifies which standard is being used. In addition,
the homework problems are categorized by the
applicable Process Standard to give prospective
teachers a chance to explore a particular process in
more depth and improve their perception of problems
that assess the process. This unique differentiation is
important because the processes connect students to
the teaching and learning of mathematical content.
• “Where Are We Going?” CHAPTER OPENERS identify
upcoming topics and help to place the material to be
presented in a manageable context.
• Unique CONCEPT MAPS visually recap ideas and
help you synthesize the material by showing how key
mathematical ideas are related.
• PreK–8 problems from actual elementary math
textbooks appear in CLASSROOM CONNECTIONS—
with explanations—giving prospective teachers
another opportunity to see that the topics they are
studying are relevant to the elementary curriculum.
Actual pages from these textbooks are also shown as
appropriate to provide context.
• A VARIETY OF HOMEWORK PROBLEMS appears at
the end of each section and chapter to increase interest
and flexibility in teaching. They reflect the content
and processes that prospective elementary school
teachers need to know and teach. They support the
national trend of integrating instruction, assessment,
content standards, and process standards.
• A VARIETY OF HOMEWORK PROBLEMS appears at
the end of each section and chapter to increase interest
and flexibility in teaching. They reflect the content
and processes that prospective elementary school
teachers need to know and teach. They support the
national trend of integrating instruction, assessment,
content standards, and process standards.
• A CHAPTER ORGANIZER grid summarizes key
learning outcomes and ideas presented in the
chapter followed by a set of review questions which
offers a variety of additional problems to reinforce
students’ learning. The chapter test is organized
by learning outcomes so students connect the link
between objectives and concepts, and how knowledge
is acquired which reflects the national trend of
integrating instruction, assessment, and NCTM
content and process standards.
• The National Center for Education Statistics
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156
administers a nationwide standardized test—National
Assessment of Educational Progress (NAEP)—to a
pooled random sample of fourth, eighth, and twelfth
graders. NAEP has released selective questions,
called RELEASED ITEMS in the textbook, from various
fourth- and eighth-grade tests to help improve
student learning. A sampling of these questions
appear in the text, as do questions from state tests,
to illustrate what elementary students will see in
standardized assessment tests.
CONTENTS
1. PROBLEM SOLVING AND REASONING. Patterns
and Inductive Reasoning. Problem-Solving Strategies.
Algebra and Problem Solving. Logic and Deductive
Reasoning. Chapter Review. Chapter Test. 2. SETS,
NUMERATION, AND ADDITION AND SUBTRACTION
WITH WHOLE NUMBERS. Sets and Operations.
Numbers and Numeration. Models and Properties
of Addition and Subtraction. Algorithms for WholeNumber Addition and Subtraction. Chapter Review.
Chapter Test. 3. MULTIPLICATION AND DIVISION
WITH WHOLE NUMBERS. Models and Properties
of Multiplication. Models of Division. Algorithms for
Whole-Number Multiplication and Division. Chapter
Review. Chapter Test. 4. ELEMENTARY NUMBER
THEORY AND INTEGERS. Divisibility of Counting
Numbers. Prime and Composite Numbers, LCM,
and GCF. Integers. Chapter Review. Chapter Test. 5.
RATIONAL NUMBERS AND FRACTIONS. Concept
of Fractions and Representations. Addition and
Subtraction with Rational Numbers. Multiplication and
Division with Rational Numbers. Ratios and Proportional
Reasoning. Chapter Review. Chapter Test. 6. DECIMALS,
REAL NUMBERS, AND PERCENTS. Decimals and
Operations. Repeating Decimals, Irrational Numbers,
and Real Numbers. Percent and Percent Change. Chapter
Review. Chapter Test. 7. ALGEBRA AND FUNCTIONS.
Representing and Creating Functions. Solving Equations.
Algebra Tiles. Chapter Review. Chapter Test. 8.
DESCRIPTIVE STATISTICS. Graphical Representation
of Data. Measures of Center and Variation. Percentiles,
Box Plot, and Outliers. Chapter Review. Chapter Test.
9. PROBABILITY. Basics of Probability. Probability
Rules. Expected Value, Odds, Simulation, and Normal
Distribution. Chapter Review. Chapter Test. 10.
INTRODUCTION TO GEOMETRY. Representation
of Building Blocks of Geometry. Pairs of Angles
and Types of Polygons. Three-Dimensional Shapes.
Chapter Review. Chapter Test. 11. MEASUREMENT.
Concept of Measurement and Measurement Systems.
Perimeter and Area. The Pythagorean Theorem and
Triangle Inequalities. Volume and Surface Area.
Chapter Review. Chapter Test. 12. TRIANGLES AND
QUADRILATERALS. Congruence Axioms for Triangles.
Euclidean Constructions. Similarity. Chapter Review.
Chapter Test. 13. COORDINATE GEOMETRY AND
PLANE TRANSFORMATIONS. Representations of Lines.
Properties of Polygons Using Coordinate Geometry.
Transformations of the Plane. Chapter Review. Chapter
Test.
© 2013, 976pp, NonBook-Disk, 9781111989934
NATURE OF MATHEMATICS,
Written for liberal arts students and based on the
belief that learning to solve problems is the principal
reason for studying mathematics, Karl Smith introduces
students to Polya’s problem-solving techniques and
shows them how to use these techniques to solve
unfamiliar problems that they encounter in their own
lives. Through the emphasis on problem solving and
estimation, along with numerous in-text study aids,
students are assisted in understanding the concepts and
mastering the techniques. In addition to the problemsolving emphasis, THE NATURE OF MATHEMATICS, 12e,
International Edition is renowned for its clear writing,
coverage of historical topics, selection of topics, level,
and excellent applications problems. Smith includes
material on such practical real-world topics as finances
(e.g. amortization, installment buying, annuities) and
voting and apportionment. With the help of this text,
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157
thousands of students have “experienced” mathematics
rather than just do problems—and benefited from a
writing style that boosts their confidence and fosters
their ability to use mathematics effectively in their
everyday lives.
NEW TO THIS EDITION
• The examples throughout the book have been
redesigned to more effectively engage students.
Each now includes a title and is presented in a fresh,
easy-to-read format.
• A “Chapter Challenge” problem appears in each
chapter, providing additional problem-solving
practice. To encourage students to stretch their
problem-solving skills, these new types of problems
present contexts other than those presented in the
chapter.
• “Historical Quest” problems, an overwhelming success
in the previous edition, appear more frequently in
the Twelfth Edition. These problems are designed to
involve students in the historical development of the
great ideas in mathematical history.
• Expanded and updated chapter openers include “What
in the World?” introductions, which draw students into
the material by relating the mathematics to common
scenarios they may encounter in their everyday lives.
• The prologue—updated for this edition—asks the
all-important question, “Why Math?”. The prologue
puts mathematics into a historical perspective for
students, and is also designed to encourage them to
begin thinking about problem solving.
• Updated for this edition, the problems accompanying
the “Why Not Math?” epilogue show students how
mathematics touches just about every course of study.
FEATURES
• Real-World Problem-Solving Emphasis: Polya’s method
of problem solving is used throughout the text.
Students learn how to apply these techniques to solve
problems they encounter in their everyday lives in such
areas as finance (installment buying, amortization,
annuities) and voting and apportionment.
• Flexibility: The chapters are independent of one
another and allow maximum teaching flexibility.
• Learning Aids: The book offers a variety of interesting
and helpful learning aids. Icons like “Caution” and
“Stop” guide students through concepts. “Historical
Notes” place students’ view of mathematics in a
historical perspective and include a category of
related problems entitled “Historical Quest”. “Chapter
Summaries” include chapter review exercises, group
research projects, and individual research projects.
Additionally, a list of important terms and types of
problems, including section references, is available
to students at www.mathnature.com.
• Exercise Sets: Problems range from easy to challenging
and are clearly marked by type. “Level 1” problems are
mechanical or drill. “Level 2” problems require the
understanding of concepts. “Level 3” problems require
problem-solving skills or original thinking.
CONTENTS
Prologue: Why Math? A Historical Overview. 1.
THE NATURE OF PROBLEM SOLVING. The Nature
of Problem Solving. Problem Solving. Inductive
and Deductive Reasoning. Scientific Notation and
Estimation. Summary. 2. THE NATURE OF SETS. Sets,
Subsets, and Venn Diagrams. Operations with Sets.
Applications of Sets. Finite and Infinite Sets. Summary.
3. THE NATURE OF LOGIC. Deductive Reasoning.
Truth Tables and the Conditional. Operators and
Laws of Logic. The Nature of Proof. Problem Solving
Using Logic. Logic Circuits (Optional). Summary. 4.
THE NATURE OF NUMERATION SYSTEMS. Early
Numeration Systems. Hindu-Arabic Numeration System.
Different Numeration Systems. Binary Numeration
System. History of Calculating Devices (Optional).
Summary. 5. THE NATURE OF NUMBERS. Natural
Numbers. Prime Numbers. Integers. Rational Numbers.
Irrational Numbers. Groups, Fields, and Real Numbers.
Discrete Mathematics. Cryptography (Optional).
Summary. 6. THE NATURE OF ALGEBRA. Polynomials.
Factoring. Evaluation, Applications, and Spreadsheets.
Equations. GUEST ESSAY: “CHAOS”. Inequalities.
Algebra in Problem Solving. Ratios, Proportions, and
Problem Solving. Percents. Modeling Uncategorized
Problems. Summary. 7. THE NATURE OF GEOMETRY.
Geometry. Polygons and Angles. Triangles. Similar
Triangles. Right Triangle Trigonometry (Optional).
Mathematics, Art, and Non-Euclidean Geometries
(Optional Sections). Summary. 8. THE NATURE OF
NETWORKS AND GRAPH THEORY. Euler Circuits and
Hamiltonian Cycles. Trees and Minimum Spanning
Trees. Topology and Fractals. GUEST ESSAY: “WHAT
GOOD ARE FRACTALS?”. Summary. 9. THE NATURE
OF MEASUREMENT. Perimeter. Area. Surface Area,
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158
Volume and Capacity. Miscellaneous Measurements
(Optional). U.S.-Metric Conversions. Summary. 10.
THE NATURE OF GROWTH. Exponential Equations.
Logarithmic Equations. Applications of Growth and
Decay. Summary. 11. THE NATURE OF SEQUENCES,
SERIES, AND FINANCIAL MANAGEMENT. Interest.
Installment Buying. Sequences. Series. Annuities.
Amortization. Summary of Financial Formulas. Summary.
12. THE NATURE OF COUNTING. Permutations.
Combinations. Counting without Counting. Rubik’s
Cube and Instant Insanity (Optional). Summary. 13.
THE NATURE OF PROBABILITY. Introduction to
Probability. Mathematical Expectation. Probability
Models. Calculated Probabilities. The Binomial
Distribution (Optional). GUEST ESSAY: “EXTRASENSORY
PERCEPTION”. Summary. 14. THE NATURE OF
STATISTICS. Frequency Distributions and Graphs.
Descriptive Statistics. The Normal Curve. Correlation
and Regression. Sampling (Optional). Summary. 15. THE
NATURE OF GRAPHS AND FUNCTIONS. Cartesian
Coordinates and Graphing Lines. Graphing Half-Planes.
Graphing Curves. Conic Sections. Functions. Summary.
16. THE NATURE OF MATHEMATICAL SYSTEMS.
Systems of Linear Equations. Problem Solving with
Systems. Matrix Solution of a System of Equations.
Inverse Matrices. Modeling with Linear Programming
(Optional). Summary. 17. THE NATURE OF VOTING
Apportionment. Apportionment Flaws. Summary.
18. THE NATURE OF CALCULUS (OPTIONAL). What
Is Calculus? Limits. Derivatives. Integrals. Summary.
Epilogue: Why Not Math? Mathematics in the Natural
Sciences, Social Sciences, and in the Humanities.
Appendices. A. Glossary. B. Selected Answers. C. Index.
© 2012, 1024pp, Paperback, 9781111428518
LARSON’S MATHEMATICAL PRACTICES,
MATHEMATICS FOR TEACHERS
© 2015, 340pp, Paperback, 9781285447148
Post-Calculus
Coming Soon!
A FIRST COURSE IN DIFFERENTIAL
EQUATIONS WITH MODELING
APPLICATIONS, INTERNATIONAL
EDITION, 10E
Dennis G. Zill, Loyola Marymount University
A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH
MODELING APPLICATIONS, 10E, International Edition
strikes a balance between the analytical, qualitative,
and quantitative approaches to the study of differential
equations. This proven and accessible text speaks to
beginning engineering and math students through a
wealth of pedagogical aids, including an abundance of
examples, explanations, “Remarks” boxes, definitions,
and group projects. Written in a straightforward,
readable, and helpful style, this book provides a
www.cengageasia.com
159
thorough treatment of boundary-value problems and
partial differential equations.
NEW TO THIS EDITION
• Exercises in this edition have been updated to better
test and challenge students. Revisions are based
on reviewer and user input, as well as the author’s
understanding of the course goals.
• Chapter 6 now starts with a new section on the review
of power series.
• This edition contains an optional section on Green’s
functions in Chapter 4 and for those who have
extra time in their course to consider this elegant
application of variation of parameters in the solution
of initial-value and boundary-value problems.
• New projects have been added to the text to show
how the concepts of Differential Equations will apply
to students’ intended careers.
FEATURES
• The four-color design adds depth of meaning to all of
the graphics, particularly three-dimensional pieces
and visuals that involve multiple curves in a graph. The
author directed the creation of each piece of art to
ensure that it is as mathematically correct as the text.
• Extended homework problems at the end of selected
section exercises were submitted and classroomtested by members of the teaching math community.
• The development of material in this text progresses
intuitively, and explanations are clear and concise.
Exercises reinforce and build on chapter content.
• This text guides students through material necessary
to progress to the next level of study; its clear
presentation and mathematical precision make it an
excellent reference tool in future courses.
• While this text is time-tested and widely accepted,
it has remained current with the addition of new
exercises, such features as “Contributed Problems,”
and the enhanced four-color presentation.
Numerical Method. Chapter 2 in Review. 3. MODELING
WITH FIRST-ORDER DIFFERENTIAL EQUATIONS. Linear
Models. Nonlinear Models. Modeling with Systems of
First-Order Differential Equations. Chapter 3 in Review.
4. HIGHER-ORDER DIFFERENTIAL EQUATIONS.
Preliminary Theory-Linear Equations. Reduction of
Order. Homogeneous Linear Equations with Constant
Coefficients. Undetermined Coefficients-Superposition
Approach. Undetermined Coefficients-Annihilator
Approach. Variation of Parameters. Cauchy-Euler
Equation. Solving Systems of Linear Differential
Equations by Elimination. Nonlinear Differential
Equations. Chapter 4 in Review. 5. MODELING WITH
HIGHER-ORDER DIFFERENTIAL EQUATIONS. Linear
Models: Initial-Value Problems. Linear Models:
Boundary-Value Problems. Nonlinear Models. Chapter
5 in Review. 6. SERIES SOLUTIONS OF LINEAR
EQUATIONS. Review of Power Series Solutions About
Ordinary Points. Solutions About Singular Points.
Special Functions. Chapter 6 in Review. 7. LAPLACE
TRANSFORM. Definition of the Laplace Transform.
Inverse Transform and Transforms of Derivatives.
Operational Properties I. Operational Properties II.
Dirac Delta Function. Systems of Linear Differential
Equations. Chapter 7 in Review. 8. SYSTEMS OF
LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
Preliminary Theory. Homogeneous Linear Systems.
Nonhomogeneous Linear Systems. Matrix Exponential.
Chapter 8 in Review. 9. NUMERICAL SOLUTIONS
OF ORDINARY DIFFERENTIAL EQUATIONS. Euler
Methods. Runge-Kutta Methods. Multistep Methods.
Higher-Order Equations and Systems. Second-Order
Boundary-Value Problems. Chapter 9 in Review.
Appendix I: Gamma Function. Appendix II: Matrices.
Appendix III: Laplace Transforms. Answers for Selected
Odd-Numbered Problems.
© 2013, 480pp, Paperback, 9781133492450
CONTENTS
1. INTRODUCTION TO DIFFERENTIAL EQUATIONS.
Definitions and Terminology. Initial-Value Problems.
Differential Equations as Mathematical Models.
Chapter 1 in Review. 2. FIRST-ORDER DIFFERENTIAL
EQUATIONS. Solution Curves Without a Solution.
Separable Variables. Linear Equations. Exact Equations
and Integrating Factors. Solutions by Substitutions. A
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160
material in their course.
FEATURES
Coming Soon!
A FIRST COURSE IN MATHEMATICAL
MODELING, INTERNATIONAL EDITION,
5E
Frank R. Giordano; William P. Fox; Steven B. Horton
Offering a solid introduction to the entire modeling
process, A FIRST COURSE IN MATHEMATICAL
MODELING, 5E, International Edition delivers an
excellent balance of theory and practice, giving students
hands-on experience developing and sharpening their
skills in the modeling process. Throughout the book,
students practice key facets of modeling, including
creative and empirical model construction, model
analysis, and model research. The authors apply a
proven six-step problem-solving process to enhance
students’ problem-solving capabilities — whatever their
level. Rather than simply emphasizing the calculation
step, the authors first ensure that students learn how
to identify problems, construct or select models,
and figure out what data needs to be collected. By
involving students in the mathematical process as
early as possible — beginning with short projects —
the book facilitates their progressive development and
confidence in mathematics and modeling.
NEW TO THIS EDITION
• A new chapter on Modeling with Decision Theory
including Probability and Expected Value, Decision
Trees, and Conditional Probabilities.
• A new chapter on Game Theory including sections on
Illustrative Modeling Examples and Total Conflict as
a Linear Program Model: Pure and Mixed Strategies.
• New and revised problems, examples, and projects.
• Chapters on Dimensional Analysis and Similitude and
Graphs of Functions as Models have been removed
from the text, and are available on the companion
website for instructors who still want to include this
• Offering new chapters on Modeling with Decision
Theory and Game Theory.
• The fifth edition is packed with scenarios and
illustrative examples, enabling students to see
theories and models in action.
• Exercises and projects give students hands-on
experience putting what they have learned into
relevant practice.
• UMAP Models are included on the website for easy
reference and review.
• Problems from the COMAP Mathematical Contest
in Modeling also are included on the website,
giving students experience clarifying, analyzing,
and proposing solutions to the same open-ended
problems on the rigorous MCM.
• Tying in a variety of current tools, technology labs
and technology worked examples are available on the
web for many technologies, including Excel, Maple,
and Mathematica.
CONTENTS
1. Modeling Change. 2. The Modeling Process,
Proportionality, and Geometric Similarity. 3. Model
Fitting. 4. Experimental Modeling. 5. Simulation
Modeling. 6. Discrete Probabilistic Modeling. 7.
Optimization of Discrete Models. 8. Modeling with
Graph Theory. 9. Modeling with Decision Theory. 10.
Game Theory. 11. Modeling with a Differential Equation.
12. Modeling with Systems of Differential Equations. 13.
Optimization of Continuous Modeling. 14. Dimensional
Analysis and Similitude. 15. Graphs of Functions as
Models. Appendix A: Problems from the Mathematics
Contest in Modeling, 1985-2007. Appendix B: An Elevator
Simulation Model. Appendix C: The Revised Simplex
Method. Appendix D. Brief Review of Integration
Techniques.
© 2014, 704pp, Paperback, 9781285077499
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161
A TRANSITION TO ADVANCED
MATHEMATICS, INTERNATIONAL
EDITION, 7E
Doug Smith, University of North Carolina at Wilmington; Maurice
Eggen, Trinity University; Richard St. Andre, Central Michigan
University
A TRANSITION TO ADVANCED MATHEMATICS, 7e,
International Edition helps students make the transition
from calculus to more proofs-oriented mathematical
study. The most successful text of its kind, the 7th
edition continues to provide a firm foundation in
major concepts needed for continued study and
guides students to think and express themselves
mathematically—to analyze a situation, extract
pertinent facts, and draw appropriate conclusions.
The authors place continuous emphasis throughout
on improving students’ ability to read and write proofs,
and on developing their critical awareness for spotting
common errors in proofs. Concepts are clearly explained
and supported with detailed examples, while abundant
and diverse exercises provide thorough practice
on both routine and more challenging problems.
Students will come away with a solid intuition for
the types of mathematical reasoning they’ll need to
apply in later courses and a better understanding of
how mathematicians of all kinds approach and solve
problems.
NEW TO THIS EDITION
• An expanded Preface to the Student reviews what
students are expected to know about standard number
systems, sets, functions, and basic terminology at the
beginning of the course, outlines why the ability to do
proofs is important, and provides practice exercises
verifying properties of integers, rational numbers,
and real numbers.
• Several key sections crucial to student understanding
have been extensively revised for improved clarity.
Chapter 1 (Logic and Proofs) now closes with a
summary of proof methods, reinforced with revamped
examples and exercises. Results from elementary
number theory in the first two chapters are now
better highlighted and tied together more cohesively.
Chapter 4 (Functions) is reorganized for improved
flow, with review of the most basic properties and
terminology moved to the Preface to the Student
and study of additional properties of functions
now included. The section on countable sets in
Chapter 5 has been completely rewritten for greater
accessibility.
• Exercise sets have been thoroughly refreshed, with
new exercises in almost every section and expanded
Proofs to Grade exercises.
• Throughout the text biographical footnotes have
been added to provide a historical perspective on
the development of the foundations of mathematics.
FEATURES
• The authors follow a logical development of topics,
and write in a readable style that is consistent
and concise. As each new mathematical concept
is introduced the emphasis remains on improving
students’ ability to write proofs.
• Worked examples and exercises throughout the text,
ranging from the routine to the challenging, reinforce
the concepts.
• Proofs to Grade exercises test students’ ability
to distinguish correct reasoning from logical or
conceptual errors.
• A flexible organization allows instructors to expand
coverage or emphasis on certain topics and include a
number of optional topics without any disruption to
the flow or completeness of the core material.
CONTENTS
1. LOGIC AND PROOFS. Propositions and Connectives.
Conditionals and Biconditionals. Quantifiers. Basic Proof
Methods I. Basic Proof Methods II. Proofs Involving
Quantifiers. Additional Examples of Proofs 2. SET
THEORY. Basic Notions of Set Theory. Set Operations.
Extended Set Operations and Indexed Families of Sets.
Induction. Equivalent Forms of Induction. Principles of
Counting. 3. RELATIONS AND PARTITIONS. Relations.
Equivalence Relations. Partitions. Ordering Relations.
Graphs. 4. FUNCTIONS. Functions as Relations.
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162
Constructions of Functions. Functions That Are Onto;
One-to-One Functions. One-to-One Correspondences
and Inverse Functions. Images of Sets. Sequences. 5.
CARDINALITY. Equivalent Sets; Finite Sets. Infinite Sets.
Countable Sets. The Ordering of Cardinal Numbers.
Comparability of Cardinal Numbers and the Axiom of
Choice. 6. CONCEPTS OF ALGEBRA: GROUPS. Algebraic
Structures. Groups. Subgroups. Operation Preserving
Maps. Rings and Fields. 7. CONCEPTS OF ANALYSIS:
COMPLETENESS OF THE REAL NUMBERS. Ordered
Field Properties of the Real Numbers. The Heine-Borel
Theorem. The Bolzano-Weierstrass Theorem. The
Bounded Monotone Sequence Theorem. Comparability
of Cardinals and the Axiom of Choice.
© 2011, 416pp, Paperback, 9780495826705
which is carefully explained and proved in detail.
• There are many more examples and exercises than in
the previous edition: There are about 350 examples
and 1600 exercises (18% of which are new).
FEATURES
• The text may be used for either courses that cover
rings before groups (as in earlier editions) OR courses
that cover groups before rings.
• The flexible design of this text makes it suitable for
courses of various lengths and different levels of
mathematical sophistication.
• The chapters are organized around two themes,
arithmetic and congruence, that are developed first
for the integers and then for rings, polynomials, and
groups.
• The emphasis throughout is on clarity of exposition.
CONTENTS
1. Arithmetic in Z Revisited. 2. Congruence in Z
and Modular Arithmetic. 3. Rings. 4. Arithmetic in
F[x]. 5. Congruence in F[x] and Congruence-Class
Arithmetic. 6. Ideals and Quotient Rings. 7. Groups.
8. Normal Subgroups and Quotient Groups 9. Topics
in Group Theory. 10. Arithmetic in Integral Domains.
11. Field Extensions. 12. Galois Theory. 13. Public-Key
Cryptography. 14. The Chinese Remainder Theorem. 15.
Geometric Constructions. 16. Algebraic Coding Theory.
17. Lattices and Boolean Algebras (available online only).
ABSTRACT ALGEBRA, 3E
An Introduction
© 2013, 616pp, Hardback, 9781111569624
Thomas W. Hungerford, Cleveland State University
Abstract Algebra: An Introduction is set apart by its
thematic development and organization. The chapters
are organized around two themes: arithmetic and
congruence. Each theme is developed first for the
integers, then for polynomials, and finally for rings
and groups. This enables students to see where many
abstract concepts come from, why they are important,
and how they relate to one another. New to this edition
is a “groups first” option that enables those who prefer
to cover groups before rings to do so easily.
NEW TO THIS EDITION
• Extensively revised to include an alternate path
allowing instructors to cover Rings before Groups as
in previous editions OR Groups before Rings.
• For the benefit of beginners, the proofs early in the
book are broken into clearly marked steps, each of
CONTEMPORARY ABSTRACT ALGEBRA,
Joseph A. Gallian, University of Minnesota, Duluth
CO N T E M P O R A RY A B S T R AC T A LG E B R A , 8 E ,
International Edition provides a solid introduction
to the traditional topics in abstract algebra while
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163
conveying to students that it is a contemporary
subject used daily by working mathematicians,
computer scientists, physicists, and chemists. The
text includes numerous figures, tables, photographs,
charts, biographies, computer exercises, and suggested
readings giving the subject a current feel which makes
the content interesting and relevant for students.
NEW TO THIS EDITION
• Over 200 new exercises!
• New Examples!
• Refreshed quotations, historical notes, and
biographies!
FEATURES
• “Why Is Abstract Algebra Useful?” essay on the
author’s website shows students the importance
of studying abstract algebra and its applicability
to everyday life. This motivational essay can be
incorporated into a lesson on the first day of class,
or can serve as a motivational tool further along in
the course.
• Coverage of proof writing is provided on the
instructor’s website in the updated essay “Advice for
students learning proofs.” This essay provides basic
guidance for students encountering proof writing for
the first time or needing to freshen their skills.
• This text focuses on abstract algebra as a contemporary
subject, with concepts and methodologies currently
being used by computer scientists, physics, and
chemists.
• Extensive coverage of groups, rings, and fields, plus a
variety of non-traditional special topics.
• A good mixture of now more that 1750 computational
and theoretical exercises appearing in each chapter
and in Supplementary Exercise sets that synthesize
concepts from multiple chapters.
• Emphasis on computation and proof writing, with
an abundance of exercises to help students develop
both skills.
• Lines from popular songs, poems, and quotations
give the text a fresh, contemporary feel and keep
students engaged.
CONTENTS
PART I: INTEGERS AND EQUIVALENCE RELATIONS.
Preliminaries. Properties of Integers. Complex
Numbers. Modular Arithmetic. Mathematical Induction.
Equivalence Relations. Functions (Mappings). Exercises.
PART I: GROUPS. 1. Introduction to Groups. Symmetries
of a Square. The Dihedral Groups. Exercises. Biography of
Neils Abel 2. Groups. Definition and Examples of Groups.
Elementary Properties of Groups. Historical Note.
Exercises. 3. Finite Groups; Subgroups. Terminology
and Notation. Subgroup Tests. Examples of Subgroups.
Exercises. 4. Cyclic Groups. Properties of Cyclic
Groups. Classification of Subgroups of Cyclic Groups.
Exercises. Biography of J. J. Sylvester. Supplementary
Exercises for Chapters 1-4. 5. Permutation Groups.
Definition and Notation. Cycle Notation. Properties
of Permutations. A Check-Digit Scheme Based on
D5. Exercises. Biography of Augustin Cauchy. 6.
Isomorphisms. Motivation. Definition and Examples.
Cayley’s Theorem. Properties of Isomorphisms.
Automorphisms. Exercises. Biography of Arthur Cayley.
7. Cosets and Lagrange’s Theorem. Properties of Cosets.
Lagrange’s Theorem and Consequences. An Application
of Cosets to Permutation Groups. The Rotation Group of
a Cube and a Soccer Ball. Exercises. Biography of Joseph
Lagrange. 8. External Direct Products. Definition and
Examples. Properties of External Direct Products. The
Group of Units Modulo n as an External Direct Product.
Applications. Exercises. Biography of Leonard Adleman.
Supplementary Exercises for Chapters 5-8 9. Normal
Subgroups and Factor Groups. Normal Subgroups.
Factor Groups. Applications of Factor Groups. Internal
Direct Products. Exercises. Biography of Évariste
Galois 10. Group Homomorphisms. Definition and
Examples. Properties of Homomorphisms. The First
Isomorphism Theorem. Exercises. Biography of Camille
Jordan. 11. Fundamental Theorem of Finite Abelian
Groups. The Fundamental Theorem. The Isomorphism
Classes of Abelian Groups. Proof of the Fundamental
Theorem. Exercises. Supplementary Exercises for
Chapters 9-11. PART III: RINGS. 12. Introduction to
Rings. Motivation and Definition. Examples of Rings.
Properties of Rings. Subrings. Exercises. Biography
of I. N. Herstein. 13. Integral Domains. Definition and
Examples. Fields. Characteristic of a Ring. Exercises.
Biography of Nathan Jacobson. 14. Ideals and Factor
Rings. Ideals. Factor Rings. Prime Ideals and Maximal
Ideals. Exercises. Biography of Richard Dedekind.
Biography of Emmy Noether. Supplementary Exercises
for Chapters 12-14. 15. Ring Homomorphisms. Definition
and Examples. Properties of Ring Homomorphisms.
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164
The Field of Quotients. Exercises. 16. Polynomial Rings.
Notation and Terminology. The Division Algorithm and
Consequences. Exercises. Biography of Saunders Mac
Lane. 17. Factorization of Polynomials. Reducibility Tests.
Irreducibility Tests. Unique Factorization in Z[x]. Weird
Dice: An Application of Unique Factorization. Exercises.
Biography of Serge Lang. 18. Divisibility in Integral
Domains. Irreducibles, Primes. Historical Discussion of
Fermat’s Last Theorem. Unique Factorization Domains.
Euclidean Domains. Exercises. Biography of Sophie
Germain. Biography of Andrew Wiles. Supplementary
Exercises for Chapters 15-18. PART IV: FIELDS. 19.
Vector Spaces. Definition and Examples. Subspaces.
Linear Independence. Exercises. Biography of Emil
Artin. Biography of Olga Taussky-Todd. 20. Extension
Fields. The Fundamental Theorem of Field Theory.
Splitting Fields. Zeros of an Irreducible Polynomial.
Exercises. Biography of Leopold Kronecker. 21. Algebraic
Extensions. Characterization of Extensions. Finite
Extensions. Properties of Algebraic Extensions
Exercises. Biography of Irving Kaplansky. 22. Finite
Fields. Classification of Finite Fields. Structure of Finite
Fields. Subfields of a Finite Field. Exercises. Biography
of L. E. Dickson. 23. Geometric Constructions. Historical
Discussion of Geometric Constructions. Constructible
Numbers. Angle-Trisectors and Circle-Squarers.
Exercises. Supplementary Exercises for Chapters 1923. PART V: SPECIAL TOPICS. 24. Sylow Theorems.
Conjugacy Classes. The Class Equation. The Probability
That Two Elements Commute. The Sylow Theorems.
Applications of Sylow Theorems. Exercises. Biography
of Ludvig Sylow. 25. Finite Simple Groups. Historical
Background. Nonsimplicity Tests. The Simplicity of A5.
The Fields Medal. The Cole Prize. Exercises. Biography
of Michael Aschbacher. Biography of Daniel Gorenstein.
Biography of John Thompson. 26. Generators and
Relations. Motivation. Definitions and Notation.
Free Group. Generators and Relations. Classification
of Groups of Order up to 15. Characterization of
Dihedral Groups. Realizing the Dihedral Groups
with Mirrors. Exercises. Biography of Marshall Hall,
Jr.. 27. Symmetry Groups. Isometries. Classification
of Finite Plane Symmetry Groups. Classification of
Finite Group of Rotations in R³. Exercises. 28. Frieze
Groups and Crystallographic Groups. The Frieze
Groups. The Crystallographic Groups. Identification of
Plane Periodic Patterns. Exercises. Biography of M. C.
Escher. Biography of George Pólya. Biography of John
H. Conway. 29. Symmetry and Counting. Motivation.
Burnside’s Theorem. Applications. Group Action.
Exercises. Biography of William Burnside. 30. Cayley
Digraphs of Groups. Motivation. The Cayley Digraph
of a Group. Hamiltonian Circuits and Paths. Some
Applications. Exercises. Biography of William-Rowan
Hamilton. Biography of Paul Erdös. 31. Introduction to
Algebraic Coding Theory. Motivation. Linear Codes.
Parity-Check Matrix Decoding. Coset Decoding.
Historical Note: The Ubiquitous Reed-Solomon Codes.
Exercises. Biography of Richard W. Hamming. Biography
of Jessie MacWilliams. Biography of Vera Pless. 32. An
Introduction to Galois Theory. Fundamental Theorem
of Galois Theory. Solvability of Polynomials by. Radicals.
Insolvability of a Quintic. Exercises. Biography of
Philip Hall. 33. Cyclotomic Extensions. Motivation.
Cyclotomic Polynomials. The Constructible Regular
n-gons. Exercises. Biography of Carl Friedrich Gauss.
Biography of Manjul Bhargava. Supplementary Exercises
for Chapters 24-33.
© 2013, 656pp, Paperback, 9781133606758
Coming Soon!
DIFFERENTIAL EQUATIONS WITH
BOUNDARY-VALUE PROBLEMS,
Dennis G. Zill, Loyola Marymount University; Warren S. Wright,
Loyola Marymount University
DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE
PROBLEMS, 8E, International Edition strikes a balance
between the analytical, qualitative, and quantitative
approaches to the study of differential equations.
This proven and accessible text speaks to beginning
engineering and math students through a wealth of
pedagogical aids, including an abundance of examples,
explanations, “Remarks” boxes, definitions, and group
www.cengageasia.com
165
projects. Written in a straightforward, readable, and
helpful style, the book provides a thorough treatment
of boundary-value problems and partial differential
equations.
NEW TO THIS EDITION
• Exercises in this edition have been updated to better
test and challenge students. Revisions are based
on reviewer and user input, as well as the author’s
understanding of the course goals.
• Chapter 6 now starts with a new section on the review
of power series.
• This edition contains an optional section on Green’s
functions in Chapter 4 and for those who have
extra time in their course to consider this elegant
application of variation of parameters in the solution
of initial-value and boundary-value problems.
• New projects have been added to the text to show
how the concepts of Differential Equations will apply
to students’ intended careers.
FEATURES
• The four-color design adds depth of meaning to all of
the graphics, particularly three-dimensional pieces
and visuals that involve multiple curves in a graph. The
author directed the creation of each piece of art to
ensure that it is as mathematically correct as the text.
• Extended homework problems at the end of selected
section exercises were submitted and classroomtested by members of the teaching math community.
• The development of material in this text progresses
intuitively, and explanations are clear and concise.
Exercises reinforce and build on chapter content.
• This text guides students through material necessary
to progress to the next level of study; its clear
presentation and mathematical precision make it an
excellent reference tool in future courses.
• While this text is time-tested and widely accepted,
it has remained current with the addition of new
exercises, such features as “Contributed Problems,”
and the enhanced four-color presentation.
CONTENTS
1. INTRODUCTION TO DIFFERENTIAL EQUATIONS.
Definitions and Terminology. Initial-Value Problems.
Differential Equations as Mathematical Models.
Chapter 1 in Review. 2. FIRST-ORDER DIFFERENTIAL
EQUATIONS. Solution Curves Without a Solution.
Separable Variables. Linear Equations. Exact Equations
and Integrating Factors. Solutions by Substitutions. A
Numerical Method. Chapter 2 in Review. 3. MODELING
WITH FIRST-ORDER DIFFERENTIAL EQUATIONS. Linear
Models. Nonlinear Models. Modeling with Systems of
First-Order Differential Equations. Chapter 3 in Review.
4. HIGHER-ORDER DIFFERENTIAL EQUATIONS.
Preliminary Theory-Linear Equations. Reduction of
Order. Homogeneous Linear Equations with Constant
Coefficients. Undetermined Coefficients-Superposition
Approach. Undetermined Coefficients-Annihilator
Approach. Variation of Parameters. Cauchy-Euler
Equation. Solving Systems of Linear Differential
Equations by Elimination. Nonlinear Differential
Equations. Chapter 4 in Review. 5. MODELING WITH
HIGHER-ORDER DIFFERENTIAL EQUATIONS. Linear
Models: Initial-Value Problems. Linear Models:
Boundary-Value Problems. Nonlinear Models. Chapter
5 in Review. 6. SERIES SOLUTIONS OF LINEAR
EQUATIONS. Review of Power Series Solutions About
Ordinary Points. Solutions About Singular Points.
Special Functions. Chapter 6 in Review. 7. LAPLACE
TRANSFORM. Definition of the Laplace Transform.
Inverse Transform and Transforms of Derivatives.
Operational Properties I. Operational Properties II.
Dirac Delta Function. Systems of Linear Differential
Equations. Chapter 7 in Review. 8. SYSTEMS OF
LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
Preliminary Theory. Homogeneous Linear Systems.
Nonhomogeneous Linear Systems. Matrix Exponential.
OF ORDINARY DIFFERENTIAL EQUATIONS. Euler
Methods. Runge-Kutta Methods. Multistep Methods.
Higher-Order Equations and Systems. Second-Order
Boundary-Value Problems. Chapter 9 in Review. 10.
PLANE AUTONOMOUS SYSTEMS. Autonomous
Systems. Stability of Linear Systems. Linearization and
Local Stability. Autonomous Systems as Mathematical
Models. Chapter 10 in Review. 11. ORTHOGONAL
FUNCTIONS AND FOURIER SERIES. Orthogonal
Functions. Fourier Series and Orthogonal Functions.
Fourier Cosine and Sine Series. Sturm-Liouville Problem.
Bessel and Legendre Series. Chapter 11 in Review. 12.
BOUNDARY-VALUE PROBLEMS IN RECTANGULAR
COORDINATES. Separable Partial Differential
Equations. Classical PDE’s and Boundary-Value
Problems. Heat Equation. Wave Equation. Laplace’s
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Equation. Nonhomogeneous Boundary-Value Problems.
Orthogonal Series Expansions. Higher-Dimensional
Problems. Chapter 12 in Review. 13. BOUNDARY-VALUE
PROBLEMS IN OTHER COORDINATE SYSTEMS.
Polar Coordinates. Polar and Cylindrical Coordinates.
Spherical Coordinates. Chapter 13 in Review. 14.
INTEGRAL TRANSFORM METHOD. Error Function.
Laplace Transform. Fourier Integral. Fourier Transforms.
OF PARTIAL DIFFERENTIAL EQUATIONS. Laplace’s
Equation. Heat Equation. Wave Equation. Chapter 15
in Review. Appendix I: Gamma Function. Appendix II:
Matrices. Appendix III: Laplace Transforms. Answers
for Selected Odd-Numbered Problems.
© 2013, 664pp, Paperback, 9781133492467
adept at moving between different representations
to solve nonlinear differential equations equally
well as traditional linear equations. Certain models
reappear throughout the text as running themes to
synthesize different concepts from multiple angles,
and a dynamical systems focus emphasizes predicting
the long-term behavior of these recurring models.
Students will discover how to identify and harness the
mathematics they will use in their careers, and apply
it effectively outside the classroom.
NEW TO THIS EDITION
• New in-depth models on timely and relevant
applications such as SIR infectious disease modeling.
• Chapters on First-Order Systems, Linear Systems,
and Forcing and Resonance have been extensively
rewritten for better clarity and readability.
• Several sections, particularly in Chapters 2-4, have
been reorganized for teaching flexibility and to better
fit into class time constraints.
• Exercise sets have been thoroughly refreshed with
updated problems throughout the text.
FEATURES
DIFFERENTIAL EQUATIONS,
INTERNATIONAL EDITION (WITH DE
TOOLS PRINTED ACCESS CARD), 4E
Paul Blanchard, Boston University; Robert L. Devaney; Glen R. Hall,
Boston University
Incorporating an innovative modeling approach, this
text for a one-semester differential equations course
emphasizes conceptual understanding to help students
relate information taught in the classroom to real-world
experiences. Going beyond a traditional emphasis
on technique, the authors focus on understanding
how differential equations are formulated and
interpreting their meaning to applied models from
a variety of disciplines. A three-pronged qualitative,
numeric, and analytic approach stresses visualizing
differential equations geometrically, utilizing the latest
computational technology to investigate the behavior
of solutions, and predicting the behavior of solutions
as they apply to models. The presentation weaves
various points of view together so students become
• The book’s modeling approach emphasizes
understanding of the meaning of variables and
parameters in a differential equation and interpreting
this meaning in an applied setting.
• Revisited models in the text reinforce recurring
themes and synthesize multiple concepts to solve
practical problems. This helps students develop a
natural intuition for how to approach an applied
problem in real life without a road map.
• A large number of well-chosen exercises integrate
the qualitative, numerical, and analytic arguments
behind a solution and require students to demonstrate
understanding of the concepts behind the problem.
• Lab activities at the end of each chapter offer deeper
explorations of models, and require students to
summarize their results in a report that demonstrates
the necessary qualitative, numerical, and analytic
arguments.
• Certain exercises make optional use of specific
applets in the DE Tools suite to harness the power of
technology in solving differential equations.
CONTENTS
1. FIRST-ORDER DIFFERENTIAL EQUATIONS. Modeling
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via Differential Equations. Analytic Technique:
Separation of Variables. Qualitative Technique: Slope
Fields. Numerical Technique: Euler’s Method. Existence
and Uniqueness of Solutions. Equilibria and the Phase
Line. Bifurcations. Linear Equations. Integrating Factors
for Linear Equations. 2. FIRST-ORDER SYSTEMS.
Modeling via Systems. The Geometry of Systems.
Analytic Methods for Special Systems. Euler’s Method
for Systems. The Lorenz Equations. 3. LINEAR SYSTEMS.
Properties of Linear Systems and the Linearity Principle.
Straight-Line Solutions. Phase Planes for Linear Systems
with Real Eigenvalues. Complex Eigenvalues. Special
Cases: Repeated and Zero Eigenvalues. Second-Order
Linear Equations. The Trace-Determinant Plane. Linear
Systems in Three Dimensions. 4. FORCING AND
RESONANCE. Forced Harmonic Oscillators. Sinusoidal
Forcing. Undamped Forcing and Resonance. Amplitude
and Phase of the Steady State. The Tacoma Narrows
Bridge. 5. NONLINEAR SYSTEMS. Equilibrium Point
Analysis. Qualitative Analysis. Hamiltonian Systems.
Dissipative Systems. Nonlinear Systems in Three
Dimensions. Periodic Forcing of Nonlinear Systems and
Chaos. 6. LAPLACE TRANSFORMS. Laplace Transforms.
Discontinuous Functions. Second-Order Equations.
Delta Functions and Impulse Forcing. Convolutions.
The Qualitative Theory of Laplace Transforms. 7.
NUMERICAL METHODS. Numerical Error in Euler’s
Method. Improving Euler’s Method. The Runge-Kutta
Method. The Effects of Finite Arithmetic. 8. DISCRETE
DYNAMICAL SYSTEMS. The Discrete Logistic Equation.
Fixed Points and Periodic Points. Bifurcations. Chaos.
Chaos in the Lorenz System. APPENDICES. A. Changing
Variables. B. The Ultimate Guess. C. Complex Numbers
and Euler’s Formula.
© 2011, 864pp, Paperback, 9781133110590
ELEMENTARY LINEAR ALGEBRA,
The cornerstone of ELEMENTARY LINEAR ALGEBRA
7E, International Edition is Larson’s clear, careful,
and concise presentation of material—written so
that students can fully understand how mathematics
works. This program balances theory with examples,
applications, and geometric intuition for a complete,
step-by-step learning system. Featuring a new design
that highlights the relevance of the mathematics and
improves readability for students, the Seventh Edition
also incorporates new conceptual Capstone exercises
that reinforce multiple concepts in each section. Data
and applications reflect current statistics and examples
to engage students and demonstrate the link between
theory and practice. Cengage Learning’s Enhanced
WebAssign®, which allows you to create online
homework assignments that draw from thousands of
the text’s end-of-chapter questions, is available with
the text.
NEW TO THIS EDITION
• Enhanced WebAssign® combines the exceptional
mathematics content in this text with the most
powerful online homework solution, WebAssign.
Enhanced WebAssign engages students with
immediate feedback and rich tutorial content to help
them develop a deeper conceptual understanding
of their subject matter. Students have access to an
interactive eBook offering links to YouTube videos,
video solutions, and more to bring the mathematics to
life. You can build online assignments by selecting from
thousands of text-specific problems, supplemented
with problems from any Cengage Learning textbook.
• A new, more student-friendly design includes a greater
number of images that make content more relevant
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168
for students. The trim size and font size in the exercise
sets have been increased, making the text easier for
students to read.
• To motivate students by emphasizing the relevance
of the content, each chapter opener contains a list of
sections, five photos with references to applications,
and an arrow indicating the section in which each
application appears.
• New Capstone exercises, each of which covers
several concepts, have been added in each section.
Conceptual in nature, they reinforce key ideas learned
in the section without being time-consuming or
tedious for students.
FEATURES
• Coverage of Computer Algebra Systems (CAS)
includes an online technology guide. Appendix B—also
available online—offers an introduction to MATLAB,
Maple, Mathematica, and Graphing Calculators; a
walkthrough of the keystrokes needed for select
examples; an applications section; and “Technology
Pitfalls” students may encounter in using their CAS.
• All real data in the exercises and examples has been
updated to reflect current statistics and information.
Many new exercises have been added to the text as
well.
• Learning objectives are available at the beginning of
every section and online at the student website for
quick reference and/or review.
• Guided Proofs help students successfully complete
theoretical proofs by leading them, step-by-step,
through the logical sequence of statements necessary
to reach the correct conclusion.
• Pedagogical support—including self-assessment
tools, review sections, and writing activities—allows
students to check their understanding of each section
and helps them develop critical thinking skills.
of Determinants. 4. VECTOR SPACES. Vectors in Rn.
Vector Spaces. Subspaces of Vector Spaces. Spanning
Sets and Linear Independence. Basis and Dimension.
Rank of a Matrix and Systems of Linear Equations.
Coordinates and Change of Basis. Applications of Vector
Spaces. 5. INNER PRODUCT SPACES. Length and Dot
Product in Rn. Inner Product Spaces. Orthogonal Bases:
Gram-Schmidt Process. Mathematical Models and Least
Squares Analysis. Applications of Inner Product Spaces.
6. LINEAR TRANSFORMATIONS. Introduction to Linear
Transformations. The Kernel and Range of a Linear
Transformation. Matrices for Linear Transformations.
Transition Matrices and Similarity. Applications
of Linear Transformations. 7. EIGENVALUES AND
EIGENVECTORS. Eigenvalues and Eigenvectors.
Diagonalization. Symmetric Matrices and Orthogonal
Diagonalization. Applications of Eigenvalues and
Eigenvectors. 8. COMPLEX VECTOR SPACES (online).
Complex Numbers. Conjugates and Division of Complex
Numbers. Polar Form and Demoivre’s Theorem. Complex
Vector Spaces and Inner Products. Unitary and Hermitian
Spaces. 9. LINEAR PROGRAMMING (online). Systems
of Linear Inequalities. Linear Programming Involving
Two Variables. The Simplex Method: Maximization. The
Simplex Method: Minimization. The Simplex Method:
Mixed Constraints. 10. NUMERICAL METHODS (online).
Gaussian Elimination with Partial Pivoting. Iterative
Methods for Solving Linear Systems. Power Method for
Approximating Eigenvalues. Applications of Numerical
Methods.
© 2013, 448pp, Paperback, 9781133111344
CONTENTS
1. SYSTEMS OF LINEAR EQUATIONS Introduction to
Systems of Equations. Gaussian Elimination and GaussJordan Elimination. Applications of Systems of Linear
Equations. 2. MATRICES. Operations with Matrices.
Properties of Matrix Operations. The Inverse of a
Matrix. Elementary Matrices. Applications of Matrix
Operations. 3. DETERMINANTS. The Determinant of a
Matrix. Evaluation of a Determinant Using Elementary
Operations. Properties of Determinants. Applications
ELEMENTS OF MODERN ALGEBRA, 8E
Linda Gilbert, University of South Carolina, Upstate
ELEMENTS OF MODERN ALGEBRA, Eighth Edition,
is intended for an introductory course in abstract
algebra taken by Math and Math for Secondary
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169
Education majors. Helping to make the study of
abstract algebra more accessible, this text gradually
introduces and develops concepts through helpful
features that provide guidance on the techniques of
proof construction and logic analysis. The text develops
mathematical maturity for students by presenting the
material in a theorem-proof format, with definitions
and major results easily located through a user-friendly
format. The treatment is rigorous and self-contained,
in keeping with the objectives of training the student
in the techniques of algebra and of providing a bridge
to higher-level mathematical courses. The text has a
flexible organization, with section dependencies clearly
mapped out and optional topics that instructors can
cover or skip based on their course needs. Additionally,
problem sets are carefully arranged in order of difficulty
to cater assignments to varying student ability levels.
NEW TO THIS EDITION
• Alerts that draw attention to counterexamples, special
cases, proper symbol or terminology usage, and
common misconceptions. Frequently these alerts lead
to True/False statements in the exercises that further
reinforce the precision required in mathematical
communication.
• More emphasis placed on special groups, such as the
general linear and special linear groups, the dihedral
group, and the group of units.
• Moving some definitions from the exercises to the
sections for greater emphasis.
• Using marginal notes to outline the steps of the
induction arguments required in the examples.
• More than 200 new theoretical and computational
exercises have been added.
• Many new examples have also been added to this
edition.
construction skills.
• Symbolic marginal notes are used to help students
analyze the logic in the proofs of theorems without
interrupting the natural flow of the proof.
CONTENTS
1. FUNDAMENTALS. Sets. Mappings. Properties of
Composite Mappings (Optional). Binary Operations.
Permutations and Inverses. Matrices. Relations. 2. THE
INTEGERS. Postulates for the Integers (Optional).
Mathematical Induction. Divisibility. Prime Factors and
Greatest Common Divisor. Congruence of Integers.
Congruence Classes. Introduction to Coding Theory
(Optional). Introduction to Cryptography (Optional).
3. GROUPS. Definition of a Group. Properties of Group
Elements. Subgroups. Cyclic Groups. Isomorphisms.
Homomorphisms. 4. MORE ON GROUPS. Finite
Permutation Groups. Cayley’s Theorem. Permutation
Groups in Science and Art (Optional). Cosets of a
Subgroup. Normal Subgroups. Quotient Groups. Direct
Sums (Optional). Some Results on Finite Abelian Groups
(Optional). 5. RINGS, INTEGRAL DOMAINS, AND
FIELDS. Definition of a Ring. Integral Domains and
Fields. The Field of Quotients of an Integral Domain.
Ordered Integral Domains. 6. MORE ON RINGS.
Ideals and Quotient Rings. Ring Homomorphisms. The
Characteristic of a Ring. Maximal Ideals (Optional).
7. REAL AND COMPLEX NUMBERS. The Field of Real
Numbers. Complex Numbers and Quaternions. De
Moivre’s Theorem and Roots of Complex Numbers. 8.
POLYNOMIALS. Polynomials over a Ring. Divisibility and
Greatest Common Divisor. Factorization in _F[x]_ . Zeros
of a Polynomial. Solution of Cubic and Quartic Equations
by Formulas (Optional). Algebraic Extensions of a Field.
© 2015, 528pp, Hardback, 9781285463230
FEATURES
• Nearly 300 True/False statements that encourage the
students to thoroughly understand the statements
of definitions and results of theorems appear in this
edition.
• Descriptive labels and titles are used with definitions
and theorems to indicate their content and relevance.
• Strategy boxes appear to give guidance and
explanation about techniques of proof. This feature
forms a component of the bridge that enables
students to become more proficient in their proof
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170
Putting it All Together. Regular Induction. Induction
with Inequalities. Recursion and Extended Induction.
Uniqueness Proofs, the WOP, and a Proof of the Division.
Algorithm. 3. SETS, RELATIONS, AND FUNCTIONS. Sets.
Set Operations. Set Theory. Indexed Families of Sets.
Cartesian Products. Relations. Functions. Composition
of Functions. Cardinality.
© 2012, 144pp, Paperback, 9780547165387
INTRODUCTION TO ADVANCED
MATHEMATICS
Coming Soon!
A Guide to Understanding Proofs
Connie M. Campbell, Millsaps College
This text offers a crucial primer on proofs and the
language of mathematics. Brief and to the point, it lays
out the fundamental ideas of abstract mathematics
and proof techniques that students will need to
master for other math courses. Campbell presents
these concepts in plain English, with a focus on basic
terminology and a conversational tone that draws
natural parallels between the language of mathematics
and the language students communicate in every
day. The discussion highlights how symbols and
expressions are the building blocks of statements and
arguments, the meanings they convey, and why they
are meaningful to mathematicians. In-class activities
provide opportunities to practice mathematical
reasoning in a live setting, and an ample number of
homework exercises are included for self-study. This
text is appropriate for a course in Foundations of
Advanced Mathematics taken by students who’ve had a
semester of calculus, and is designed to be accessible to
students with a wide range of mathematical proficiency.
It can also be used as a self-study reference, or as a
supplement in other math courses where additional
proofs practice is needed.
CONTENTS
1. LOGIC. Introduction and Terminology. Statements
and Truth Tables. Logical Equivalence and Logical
Deductions. The Contrapositive, Negation, and
Converse of an Implication Statement. Quantifiers. 2.
PROOF WRITING. Terminology and Goals. Existence
Proofs and Counterexamples. Direct Proofs (“If, then”
or “For every” Statements). Using Cases in Proofs.
Contrapositive Arguments. Contradiction Arguments.
LINEAR ALGEBRA, 3E
A Modern Introduction, International Edition
David Poole, Trent University
David Poole’s innovative book emphasizes vectors and
geometric intuition from the start and better prepares
students to make the transition from the computational
aspects of the course to the theoretical. Designed
for a one- or two-semester introductory course and
written in simple, “mathematical English” Poole focuses
his approach on benefiting student visualization
and connection to the material. He offers concrete
examples to engage the student before presenting
abstraction, and immediately follows up theoretical
discussion with further examples and an array of
applications from a variety of disciplines. Students from
a variety of backgrounds and learning styles benefit
from Poole’s practical approach, which covers vectors
and vector geometry early in order to enable students
to visualize the mathematics while they are doing
matrix operations. With a concrete understanding of
vector geometry, students are able to visualize and
understand the meaning of the calculations that they
will encounter and develop mathematical maturity for
thinking abstractly.
NEW TO THIS EDITION
• Reorganized Chapter 1 with earlier introduction to
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171
modular arithmetic and finite linear algebra, and a new
vignette in Chapter 4 on Lewis Carroll’s condensation
method.
• Over 300 new or revised exercises as well as new
applications of linear economic models, a topic of
importance to business and economics students
• Enhanced WebAssign, new for the Third Edition,
offering online homework and course management
built around the book.
• “Technology Bytes”, an extensive online appendix that
shows Maple, Mathematica, and MATLAB instructions
key for working out examples and exercises from the
text in a computer algebra system.
• Complete Solutions Manual available for instructors
via the Solutions Builder for easy, online access.
FEATURES
• Explorations (1 per chapter) providing deeper
discovery-based guides on key concepts, designed
for individual or group work.
• 400+ examples, usually worked in greater detail and
more emphasis on readability than most books.
• Over 2000 exercises, and applied problems from
a wide variety of engineering, physical science,
biological science, and business disciplines.
• Context-sensitive margin notes for extra help and
cross-references.
• Vignettes highlighting real-world applications
in business, science, and society with expanded
discussion of the concepts behind the applications.
CONTENTS
1. VECTORS. Introduction: The Racetrack Game. The
Geometry and Algebra of Vectors. Length and Angle:
The Dot Product. Exploration: Vectors and Geometry.
Lines and Planes. Exploration: The Cross Product.
Applications: Force Vectors; Code Vectors. Vignette: The
Codabar System. 2. SYSTEMS OF LINEAR EQUATIONS.
Introduction: Triviality. Introduction to Systems of Linear
Equations. Direct Methods for Solving Linear Systems.
Exploration: Lies My Computer Told Me. Exploration:
Partial Pivoting. Exploration: Counting Operations: An
Introduction to the Analysis of Algorithms. Spanning
Sets and Linear Independence. Applications: Allocation
of Resources; Balancing Chemical Equations; Network
Analysis; Electrical Networks; Linear Economic
Models; Finite Linear Games. Vignette: The Global
Positioning System. Iterative Methods for Solving
Linear Systems. 3. MATRICES. Introduction: Matrices
in Action. Matrix Operations. Matrix Algebra. The
Inverse of a Matrix. The LU Factorization. Subspaces,
Basis, Dimension, and Rank. Introduction to Linear
Transformations. Vignette: Robotics. Applications:
Markov Chains; Linear Economic Models; Population
Growth; Graphs and Digraphs; Error-Correcting Codes.
4. EIGENVALUES AND EIGENVECTORS. Introduction:
A Dynamical System on Graphs. Introduction to
Eigenvalues and Eigenvectors. Determinants. Vignette:
Lewis Carroll’s Condensation Method. Exploration:
Geometric Applications of Determinants. Eigenvalues
and Eigenvectors of n x n Matrices. Similarity and
Diagonalization. Iterative Methods for Computing
Eigenvalues. Applications and the Perron-Frobenius
Theorem: Markov Chains; Population Growth; The
Perron-Frobenius Theorem; Linear Recurrence Relations;
Systems of Linear Differential Equations; Discrete Linear
Dynamical Systems. Vignette: Ranking Sports Teams
and Searching the Internet. 5. ORTHOGONALITY.
Introduction: Shadows on a Wall. Orthogonality in Rn.
Orthogonal Complements and Orthogonal Projections.
The Gram-Schmidt Process and the QR Factorization.
Exploration: The Modified QR Factorization. Exploration:
Approximating Eigenvalues with the QR Algorithm.
Orthogonal Diagonalization of Symmetric Matrices.
Applications: Dual Codes; Quadratic Forms; Graphing
Quadratic Equations. 6. VECTOR SPACES. Introduction:
Fibonacci in (Vector) Space. Vector Spaces and
Subspaces. Linear Independence, Basis, and Dimension.
Exploration: Magic Squares. Change of Basis. Linear
Transformations. The Kernel and Range of a Linear
Transformation. The Matrix of a Linear Transformation.
Exploration: Tilings, Lattices and the Crystallographic
Restriction. Applications: Homogeneous Linear
Differential Equations; Linear Codes. 7. DISTANCE AND
APPROXIMATION. Introduction: Taxicab Geometry.
Inner Product Spaces. Exploration: Vectors and
Matrices with Complex Entries. Exploration: Geometric
Inequalities and Optimization Problems. Norms and
Distance Functions. Least Squares Approximation.
The Singular Value Decomposition. Vignette: Digital
Image Compression. Applications: Approximation
of Functions; Error-Correcting Codes. Appendix A:
Mathematical Notation and Methods of Proof. Appendix
B: Mathematical Induction. Appendix C: Complex
Numbers. Appendix D: Polynomials.
© 2011, 768pp, Paperback, 9780538735445
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Coming Soon!
LINEAR ALGEBRA, 4E
A Modern Introduction
David Poole, Trent University
work.
• Ample applied problems from a wide variety
of disciplines, including mathematics, physics,
engineering, biology, chemistry, computer science,
economics, geography, psychology, and sociology.
• Context-sensitive margin notes for extra help and
cross-references.
• Vignettes showcase modern applications of linear
algebra.
• Biographical sketches highlight many of the
mathematicians who contributed to the development
of linear algebra.
CONTENTS
David Poole’s innovative LINEAR ALGEBRA: A
MODERN INTRODUCTION, 4e emphasizes a vectors
approach and better prepares students to make
the transition from computational to theoretical
mathematics. Balancing theory and applications,
the book is written in a conversational style and
combines a traditional presentation with a focus on
student-centered learning. Theoretical, computational,
and applied topics are presented in a flexible yet
integrated way. Stressing geometric understanding
before computational techniques, vectors and vector
geometry are introduced early to help students
visualize concepts and develop mathematical maturity
for abstract thinking. Additionally, the book includes
ample applications drawn from a variety of disciplines,
which reinforce the fact that linear algebra is a valuable
tool for modeling real-life problems.
NEW TO THIS EDITION
• Writing Projects offer students opportunities to
research and write about linear algebra. Projects are
designed for individual or group work.
• Chapter 8: Codes is an online chapter combining all
material on codes previously interspersed throughout
the text.
• More than 100 new or revised exercises.
FEATURES
• “Technology Bytes”, an extensive online appendix that
shows Maple, Mathematica, and MATLAB instructions
key for working out examples and exercises from the
text in a computer algebra system.
• Explorations provide deeper discovery-based guides
on key concepts, designed for individual or group
1. VECTORS. Introduction: The Racetrack Game. The
Geometry and Algebra of Vectors. Length and Angle:
The Dot Product. Exploration: Vectors and Geometry.
Lines and Planes. Exploration: The Cross Product.
Writing Project: Origins of the Dot Product and the
Cross Product. Applications. 2. SYSTEMS OF LINEAR
EQUATIONS. Introduction: Triviality. Introduction
to Systems of Linear Equations. Direct Methods for
Solving Linear Systems. Writing Project: A History of
Gaussian Elimination. Explorations: Lies My Computer
Told Me; Partial Pivoting; Counting Operations: An
Introduction to the Analysis of Algorithms. Spanning
Sets and Linear Independence. Applications. Vignette:
The Global Positioning System. Iterative Methods for
Solving Linear Systems. 3. MATRICES. Introduction:
Matrices in Action. Matrix Operations. Matrix Algebra.
The Inverse of a Matrix. The LU Factorization. Subspaces,
Basis, Dimension, and Rank. Introduction to Linear
Transformations. Vignette: Robotics. Applications. 4.
EIGENVALUES AND EIGENVECTORS. Introduction:
A Dynamical System on Graphs. Introduction to
Eigenvalues and Eigenvectors. Determinants. Writing
Project: Which Came First-the Matrix or the Determinant?
Vignette: Lewis Carroll’s Condensation Method.
Exploration: Geometric Applications of Determinants.
Eigenvalues and Eigenvectors of n x n Matrices. Writing
Project: The History of Eigenvalues. Similarity and
Diagonalization. Iterative Methods for Computing
Eigenvalues. Applications and the Perron-Frobenius
Theorem. Vignette: Ranking Sports Teams and Searching
the Internet. 5. ORTHOGONALITY. Introduction:
Shadows on a Wall. Orthogonality in Rn. Orthogonal
Complements and Orthogonal Projections. The GramSchmidt Process and the QR Factorization. Explorations:
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173
The Modified QR Factorization; Approximating
Eigenvalues with the QR Algorithm. Orthogonal
Diagonalization of Symmetric Matrices. Applications.
6. VECTOR SPACES. Introduction: Fibonacci in
(Vector) Space. Vector Spaces and Subspaces. Linear
Independence, Basis, and Dimension. Writing Project:
The Rise of Vector Spaces. Exploration: Magic Squares.
Change of Basis. Linear Transformations. The Kernel
and Range of a Linear Transformation. The Matrix of
a Linear Transformation. Exploration: Tilings, Lattices
and the Crystallographic Restriction. Applications.
7. DISTANCE AND APPROXIMATION. Introduction:
Taxicab Geometry. Inner Product Spaces. Explorations:
Vectors and Matrices with Complex Entries; Geometric
Inequalities and Optimization Problems. Norms and
Distance Functions. Least Squares Approximation. The
Singular Value Decomposition. Vignette: Digital Image
Compression. Applications. 8. CODES. (Online) Code
Vectors. Vignette: The Codabar System. Error-Correcting
Codes. Dual Codes. Linear Codes. The Minimum
Distance of a Code. Appendix A: Mathematical Notation
and Methods of Proof. Appendix B: Mathematical
Induction. Appendix C: Complex Numbers. Appendix
D: Polynomials.
© 2015, 720pp, Hardback, 9781285463247
comprehensive text, the book maintains clarity by
explaining the profound ideas of linear algebra in simple
terms. Theorems, corollaries, properties, definitions,
proofs, and worked examples are presented in a brief
and easy-to-understand style so that students can fully
comprehend how mathematics works.
FEATURES
• Written and organized for non-mathematics majors
with focus on the algebra of matrix, linear equations,
eigenvalues and eigenvectors of a matrix, matrix
diagonalization, and quadratic forms.
• Easy for instructors to customize for courses ranging
from 35 to 72 teaching hours.
• Lucid and brief proofs are provided for difficult
theorems to help students better grasp the theory
and concepts behind them.
• Includes more than 450 questions that are carefully
categorized at different levels of difficulty (basic and
tough).
• Supplementary exercises are also provided for further
practice. This allows instructors to select exercises
according to the abilities and competencies of their
classes.
CONTENTS
1. Determinants. 2. Matrices. 3. Systems of Linear
Equations. 4. Vector Spaces and Linear Transformations.
5. Eigenvalues and Eigenvectors, Diagonalization of
Matrices. 6. Quadratic Forms. 7. Applications. Appendix
A. Inner Product Space, Hermitian Quadratic Form.
Appendix B. Jordan Canonical Form (Abstract).
© 2010, 400pp, Hardback, 9789814232005
LINEAR ALGEBRA
Theory and Applications
Yuma Ju, Tsinghua University, Beijing; Wenxun Xing, Tsinghua
University, Beijing; Cuiqin Lin, Tsinghua University, Beijing; Jinde Hu ,
Tsinghua University, Beijing
Linear Algebra: Theor y and Applic ations is
conceptualized and written by distinguished authors
as a main text or as a reference book for students who
need to apply linear algebraic techniques for solving
problems related to their specific disciplines. As a
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• Numerous exercises providing practice on
mathematical concepts and applying techniques in
Maple, Student Projects for group or individual work
help students apply the modeling process in fully
integrated fashion and synthesize the mathematical
techniques they have learned.
• Flexible coverage allowing instructors to choose
topics based on level, topic emphasis, and one- or
two-semester sequences. Core chapters require only
basic calculus, while later chapters requiring some
multivariable calculus, linear algebra, and probability
can be omitted without loss of continuity.
MATHEMATICAL MODELING WITH
MAPLE, INTERNATIONAL EDITION
CONTENTS
William P. Fox
With an innovative approach that leverages the
power of the Maple® computer algebra system as an
analytical tool, MATHEMATICAL MODELING WITH
MAPLE, International Edition offers an effective
introduction to mathematical modeling of compelling
real world applications. Intended for students with
a background in calculus, the text shows how to
formulate, build, solve, analyze, and critique models
of applications in math, engineering, computer
science, business, and the physical and life sciences.
The book utilizes Maple for computations, plotting
results graphically, and dynamically analyzing results
within the modeling process. Easy-to-follow software
instructions are provided, and Maple syntax in the book
is also offered online as Maple workbooks allowing
students to quickly and interactively work problems
as they read. MATHEMATICAL MODELING WITH
MAPLE, International Edition helps students develop
their analytical skills while harnessing the power of
cutting-edge modern technology, allowing them to
become competent, confident problem solvers for the
21st century.
FEATURES
• Focuses on three core aspects of modeling: Creative
and Empirical Modeling, Model Analysis, and Model
Research. Students will learn a structured approach to
constructing models, learn how to work backwards to
analyze assumptions, and apply what they’ve learned
to other scenarios.
• Careful introduction to Maple, intuitively exposing
students to the syntax and graphing capabilities
of the software in tandem with showing them its
effectiveness in assisting the modeling process.
1. INTRODUCTION TO MAPLE. The Structure of
Maple. A General Introduction to Maple. Maple
Quick Review. Maple Training. 2. INTRODUCTION,
OVERVIEW, AND THE PROCESS OF MATHEMATICAL
MODELING. Introduction. The Modeling Process.
Illustrative Examples. 3. DISCRETE DYNAMICAL
MODELS. Introduction. Modeling Discrete Change.
Tower of Hanoi. Drug Dosage Problem. Time Value of
Money. Simple Mortgage. The Spotted Owl. Equilibrium
Values and Long-term Behavior. Nonlinear Discrete
Dynamical Systems. Growth of a Yeast Culture. Spread
of a Contagious Disease. Systems of Discrete Dynamical
Systems. Merchants. Competitive Hunter Model. Fast
Food Tendencies. Modeling Predator-Prey, SIR, and
Military. Predator-Prey. SIR of an Epidemic. Modeling
Military Insurgencies. 4. MODEL FITTING CRITERION.
Introduction. Different Curve Fitting Criterion. Plotting
the Residuals for a Least-Squares Fit. Bass Fish.
Population. Bounding on Chebyshev’s. 5. MODELING
WITH PROPORTIONALIT Y AND GEOMETRIC
SIMILARITY. Introduction. Proportionality. Kepler’s
Law. Bass Fishing Derby. Geometric Similarity. Heart
Sizes. Crew Races. Terror Bird. 6. EMPIRICAL MODEL
BUILDING. Introduction. Simple One Term Models.
Bass Fishing Derby. Terror Bird Revisited. Fitting an (n
− 1)st order Polynomials to N Data Points. Polynomial
Smoothing. Cost of a U.S. Postage Stamp. The Cubic
Spline Model. Population Fruit Flies. Vehicle Stopping
Distance. Cost of a U.S. Postage Stamp. 7. LINEAR
PROGRAMMING. Introduction. Formulating Linear
Programming Problems. Product Mix of New Drinks.
Financial Planning. Blending. Production Planning.
Graphical simplex. CPU Memory Chips. Feasible
Region. Minimization Problem. Unbounded Case.
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Graphical Sensitivity Analysis. The Simplex Method
and Tableaus. Linear Programming with Maple. Data
Envelopment Analysis. Ranking Banks. Ranking Banks
as an LP. Sensitivity Analysis with Maple. 8. SINGLE
VARIABLE OPTIMIZATION. Introduction. Single Variable
Optimization and Basic Theory. Applications of MaxMin Theory. Chemical Company. Manufacturing. SP6
Computer Development. Applied Optimization Models.
Inventory Problem. Oil Rig Location. Numerical Search
Methods. Unrestricted Methods. Dichotomous Search.
Golden Section Search. Fibonacci Search. Interpolation
Methods. 9. MODELING USING UNCONSTRAINED
OPTIMIZATION: MAXIMIZATION AND MINIMIZATION
WITH SEVERAL VARIABLES. Introduction. Basic Theory.
The Hessian Matrix. Unconstrained Optimization.
Least Squares. Find the Island. Numerical Search
Methods. Gradient Search. Modified Newton’s Method.
10. EQUALITY AND INEQUALITY CONSTRAINED
MULTIVARIABLE OPTIMIZATION. Introduction.
Equality Constraints: Method of LaGrange Multipliers.
Basic Theory. Graphical Representations. Cobb Douglas.
Oil Transfers. Inequality Constraints: Kuhn-Tucker
(KTC Condition). Spanning Cones. Two-variable Linear.
Maximize Profit from Perfume. Minimum Variance
of Investment Returns. 11. MODELS WITH LINEAR
ALGEBRA. Introduction. Introduction to Systems of
Equations. Models with Unique Solutions Using Systems
of Equations. A Bridge Too Far. Leontief Economic
Models. Least Squares Revisited. Natural Cubic
Splines Revisited. Models with Infinite Solutions using
Systems of Equations. Basic Chemical Balancing. Redox
Equations. 12. ORDINARY FIRST ORDER DIFFERENTIAL
EQUATIONS MODELS. Introduction. Applied First
Order Models. Radioactive Decay. Newton’s Law of
Cooling. Mixtures. Population Models. Spread of a
Disease. Slope Fields and Qualitative Assessment of
Autonomous ODEs. Analytical Solutions to First ODEs.
Separation of Variables. Linear Equations. Numerical
Methods for Solutions to First Order Differential
Equations. Euler’s Method. Improved Euler’s Method.
Runga-Kutta 4 Method. 13. SYSTEMS OF LINEAR FIRST
ORDER DIFFERENTIAL EQUATIONS. Introduction.
Applied Systems of ODEs and Models. Economic
Supply and Demand. Circuits. Competition. PredatorPrey. Diffusion. Insurgencies. Phase Portraits and
Qualitative Assessment of Autonomous Systems. Fish
Pond. Solving Homogeneous and Non-homogeneous
Systems of ODEs with Constant Coefficients. Applied
Systems with Maple. Diffusion. Diffusion through Two
Membranes. Electrical Circuits. Numerical Methods to
Systems of ODEs with Maple. Predator-Prey Model.
14. DISCRETE PROBABILITY MODELS. Introduction.
Introduction to Classical Probability. Reliability Models
in Engineering and Science. Overbooking Airlines
Model. Markov Chains. 15. CONTINUOUS PROBABILITY
MODELS. Introduction. Reliability Revisited. Modeling
using the Normal Distribution. Confidence Interval and
Hypothesis Testing. Regression: Linear, Transformed,
and Nonlinear. 16. SIMULATION MODELS. Introduction.
Introduction. Monte Carlo Simulation. Deterministic
Behavior. Area Problems. Volume Problems. Probabilistic
Behavior. Applied Simulation Models. Missile Attacks.
Gasoline Inventory. 17. MODELING WITH GAME
THEORY. Introduction. Zero-sum Games. PredatorPrey. Hitter-Pitcher Duel. Non- Zero-sum Games. Nash
Arbitration. Illustrative Example: Artist’s Guild Strike.
© 2012, 592pp, Paperback, 9781111576516
NUMERICAL ANALYSIS, INTERNATIONAL
EDITION, 9E
Richard L. Burden, Youngstown State University; J. Douglas Faires,
Youngstown State University
This well-respected text gives an introduction to the
modern approximation techniques and explains how,
why, and when the techniques can be expected to work.
The authors focus on building students’ intuition to
help them understand why the techniques presented
work in general, and why, in some situations, they
fail. With a wealth of examples and exercises, the text
demonstrates the relevance of numerical analysis to
a variety of disciplines and provides ample practice
for students. The applications chosen demonstrate
concisely how numerical methods can be, and often
must be, applied in real-life situations. In this edition,
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the presentation has been fine-tuned to make the
book even more useful to the instructor and more
interesting to the reader. Overall, students gain a
theoretical understanding of, and a firm basis for future
study of, numerical analysis and scientific computing.
A more applied text with a different menu of topics is
the authors’ highly regarded NUMERICAL METHODS,
Third Edition.
NEW TO THIS EDITION
• Updated technology coverage and programs to reflect
current standards, incorporating more modern timesaving techniques.
• Added exercises and applications per request from
the market.
• The authors have further curbed the use of theory
and increased use of methods to keep up with
Engineering-service trend while maintaining spread
across audiences.
FEATURES
• Limits course prerequisites to calculus with no overt
Differential Equations or Linear Algebra dependencies.
• Balances theory and methods to stake a wide middle
ground between audiences who need to know the
mathematics and audiences who only need to know
the essential techniques.
• Flexible coverage to suit one- or two-semester courses
and differing student levels, with careful attention
paid to marking optional material and alternate paths
for instructors.
• Theory coverage emphasizes mathematical thought
and is especially accessible for students who’ve
optionally taken undergrad math foundations courses
like Real Analysis or Transition to Advanced Math.
• Over 2,500 exercises from simple drill to advanced
theoretical problems.
• Numerous real-life applications to engineering,
computer science, physical sciences, biological
sciences, and social sciences.
• Technology-neutral algorithms easily adapted to
various software. Specific instructions given for Maple
in limited cases where software-specific questions are
absolutely required.
CONTENTS
1. MATHEMATICAL PRELIMINARIES AND ERROR
ANALYSIS. Review of Calculus. Round-off Errors and
Computer Arithmetic. Algorithms and Convergence.
Numerical Software. 2. SOLUTIONS OF EQUATIONS
IN ONE VARIABLE. The Bisection Method. FixedPoint Iteration. Newton’s Method and its Extensions.
Error Analysis for Iterative Methods. Accelerating
Convergence. Zeros of Polynomials and Müller’s Method.
Survey of Methods and Software. 3. INTERPOLATION
AND POLYNOMIAL APPROXIMATION. Interpolation
and the Lagrange Polynomial. Data Approximation
and Neville’s Method Divided Differences. Hermite
Interpolation. Cubic Spline Interpolation. Parametric
Curves. Survey of Methods and Software. 4. NUMERICAL
DIFFERENTIATION AND INTEGRATION. Numerical
Differentiation. Richardson’s Extrapolation. Elements
of Numerical Integration. Composite Numerical
Integration. Romberg Integration. Adaptive Quadrature
Methods. Gaussian Quadrature. Multiple Integrals.
Improper Integrals. Survey of Methods and Software.
5. INITIAL-VALUE PROBLEMS FOR ORDINARY
DIFFERENTIAL EQUATIONS. The Elementary Theory
of Initial-Value Problems. Euler’s Method. Higher-Order
Taylor Methods. Runge-Kutta Methods. Error Control and
the Runge-Kutta-Fehlberg Method. Multistep Methods.
Variable Step-Size Multistep Methods. Extrapolation
Methods. Higher-Order Equations and Systems of
Differential Equations. Stability. Stiff Differential
Equations. Survey of Methods and Software. 6. DIRECT
METHODS FOR SOLVING LINEAR SYSTEMS. Linear
Systems of Equations. Pivoting Strategies. Linear Algebra
and Matrix Inversion. The Determinant of a Matrix.
Matrix Factorization. Special Types of Matrices. Survey
of Methods and Software. 7. ITERATIVE TECHNIQUES
IN MATRIX ALGEBRA. Norms of Vectors and Matrices.
Eigenvalues and Eigenvectors. The Jacobi and GaussSiedel Iterative Techniques. Iterative Techniques for
Solving Linear Systems. Relaxation Techniques for
Solving Linear Systems. Error Bounds and Iterative
Refinement. The Conjugate Gradient Method. Survey of
Methods and Software. 8. APPROXIMATION THEORY.
Discrete Least Squares Approximation. Orthogonal
Polynomials and Least Squares Approximation.
Chebyshev Polynomials and Economization of Power
Series. Rational Function Approximation. Trigonometric
Polynomial Approximation. Fast Fourier Transforms.
Survey of Methods and Software. 9. APPROXIMATING
EIGENVALUES. Linear Algebra and Eigenvalues.
Orthogonal Matrices and Similarity Transformations.
The Power Method. Householder’s Method.The QR
Algorithm.Singular Value Decomposition. Survey of
Methods and Software. 10. NUMERICAL SOLUTIONS
OF NONLINEAR SYSTEMS OF EQUATIONS. Fixed
Points for Functions of Several Variables. Newton’s
Method. Quasi-Newton Methods. Steepest Descent
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Techniques. Homotopy and Continuation Methods.
Survey of Methods and Software. 11. BOUNDARYVALUE PROBLEMS FOR ORDINARY DIFFERENTIAL
EQUATIONS. The Linear Shooting Method. The Shooting
Method for Nonlinear Problems. Finite-Difference
Methods for Linear Problems. Finite-Difference Methods
for Nonlinear Problems. The Rayleigh-Ritz Method.
Survey of Methods and Software. 12. NUMERICAL
SOLUTIONS TO PARTIAL DIFFERENTIAL EQUATIONS.
Elliptic Partial-Differential Equations. Parabolic PartialDifferential Equations. Hyperbolic Partial-Differential
Equations. An Introduction to the Finite-Element
Method. Survey of Methods and Software.
© 2011, 888pp, Paperback, 9780538735643
• NEW! A section of Fourier Series and Fast Fourier
Transforms has been added.
• The first two chapters in the previous edition on
Mathematical Preliminaries, Taylor Series, OatingPoint Representation, and Errors have been combined
into a single introductory chapter to allow instructors
and students to move quickly.
• Some sections and material have been re-moved from
the new edition such as the introductory section
on numerical integration. Some material and many
bibliographical items have been moved from the
textbook to the website.
• The two chapters, in the previous edition, on Ordinary
Differential Equations have been combined into one
chapter.
• Many of the pseudocodes from the text have been
programmed in MATLAB, Mathematica, and Maple
and appear in the website so that they are easily
accessible.
• More figures and numerical examples have been
added.
FEATURES
NUMERICAL MATHEMATICS AND
COMPUTING, INTERNATIONAL EDITION,
7E
E. Ward Cheney, University of Texas at Austin; David R. Kincaid,
University of Texas at Austin
Authors Ward Cheney and David Kincaid show students
of science and engineering the potential computers
have for solving numerical problems and give them
ample opportunities to hone their skills in programming
and problem solving. NUMERICAL MATHEMATICS
AND COMPUTING, 7E, International Edition also helps
students learn about errors that inevitably accompany
scientific computations and arms them with methods
for detecting, predicting, and controlling these errors.
NEW TO THIS EDITION
• UPDATED! The Solving Systems of Linear Equations
chapter has been moved earlier in the text to provide
more clarity throughout the text.
• NEW! Exercises, computer exercises, and application
exercises have been added to the text.
• More Accessible: Computer codes and other material
are now included on the text website--giving you and
your students easy access without tedious typing.
Matlab, Mathematica, and Maple computer codes and
the ¿Overview of Mathematical Software appendix
are all now available online.
• Visual Learning: Because concrete codes and visual
aids are helpful to every reader, the authors have
added even more figures and numerical examples
throughout the text--ensuring students gain solid
understanding before advancing to new topics.
CONTENTS
1. INTRODUCTION. Preliminary Remarks. Review of
Taylor Series. 2. FLOATING-POINT REPRESENTATION
AND ERRORS. Floating-Point Representation. Loss of
Significance. 3. LOCATING ROOTS OF EQUATIONS.
Bisection Method. Newton’s Method. Secant
Method. 4. INTERPOLATION AND NUMERICAL
DIFFERENTIATION. Polynomial Interpolation. Errors
in Polynomial Interpolation. Estimating Derivatives
and Richardson Extrapolation. 5. NUMERICAL
INTEGRATION. Lower and Upper Sums. Trapezoid
Rule. Romberg Algorithm. 6. ADDITIONAL TOPICS
ON NUMERICAL INTEGRATION. Simpson’s Rule
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and Adaptive Simpson’s Rule. Gaussian Quadrature
Formulas. 7. SYSTEMS OF LINEAR EQUATIONS. Naive
Gaussian Elimination. Gaussian Elimination with Scaled
Partial Pivoting. Tridiagonal and Banded Systems.
8. ADDITIONAL TOPICS CONCERNING SYSTEMS
OF LINEAR EQUATIONS. Matrix Factorizations.
Iterative Solutions of Linear Systems. Eigenvalues and
Eigenvectors. Power Method. 9. APPROXIMATION BY
SPLINE FUNCTIONS. First-Degree and Second-Degree
Splines. Natural Cubic Splines. B Splines: Interpolation
and Approximation. 10. ORDINARY DIFFERENTIAL
EQUATIONS. Taylor Series Methods. Runge-Kutta
Methods. Stability and Adaptive Runge-Kutta and
Multistep Methods. 11. SYSTEMS OF ORDINARY
DIFFERENTIAL EQUATIONS. Methods for First-Order
Systems. Higher-Order Equations and Systems.
Adams-Bashforth-Moulton Methods. 12. SMOOTHING
OF DATA AND THE METHOD OF LEAST SQUARES.
Method of Least Squares. Orthogonal Systems and
Chebyshev Polynomials. Other Examples of the LeastSquares Principle. 13. MONTE CARLO METHODS AND
SIMULATION. Random Numbers. Estimation of Areas
and Volumes by Monte Carlo Techniques. Simulation.
14. BOUNDARY-VALUE PROBLEMS FOR ORDINARY
DIFFERENTIAL EQUATIONS. Shooting Method
Shooting Method Algorithm. A Discretization Method.
15. PARTIAL DIFFERENTIAL EQUATIONS. Parabolic
Problems. Hyperbolic Problems. Elliptic Problems.
16. MINIMIZATION OF FUNCTIONS. One-Variable
Case. Multivariate Case. 17. LINEAR PROGRAMMING.
Standard Forms and Duality. Simplex Method.
Approximate Solution of Inconsistent Linear Systems.
APPENDIX A. ADVICE ON GOOD PROGRAMMING
PRACTICES. Programming Suggestions. APPENDIX
B. REPRESENTATION OF NUMBERS IN DIFFERENT
BASES. Representation of Numbers in Different
Bases. APPENDIX C. ADDITIONAL DETAILS ON IEEE
FLOATING-POINT ARITHMETIC. More on IEEE Standard
Floating-Point Arithmetic. APPENDIX D. LINEAR
ALGEBRA CONCEPTS AND NOTATION. Elementary
Concepts. Abstract Vector Spaces. ANSWERS FOR
SELECTED PROBLEMS. BIBLIOGRAPHY. INDEX.
© 2013, 704pp, Paperback, 9781133491811
Coming Soon!
NUMERICAL METHODS,
Douglas Faires, Youngstown State University; Richard L. Burden,
NUMERICAL METHODS, 4E, International Edition
emphasizes the intelligent application of approximation
techniques to the type of problems that commonly
occur in engineering and the physical sciences. Students
learn why the numerical methods work, what kinds of
errors to expect, and when an application might lead
to difficulties. The authors also provide information
about the availability of high-quality software for
numerical approximation routines. The techniques are
the same as those covered in the authors’ top-selling
Numerical Analysis text, but this text provides an
overview for students who need to know the methods
without having to perform the analysis. This concise
approach still includes mathematical justifications,
but only when they are necessary to understand the
methods. The emphasis is placed on describing each
technique from an implementation standpoint, and on
convincing the student that the method is reasonable
both mathematically and computationally.
NEW TO THIS EDITION
• New examples and exercises appear throughout the
text, offering fresh options for assignments.
• Chapter 7, “Iterative Methods for Solving Linear
Systems,” includes a new section on Conjugate
Gradient Methods.
• Chapter 10, “Solutions of Systems of Nonlinear
Equations,” includes a new section on Homotopy and
Continuation Methods.
• Revised techniques for algorithms and programs
are included in six languages: FORTRAN, Pascal, C,
MAPLE, Mathematica, and MATLAB.
• All of the Maple material in the text is updated to
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179
conform with the newest release (Maple 7). All of
the material on the CD that accompanies the book is
updated to conform to the latest available versions
of Maple, Mathematica, and MATLAB.
• This edition includes many more examples of Maple
code.
FEATURES
• Worked examples using computer algebra systems
help students understand why the software usually
works, why it might fail, and what to do when a
software program fails.
• The exercise sets include problems reflecting a wide
range of difficulty as well as problems that offer good
illustrations of the methods being discussed, while
requiring little calculation.
• The book contains instructions for a wide range of
popular computer algebra systems.
• This text is designed for use in a one-semester course,
but contains more material than needed. Instructors
have flexibility in choosing topics and students gain
a useful reference for future work.
CONTENTS
1. MATHEMATICAL PRELIMINARIES AND ERROR
ANALYSIS. Introduction. Review of Calculus.
Round-off Error and Computer Arithmetic. Errors
in Scientific Computation. Computer Software. 2.
SOLUTIONS OF EQUATIONS OF ONE VARIABLE.
Introduction. The Bisection Method. The Secant
Method. Newton’s Method. Error Analysis and
Accelerating Convergence. Müller’s Method. Survey
of Methods and Software. 3. INTERPOLATION AND
POLYNOMIAL APPROXIMATION. Introduction.
Lagrange Polynomials. Divided Differences. Hermite
Interpolation. Spline Interpolation. Parametric Curves.
INTEGRATION AND DIFFERENTIATION. Introduction.
Basic Quadrature Rules. Composite Quadrature Rules.
Romberg Integration. Gaussian Quadrature. Adaptive
Quadrature. Multiple Integrals. Improper Integrals.
Numerical Differentiation. Survey of Methods and
Software. 5. NUMERICAL SOLUTION OF INITIAL-VALUE
PROBLEMS. Introduction. Taylor Methods. Runge-Kutta
Methods. Predictor-Corrector Methods. Extrapolation
Methods. Adaptive Techniques. Methods for Systems
of Equations. Stiff Differentials Equations. Survey of
Methods and Software. 6. DIRECT METHODS FOR
SOLVING LINEAR SYSTEMS. Introduction. Gaussian
Elimination. Pivoting Strategies. Linear Algebra and
Matrix Inversion. Matrix Factorization. Techniques for
Special Matrices. Survey of Methods and Software. 7.
ITERATIVE METHODS FOR SOLVING LINEAR SYSTEMS.
Introduction. Convergence of Vectors. Eigenvalues and
Eigenvectors. Conjugate Gradient Methods. The Jacobi
and Gauss-Seidel Methods. The SOR Method. Error
Bounds and Iterative Refinement. Survey of Methods and
Software. 8. APPROXIMATION THEORY. Introduction.
Discrete Least Squares Approximation. Continuous
Least Squares Approximation. Chebyshev Polynomials.
Rational Function Approximation. Trigonometric
Polynomial Approximation. Fast Fourier Transforms.
Survey of Methods and Software. 9. APPROXIMATING
EIGENVALUES. Introduction. Isolating Eigenvalues. The
Power Method. Householder’s Method. The QR Method.
Survey of Methods and Software. 10. SOLUTIONS OF
SYSTEMS OF NONLINEAR EQUATIONS. Introduction.
Newton’s Methods for Systems. Quasi-Newton
Methods. The Steepest Descent Method. Survey of
Methods and Software. Homotopy and Continuation
Methods. 11. BOUNDARY-VALUE PROBLEMS FOR
ORDINARY DIFFERENTIAL EQUATIONS. Introduction.
The Linear Shooting Method. Linear Finite Difference
Methods. The Nonlinear Shooting Method. Nonlinear
Finite-Difference Methods. Variational Techniques.
METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS.
Introduction. Finite-Difference Methods for Elliptic
Problems. Finite-Difference Methods for Parabolic
Problems. Finite-Difference Methods for Hyperbolic
Problems. Introduction to the Finite-Element Method.
Survey of Methods and Software.
© 2013, 608pp, Paperback, 9780495385691
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180
STUDENT RESOURCE WITH SOLUTIONS
MANUAL FOR ZILL’S A FIRST COURSE
IN DIFFERENTIAL EQUATIONS WITH
MODELING APPLICATIONS, 10TH, 10E
Dennis G. Zill, Loyola Marymount University
WITH MODELING APPLICATIONS, 10th Edition
INSTRUCTOR DESCRIPTION: This manual contains
fully worked-out solutions to all of the odd-numbered
exercises in the text, giving students a way to check
their answers and ensure that they took the correct
steps to arrive at an answer.
FOR FAIRES/BURDEN’S NUMERICAL
METHODS, 4TH, 4E
Douglas Faires, Youngstown State University; Richard L. Burden,
© 2013, 320pp, Paperback, 9780495392989
© 2013, 256pp, Paperback, 9781133491927
CHENEY/KINCAID’S NUMERICAL
MATHEMATICS AND COMPUTING, 7TH, 7E
E. Ward Cheney, University of Texas at Austin; David R. Kincaid,
University of Texas at Austin
Go beyond the answers—see what it takes to get there
and improve your grade! This manual provides workedout, step-by-step solutions to the odd-numbered
problems in the text. This gives you the information
you need to truly understand how these problems are
solved.
© 2013, 176pp, Paperback, 9781133491804
GALLIAN’S CONTEMPORARY ABSTRACT
ALGEBRA, 8TH, 8E
Joseph A. Gallian, University of Minnesota, Duluth
CONTEMPORARY ABSTRACT ALGEBRA, 8th Edition,
this manual shows you how to approach and solve
problems using the same step-by-step explanations
found in your textbook examples.
© 2013, 144pp, Paperback, 9781133608530
www.cengageasia.com
181
Precalculus
LARSON/FALVO’S ELEMENTARY LINEAR
ALGEBRA, 7TH, 7E
David C. Falvo, The Pennsylvania State University, The Behrend College
© 2013, 256pp, Paperback, 9781133111320
ALGEBRA & TRIGONOMETRY, 9E
Larson’s ALGEBRA AND TRIGONOMETRY is ideal for
a two-term course and known for delivering sound,
consistently structured explanations and carefully
written exercises of the mathematical concepts. With
the Ninth Edition, the author continues to revolutionize
the way students learn material by incorporating more
real-world applications, on-going review and innovative
technology. How Do You See It? exercises give students
practice applying the concepts, and new Summarize
features, Checkpoint problems and a Companion
Website reinforce understanding of the skill sets to help
students better prepare for tests. Enhanced WebAssign
features fully-integrated content from the text, with
the addition of End-of-Section problems and Chapter
Tests, as well as problem-specific videos, animations
and lecture videos.
NEW TO THIS EDITION
FOR ZILL/WRIGHT’S DIFFERENTIAL
EQUATIONS WITH BOUNDARY-VALUE
PROBLEMS, 8TH, 8E
Dennis G. Zill, Loyola Marymount University; Warren S. Wright,
Loyola Marymount University
This manual contains fully worked-out solutions to all of
the odd-numbered exercises in the text, giving students
a way to check their answers and ensure that they took
the correct steps to arrive at an answer.
© 2013, 384pp, Paperback, 9781133491958
• Fresh Chapter Openers highlight real-life problems
that connect to the examples and exercises presenting
in the following chapter.
• Innovative Summarize Features help students
organize the lesson’s key concepts into a concise
summary, providing a valuable study tool at the end
of each section.
• Unprecedented How Do You See It? Exercises in every
section present real-life problems that students solve
by visual inspection using the concepts in the lesson.
• Original Checkpoint Problems encourage immediate
practice and check students’ understanding of the
concepts in the paired example.
• New Series Companion Website features chapter
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182
projects, data tables, assessments, study tools, video
solutions and more to support students outside the
text.
• Enhanced Exercise Sets deliver more rigor, relevancy
and coverage than ever before and feature multi-step,
real-life exercises to reinforce problem-solving skills
and mastery of concepts
• Expanded Section Objectives offer students the
opportunity to preview what will be presented in the
upcoming section.
• Enriched Remarks reinforce or expand upon concepts
helping students learn how to study mathematics,
avoid common errors, address special cases, or show
alternative or additional steps to a solution of an
example.
• Up-to-the-minute student support through CalcChat.
com, an independent website, provides students with
free solutions to all odd-numbered problems in the
text.
FEATURES
• Side-By-Side Examples help students not only see that
a problem can be solved in more than one way but
how different methods—algebraically, graphically, and
numerically—yield the same result. The side-by-side
format also addresses many different learning styles.
CONTENTS
P. PREREQUISITES. Review of Real Numbers and Their
Properties. Exponents and Radicals. Polynomials and
Special Products. Factoring Polynomials. Rational
Expressions. The Rectangular Coordinate System and
Graphs. Chapter Summary. Review Exercises. Chapter
Test. Proofs in Mathematics. P.S. Problem Solving. 1.
EQUATIONS, INEQUALITIES, AND MATHEMATICAL
MODELING. Graphs of Equations. Linear Equations
in One Variable. Modeling with Linear Equations.
Quadratic Equations and Applications. Complex
Numbers. Other Types of Equations. Linear Inequalities
in One Variable. Other Types of Inequalities. Chapter
Summary. Review Exercises. Chapter Test. Proofs in
Mathematics. P.S. Problem Solving. 2. FUNCTIONS AND
THEIR GRAPHS. Linear Equations in Two Variables.
Functions. Analyzing Graphs of Functions. A Library
of Parent Functions. Transformations of Functions.
Combinations of Functions: Composite Functions.
Inverse Functions. Chapter Summary. Review Exercises.
Chapter Test. Cumulative Test for Chapters P-2. Proofs
in Mathematics. P.S. Problem Solving. 3. POLYNOMIAL
and Synthetic Division. Zeros of Polynomial Functions.
Mathematical Modeling and Variation. Chapter
Mathematics. P.S. Problem Solving. 4. RATIONAL
FUNCTIONS AND CONICS. Rational Functions and
Asymptotes. Graphs of Rational Functions. Conics.
Translations of Conics. Chapter Summary. Review
Exercises. Chapter Test. Proofs in Mathematics. P.S.
Problem Solving. 5. EXPONENTIAL AND LOGARITHMIC
FUNCTIONS. Exponential Functions and Their Graphs.
Logarithmic Functions and Their Graphs. Properties of
Logarithms. Exponential and Logarithmic Equations.
Exponential and Logarithmic Models. Chapter Summary.
Review Exercises. Chapter Test. Cumulative Test for
Chapters 3-5. Proofs in Mathematics. P.S. Problem
Solving. 6. TRIGONOMETRY. Angles and Their Measure.
Right Triangle Trigonometry. Trigonometric Functions of
Any Angle. Graphs of Sine and Cosine Functions. Graphs
of Other Trigonometric Functions. Inverse Trigonometric
Functions. Applications and Models. Chapter Summary.
Review Exercises. Chapter Test. Proofs in Mathematics.
P.S. Problem Solving. 7. ANALYTIC TRIGONOMETRY.
Using Fundamental Identities. Verifying Trigonometric
Difference Formulas. Multiple-Angle and Product-toSum Formulas. Chapter Summary. Review Exercises.
Chapter Test. Proofs in Mathematics. P.S. Problem
Solving. 8. ADDITIONAL TOPICS IN TRIGONOMETRY.
Law of Sines. Law of Cosines. Vectors in the Plane.
Vectors and Dot Products. Trigonometric Form of a
Complex Number. Chapter Summary. Review Exercises.
Chapter Test. Cumulative Test for Chapters 6-8. Proofs
in Mathematics. P.S. Problem Solving. 9. SYSTEMS
OF EQUATIONS AND INEQUALITIES. Linear and
Nonlinear Systems of Equations. Two-Variable Linear
Systems. Multivariable Linear Systems. Partial Fractions.
Systems of Inequalities. Linear Programming. Chapter
Mathematics. P.S. Problem Solving. 10. MATRICES AND
DETERMINANTS. Matrices and Systems of Equations.
Operations with Matrices. The Inverse of a Square
Matrix. The Determinant of a Square Matrix. Applications
of Matrices and Determinants. Chapter Summary.
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P.S. Problem Solving. 11. SEQUENCES, SERIES, AND
PROBABILITY. Sequences and Series. Arithmetic
Sequences and Partial Sums. Geometric Sequences
and Series. Mathematical Induction. The Binomial
Theorem. Counting Principles. Probability. Chapter
Summary. Review Exercises. Chapter Test. Cumulative
Test for Chapters 9-11. Proofs in Mathematics. P.S.
Problem Solving. APPENDIX A: Errors and the Algebra
of Calculus. APPENDIX B: Concepts in Statistics (web).
Representing Data. Measures of Central Tendency and
Dispersion. Least Squares Regression.
© 2014, 976pp, Hardback, 9781133959748
ALGEBRA AND TRIGONOMETRY, 6E
Real Mathematics, Real People
ALGEBRA AND TRIGONOMETRY: REAL MATHEMATICS,
REAL PEOPLE, 6th Edition, is an ideal student and
instructor resource for courses that require the use of
a graphing calculator. The quality and quantity of the
exercises, combined with interesting applications and
innovative resources, make teaching easier and help
students succeed. Retaining the series’ emphasis on
student support, selected examples throughout the
text include notations directing students to previous
sections to review concepts and skills needed to master
the material at hand. The book also achieves accessibility
through careful writing and design--including examples
with detailed solutions that begin and end on the same
page, which maximizes readability. Similarly, side-byside solutions show algebraic, graphical, and numerical
representations of the mathematics and support a
variety of learning styles. Reflecting its new subtitle,
this significant revision focuses more than ever on
showing students the relevance of mathematics in their
lives and future careers.
NEW TO THIS EDITION
• With the extensive revision to create the Sixth
Edition, this book’s original subtitle, “A Graphing
Approach,” no longer represents the text’s essence
(although the graphing calculator is still required).
The author’s changes and the new title, “ALGEBRA
AND TRIGONOMETRY: REAL MATHEMATICS, REAL
PEOPLE,” address a primary need in education today-relevance. The mathematics in this text is both real
and relevant, and the people introduced are either
already in or preparing for careers in which they will
use mathematics.
• New Chapter Openers highlight real modeling data
problems, each showing a graph of the data, a section
reference, and a short description of the data.
• A new Explore the Concept feature engages students
in active discovery of mathematical concepts,
strengthens critical thinking skills, and helps build
intuition.
• A new What’s Wrong? feature points out common
errors made using graphing utilities.
• A new Vocabulary and Concept Check appears at the
beginning of the exercise set for each section. Each of
these checks asks fill-in-the-blank, matching, and noncomputational questions designed to help students
learn mathematical terminology and to test basic
understanding of that section’s concepts.
• The section exercises are now grouped into
four categories: Vocabulary and Concept Check,
Procedures and Problem Solving, Conclusions, and
Cumulative Mixed Review. Many of the exercises are
titled for easy reference.
• New Algebraic-Graphical-Numerical Exercises
allow students to solve a problem using multiple
approaches. This helps students see that a problem
can be solved in more than one way--and that different
methods yield the same result.
• New Modeling Data Exercises are multi-part
applications that involve real-life data, offering
students the opportunity to generate and analyze
mathematical models.
• New Capstone Exercises, one per section, are
conceptual problems that synthesize key topics and
provide students with a better understanding of the
concepts in a section. These exercise are excellent for
• To facilitate familiarity with the basic functions, the
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184
book retains its compilation of several elementary
and non-elementary functions in a Library of Parent
Functions. As in the previous edition, each function
is introduced at the first point of use in the text with
a definition and description of basic characteristics.
New to this edition are Library of Parent Functions
Examples, which are identified in the title of the
example, and the Review of Library of Parent
Functions after Chapter 4. A summary of the functions
appears on the inside cover of the text.
CONTENTS
Each chapter concludes with a chapter summary, review
exercises, a chapter test, and proofs in mathematics. P.
PREREQUISITES. Real Numbers. Exponents and Radicals.
Polynomials and Factoring. Rational Expressions. The
Cartesian Plane. Representing Data Graphically. 1.
FUNCTIONS AND THEIR GRAPHS. Introduction to
Library of Functions. Graphs of Equations. Lines in
the Plane. Functions. Graphs of Functions. Shifting,
Reflecting, and Stretching Graphs. Combinations of
Functions. Inverse Functions. 2. SOLVING EQUATIONS
AND INEQUALITIES. Linear Equations and Problem
Solving. Solving Equations Graphically. Complex
Numbers. Solving Quadratic Equations Algebraically.
Solving Other Types of Equations Algebraically. Solving
Inequalities Algebraically and Graphically. Linear Models
and Scatter Plots. Cumulative Test: Chapters P–2.
Progressive Summary: Chapters P–2. 3. POLYNOMIAL
AND RATIONAL FUNCTIONS. Quadratic Functions.
Polynomial Functions of Higher Degree. Real Zeros
of Polynomial Functions. The Fundamental Theorem
of Algebra. Rational Functions and Asymptotes.
Graphs of Rational Functions. Quadratic Models.
Cumulative Test: Chapters 1-3. 4. EXPONENTIAL
AND LOGARITHMIC FUNCTIONS. Exponential
Functions and Their Graphs. Logarithmic Functions
and Their Graphs. Properties of Logarithms. Solving
Exponential and Logarithmic Equations. Exponential
and Logarithmic Models. Nonlinear Models. Cumulative
Test: Chapters 3–4. Progressive Summary: Chapters P–4.
5. TRIGONOMETRIC FUNCTIONS. Angles and Their
Measure. Right Triangle Trigonometry. Trigonometric
Models. Library of Parent Functions Review. 6.
ANALYTIC TRIGONOMETRY. Using Fundamental
Identities. Verifying Trigonometric Identities. Solving
Trigonometric Equations. Sum and Difference Formulas.
Multiple-Angle and Product-to-Sum Formulas. 7.
ADDITIONAL TOPICS IN TRIGONOMETRY. Law of
Number. Cumulative Test: Chapters 5–7. Progressive
Summary: Chapters P–7. 8. LINEAR SYSTEMS AND
MATRICES. Solving Systems of Equations. Systems of
Linear Equations in Two Variables. Multivariable Linear
Systems. Matrices and Systems of Equations. Operations
with Matrices. The Inverse of a Square Matrix. The
Determinant of a Square Matrix. Applications of
Matrices and Determinants. 9. SEQUENCES, SERIES,
AND PROBABILITY. Sequences and Series. Arithmetic
and Series. The Binomial Theorem. Counting Principles.
Probability. 10. TOPICS IN ANALYTIC GEOMETRY.
Circles and Parabolas. Ellipses. Hyperbolas. Parametric
Equations. Polar Coordinates. Graphs of Polar Equations.
Polar Equations of Conics. Cumulative Test: Chapters
8–10. Progressive Summary: Ch P–10. APPENDIX
A: TECHNOLOGY SUPPORT GUIDE. APPENDIX B:
CONCEPTS IN STATISTICS (Web only). Measures
of Central Tendency and Dispersion. Least Squares
Regression. APPENDIX C: VARIATION (Web only)
APPENDIX D: SOLVING LINEAR EQUATIONS AND
INEQUALITIES (Web only). APPENDIX E: SYSTEMS
OF INEQUALITIES (Web only). Solving Systems of
Inequalities. Linear Programming. APPENDIX F:
MATHEMATICAL INDUCTION (Web only).
© 2012, 1008pp, Hardback, 9781111428426
ALGEBRA AND TRIGONOMETRY, 8E
Richard N. Aufmann, Palomar College; Richard D. Nation, Palomar
College
Accessible to students and flexible for instructors,
COLLEGE ALGEBRA AND TRIGONOMETRY, Eighth
Edition, incorporates the dynamic link between
concepts and applications to bring mathematics to
life. By integrating interactive learning techniques,
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185
the Aufmann author team helps students to better
understand concepts, work independently, and obtain
greater mathematical fluency. The text also includes
technology features to accommodate courses that
allow the option of using graphing calculators. The
authors’ proven Aufmann Interactive Method allows
students to try a skill as it is presented in example
form. This interaction between the examples and
Try Exercises serves as a checkpoint to students as
they read the textbook, do their homework, or study
a section. In the eighth edition, Review Notes are
featured more prominently throughout the text to help
students recognize the key prerequisite skills needed
to understand new concepts.
NEW TO THIS EDITION
• NEW Concept Check Exercises--Each exercise set
starts with exercises that are designed to test your
students’ understanding of new concepts.
• NEW Enrichment Exercises--Each exercise set
concludes with an exercise or exercises that are
designed to extend the concepts presented in the
section or to provide exercises that challenge your
students’ problem-solving abilities.
• NEW Interactive Demonstrations--New Interactive
Demonstrations allow you to adjust parameters
and immediately see the change produced by your
adjustment. These Interactive Demonstrations run
on computers and on mobile devices. Instructions
for using each of the demonstrations are provided.
You can access these Interactive Demonstrations by
scanning a QR code, with a QR reader app, or by using
the web address supplied in the directions.
• NEW An Interactive Technology Approach via
WolframAlpha--Several Integrating Technology
features show how WolframAlpha can be used to
perform computations, solve equations, graph
functions, and find regression functions. WolframAlpha
runs on computers and mobile devices. WolframAlpha
often provides an alternative to the use of a graphing
calculator. WolframAlpha can be accessed by scanning
a QR code or by using the address: http://www.
wolframalpha.com.
FEATURES
• Mid-Chapter Quizzes help you assess your students’
understanding of the concepts studied earlier in the
chapter. The answers for all exercises in the Mid-
Chapter Quizzes are provided in the Answers to
Selected Exercises appendix, along with a reference
to the section in which a particular concept was
presented.
• Chapter Test Preps summarize the major concepts
discussed in each chapter. These Test Preps help your
students prepare for a chapter test. For each concept
there is a reference to a worked example illustrating
the concept and at least one exercise in the Chapter
Review Exercise Set relating to that concept.
• Visualize the Solution, available with both algebraic
and graphical solutions when appropriate, are
provided to help you visualize the mathematics of the
example and to create a link between the algebraic
and visual components of a solution.
• “Exploring Concepts with Technology” feature appears
after the last section in each chapter and provides
you the option to use calculators or computers to
solve computationally difficult problems. In addition,
students are challenged to think about pitfalls that
can be produced when using technology to solve
mathematical problems.
• “Integrating Technology” boxes show how technology
can be used to illustrate concepts and solve many
mathematical problems. Examples and exercises that
require a calculator or a computer to find a solution
are identified by the graphing calculator icon.
• Modeling sections and exercises rely on the use of
a graphing calculator or a computer. These optional
sections and exercises introduce the idea of a
mathematical model and help you see the relevance
of mathematical concepts.
CONTENTS
PRELIMINARY CONCEPTS. The Real Number System.
Integer and Rational Number Exponents. Polynomials.
Mid-Chapter P Quiz. Factoring. Rational Expressions.
Complex Numbers. Exploring Concepts with Technology.
Chapter P Test Prep. Chapter P Review Exercises.
Chapter P Test. 1. EQUATIONS AND INEQUALITIES.
Linear and Absolute Value Equations. Formulas and
Applications. Quadratic Equations. Mid-Chapter 1 Quiz.
Other Types of Equations. Inequalities. Variation and
Applications. Exploring Concepts with Technology.
Chapter 1 Test Prep. Chapter 1 Review Exercises. Chapter
1 Test. Cumulative Review Exercises. 2. FUNCTIONS
AND GRAPHS. Two-Dimensional Coordinate System
and Graphs. Introduction to Functions. Linear Functions.
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Mid-Chapter 2 Quiz. Quadratic Functions. Properties
of Graphs. Algebra of Functions. Modeling Data using
Regression. Exploring Concepts with Technology.
Chapter 2 Test Prep. Chapter 2 Review Exercises.
Chapter 2 Test. Chapter 2 Cumulative Review Exercises.
Remainder Theorem and Factor Theorem. Polynomial
Functions of Higher Degree. Zeros of Polynomial
Functions. Mid-Chapter 3 Quiz. Fundamental Theorem
of Algebra. Graphs of Rational Functions and Their
Applications. Exploring Concepts with Technology.
3 Test. Cumulative Review Exercises. 4. EXPONENTIAL
AND LOGARITHMIC FUNCTIONS. Inverse Functions.
Exponential Functions and Their Applications.
Logarithmic Functions and Their Applications.
Properties of Logarithms and Logarithmic Scales. MidChapter 4 Quiz. Exponential and Logarithmic Equations.
Exponential Growth and Decay. Modeling Data with
Exponential and Logarithmic Functions. Exploring
Concepts with Technology. Chapter 4 Test Prep. Chapter
4 Review Exercises. Chapter 4 Test. Cumulative Review
Exercises. 5. TRIGONOMETRIC FUNCTIONS. Angles
and Arcs. Right Triangle Trigonometry. Trigonometric
Functions of Any Angle. Trigonometric Functions of Real
Numbers. Mid-Chapter 5 Quiz. Graphs of the Sine and
Cosine Functions. Graphs of the Other Trigonometric
Functions. Graphing Techniques. Harmonic Motion--An
Application of the Sine and Cosine Functions. Exploring
Exercises. 6. TRIGONOMETRIC IDENTITIES AND
EQUATIONS. Verification of Trigonometric Identities.
Sum, Difference, and Cofunction Identities. Double- and
Half-Angle Identities. Mid-Chapter 6 Quiz. Identities
Involving the Sum of Trigonometric Functions. Inverse
Trigonometric Functions. Trigonometric Equations.
Exploring Concepts with Technology. Chapter 6 Test
Prep. Chapter 6 Review Exercises. Chapter 6 Test.
Cumulative Review Exercises. 7. APPLICATIONS OF
TRIGONOMETRY. Law of Sines. Law of Cosines and
Area. Vectors. Mid-Chapter 7 Quiz. Trigonometric
Form of Complex Numbers. De Moivre’s Theorem.
Exploring Concepts with Technology. Chapter 7 Test
Prep. Chapter 7 Review Exercises. Chapter 7 Test.
Cumulative Review Exercises. 8. TOPICS IN ANALYTIC
GEOMETRY. Parabolas. Ellipses. Hyperbolas. Rotation
of Axes. Mid-Chapter 8 Quiz. Introduction to Polar
Coordinates. Polar Equations of the Conics. Parametric
Equations of the Conics. Exploring Concepts with
Technology. Chapter 8 Test Prep. Chapter 8 Review
Exercises. Chapter 8 Test. Cumulative Review Exercises.
9. SYSTEMS OF EQUATIONS AND INEQUALITIES.
Systems of Linear Equations in Two Variables. Systems
of Linear Equations in Three Variables. Nonlinear
Systems of Equations. Mid-Chapter 9 Quiz. Partial
Fractions. Inequalities in Two Variables and Systems of
Inequalities. Linear Programming. Exploring Concepts
with Technology. Chapter 9 Test Prep. Chapter 9
Review Exercises. Chapter 9 Test. Cumulative Review
Exercises. 10. MATRICES. G a u s s i a n E l i m i n a t i o n
Method. Algebra of Matrices. Inverse of a Matrix. MidChapter 10 Quiz. Determinants. Exploring Concepts
with Technology. Chapter 10 Test Prep. Chapter 10
Review Exercises. Chapter 10 Test. Cumulative Review
Exercises. 11. SEQUENCES, SERIES, AND PROBABILITY.
Infinite Sequences and Summation Notation. Arithmetic
Sequences and Series. Geometric Sequences and Series.
Mid-Chapter 11 Quiz. Mathematical Induction. Binomial
Theorem. Permutations and Combinations. Introduction
to Probability. Exploring Concepts with Technology.
Chapter 11 Test. Cumulative Review Exercises. Solutions
to the Try Exercises. Answers to Selected Exercises.
Instructor Additional Answers. Index.
© 2015, 1088pp, Hardback, 9781285449425
ALGEBRA AND TRIGONOMETRY WITH
ANALYTIC GEOMETRY, INTERNATIONAL
EDITION, 13E
Earl W. Swokowski, late of Marquette University; Jeffery A. Cole,
Anoka-Ramsey Community College
The latest edition of Swokowski and Cole’s ALGEBRA
AND TRIGONOMETRY WITH ANALYTIC GEOMETRY,
13e, International Edition retains the elements that have
made it so popular with instructors and students alike:
clear exposition, an appealing and uncluttered layout,
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187
and applications-rich exercise sets. The excellent, timetested problems have been widely praised for their
consistency and their appropriate level of difficulty for
precalculus students. The book also covers some more
challenging topics, such as Descartes’ Rule of Signs and
the Theorems on Bounds, which have been eliminated
from other texts or relegated to an appendix. The
Thirteenth Edition features updated topical references
and data, and continues to be supported by outstanding
technology resources. Mathematically sound, this book
effectively prepares students for further courses in
mathematics.
NEW TO THIS EDITION
• New Chapter Tests at the end of each chapter
provide an additional source of exam questions and
great practice for students. The new items include
straightforward questions based on exercises in the
sections as well as questions that require students
to stretch their thinking a bit and expand their use of
the basic concepts.
• Arrow notation is introduced earlier (Section 3.2)
and revisited more often in this edition, bolstering
precalculus content to more effectively prepare
students for calculus topics.
• Approximately 20% of the exercises are new or
revised, including many featuring updated real data
and new applications.
• New Examples illustrate numerous topics: find
the inverse of a rational function (Section 5.1, with
the method for checking presented in a marginal
note); predict a quantity using the decay formula
(Section 5.3); how to show that an equation is not
an identity (Section 7.1); use the subtraction formula
for the cosine to find an exact value when given an
exact trigonometric value and the sign of another
trigonometric function (Section 7.3); and how to find
double angle values of other trigonometric functions
given that the tangent of an angle is a constant
(Section 7.4).
• Other new examples: solve a polynomial equation by
using the theorem on nth roots (Section 8.6); substitute
to aid in solving a system of equations (Section 9.2);
find terms of a sequence that is recursively defined in
terms of two preceding terms (Section 10.1); given two
terms of an arithmetic sequence, find another term
using a new formula (Section 10.2); given two terms
of a geometric sequence, find another term using a
new formula (Section 10.3); and graph a system of
inequalities using parametric equations (Section 11.4).
FEATURES
this text to encourage the practice that’s critical for
concept mastery.
• Many exercises have online tutorials associated with
them. These exercises are easily identified in the text
with icons, making it simple for students to get extra
practice as needed. The exercises are also assignable
through Enhanced WebAssign®.
• Each concept is explained with great care, including
step-by-step comments in the solutions of the
examples. Graphs, figures, charts, and tables help
students interpret graphical data, and accompany
many examples.
• The text provides many topical examples showing how
mathematical concepts have real-life applications.
• Each exercise set begins with drill problems and then
progresses to more challenging problems. Some
exercises ask students to produce and examine a
table of values as an aid to solve a problem. Others
ask students to interpret some aspect of a given table
of values. Many involve graphical solutions.
CONTENTS
Every chapter ends with Review Exercises, Discussion
Exercises, and a Chapter Test. 1. FUNDAMENTAL
CONCEPTS OF ALGEBRA. Real Numbers. Exponents and
Radicals. Algebraic Expressions. Fractional Expressions.
2. EQUATIONS AND INEQUALITIES. Equations. Applied
Problems. Quadratic Equations. Complex Numbers.
Other Types of Equations. Inequalities. More on
Inequalities. 3. FUNCTIONS AND GRAPHS. Rectangular
Coordinate Systems. Graphs of Equations. Lines.
Definition of Function. Graphs of Functions. Quadratic
Functions. Operations on Functions. 4. POLYNOMIAL
AND RATIONAL FUNCTIONS. Polynomial Functions
of Degree Greater than 2. Properties of Division.
Zeros of Polynomials. Complex and Rational Zeros of
Polynomials. Rational Functions. Variation. 5. INVERSE,
EXPONENTIAL, AND LOGARITHMIC FUNCTIONS.
Inverse Functions. Exponential Functions. The Natural
Exponential Function. Logarithmic Functions. Properties
of Logarithms. Exponential and Logarithmic Equations.
6. THE TRIGONOMETRIC FUNCTIONS. Angles.
Trigonometric Functions of Angles. Trigonometric
Functions of Real Numbers. Values of Trigonometric
Functions. Trigonometric Graphs. Additional
Trigonometric Graphs. Applied Problems. 7. ANALYTIC
TRIGONOMETRY. Verifying Trigonometric Identities.
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Trigonometric Equations. The Addition and Subtraction
Formulas. Multiple-Angle Formulas. Product-to-Sum and
Sum-to-Product Formulas. The Inverse Trigonometric
Functions. 8. APPLICATIONS OF TRIGONOMETRY.
The Law of Sines. The Law of Cosines. Vectors. The Dot
Product. Trigonometric Form for Complex Numbers. De
Moivre’s Theorem and nth Roots of Complex Numbers.
Systems of Equations. Systems of Linear Equations
in Two Variables. Systems of Inequalities. Linear
Programming. Systems of Linear Equations in More than
Two Variables. The Algebra of Matrices. The Inverse of
a Matrix. Determinants. Properties of Determinants.
Partial Fractions. 10. SEQUENCES, SERIES AND
PROBABILITY. Infinite Sequences and Summation
Notation. Arithmetic Sequences. Geometric Sequences.
Mathematical Induction. The Binomial Theorem.
Permutations. Distinguishable Permutations and
Combinations. Probability. 11. TOPICS FROM ANALYTIC
GEOMETRY. Parabolas. Ellipses. Hyperbolas. Plane
Curves and Parametric Equations. Polar Coordinates.
Polar Equations of Conics. Appendix I: Common
Graphs and Their Equations. Appendix II: A Summary
of Graph Transformations. Appendix III: Graphs of the
Trigonometric Functions and Their Inverses. Appendix
IV: Values of the Trigonometric Functions of Special
Angles on a Unit Circle.
© 2012, 992pp, Paperback, 9780840068897
ALGEBRA AND TRIGONOMETRY,
James Stewart, McMaster University; Lothar Redlin, Pennsylvania
State University, Abington Campus; Saleem Watson, California State
University, Long Beach
This best selling author team explains concepts simply
and clearly, without glossing over difficult points.
Problem solving and mathematical modeling are
introduced early and reinforced throughout, providing
students with a solid foundation in the principles of
mathematical thinking. Comprehensive and evenly
paced, the book provides complete coverage of the
function concept, and integrates a significant amount
of graphing calculator material to help students
develop insight into mathematical ideas. The authors’
attention to detail and clarity, the same as found in
James Stewart’s market-leading Calculus text, is what
makes this text the market leader.
NEW TO THIS EDITION
• Approximately 20% of the exercises in the text
are new. In addition, each exercise set has been
restructured to begin with new concept exercises, and
reorganized to more closely follow the exposition in
the corresponding section.
• The section entitled “Principles of Problem Solving” is
now a Prologue to the book. Problem Solving sections,
each highlighting a particular problem solving
principle, are now posted on the Book Companion
Website.
• Discovery Projects, which encourage and motivate
students to further explore chapter topics, are now
available on the Book Companion Website.
• All examples in the book are now paired with a new
Now Try Exercise XX, allowing students to reinforce
their understanding of a concept by practicing the
technique that is involved. This integration also
teaches and encourages students to solve rather than
just memorize.
• Chapter 3 has been completely rewritten to focus
more sharply on the fundamental and crucial concept
of function. The material on quadratic functions,
formerly in this chapter, is now part of the chapter
on polynomial functions.
• Chapter 4 now begins with a section on quadratic
functions, leading to higher degree polynomial
functions. (Section 4.1).
• Chapter 6 includes a new section on inverse
trigonometric functions and right triangles (Section
6.4), which is needed in applying the Laws of Sines and
Cosines in the following section, as well as for solving
trigonometric equations in Chapter 8.
trigonometric functions (Section 7.5) to better segue
into the section on harmonic motion that follows.
• Chapter 8 has been completely revised, including two
new sections on trigonometric equations (Sections 8.4
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189
and 8.5) that expand coverage of this topic.
• The addition of a new Chapter 10, “Vectors in Two and
Three Dimensions,” allowed the authors to reorganize
the related topics in the book around more cohesive
themes.
CONTENTS
Prologue: Principles of Problem Solving. P.
PREREQUISITES. Modeling the Real World. Real
Numbers and Their Properties. The Real Number Line
and Order. Integer Exponents. Rational Exponents and
Radicals. Algebraic Expressions. Factoring Algebraic
Expressions. Rational Expressions. Chapter P Review.
Chapter P Test. Focus on Problem Solving: General
Principles. 1. EQUATIONS AND INEQUALITIES. Chapter
Overview. Basic Equations. Modeling with Equations.
Quadratic Equations. Complex Numbers. Other Types
of Equations. Inequalities. Absolute Value Equations and
Inequalities. Chapter 1 Review. Chapter 1 Test. Focus on
Modeling: Making the Best Decisions. 2. COORDINATES
AND GRAPHS. Chapter Overview. The Coordinate
Plane. Graphs of Equations in Two Variables. Graphing
Calculators: Solving Equations Graphically. Lines.
Modeling: Variation. Chapter 2 Review. Chapter 2 Test.
Focus on Modeling: Fitting Lines to Data. Cumulative
Review Test: Chapters 1 and 2. 3. FUNCTIONS. Chapter
Overview. What Is a Function?. Graphs of Functions.
Getting Information from the Graph of a Function.
Average Rate of Change of a Function. Transformations
of Functions. Combining Functions. One-to-One
Functions and Their Inverses. Chapter 3 Review. Chapter
3 Test. Focus on Modeling: Functions as Models. 4.
POLYNOMIAL AND RATIONAL FUNCTIONS. Chapter
Overview. Quadratic Functions and Models. Polynomial
Functions and Their Graphs. Dividing Polynomials. Real
Zeros of Polynomials. Complex Numbers. Complex
Zeros and the Fundamental Theorem of Algebra.
Rational Functions. Chapter 4 Review. Chapter 4 Test.
Focus on Modeling: Fitting Polynomial Curves to Data.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Chapter Overview. Exponential Functions. The Natural
Exponential Function. Logarithmic Functions. Laws of
Modeling with Exponential and Logarithmic Functions.
Chapter 5 Review. Chapter 5 Test. Focus on Modeling:
Fitting Exponential and Power Curves to Data.
Cumulative Review Test: Chapters 3, 4, and 5. 6.
TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE
APPROACH. Chapter Overview. Angle Measure.
Trigonometry of Right Triangles. Trigonometric
Functions of Angles. Inverse Trigonometric Functions
and Triangles. The Law of Sines. The Law of Cosines.
Surveying. 7. TRIGONOMETRIC FUNCTIONS: UNIT
CIRCLE APPROACH. Chapter Overview. The Unit
Circle. Trigonometric Functions of Real Numbers.
Trigonometric Graphs. More Trigonometric Graphs.
Inverse Trigonometric Functions and Their Graphs.
Modeling Harmonic Motion. Chapter 7 Review. Chapter
7 Test. Focus on Modeling: Fitting Sinusoidal Curves
to Data. 8. ANALYTIC TRIGONOMETRY. Chapter
Overview. Trigonometric Identities. Addition and
Subtraction Formulas. Double-Angle, Half-Angle, and
Sum-Product Identities. Basic Trigonometric Equations.
More Trigonometric Equations. Chapter 8 Review.
Chapter 8 Test. Focus on Modeling: Traveling and
Standing Waves. Cumulative Review Test: Chapters 6,
7, and 8. 9. POLAR COORDINATES AND PARAMETRIC
EQUATIONS. Chapter Overview. Polar Coordinates.
Graphs of Polar Equations. Polar Form of Complex
Numbers; DeMoivre’s Theorem. Plane Curves and
Parametric Equations. Chapter 9 Review. Chapter 9
Test. Focus on Modeling: The Path of a Projectile. 10.
VECTORS IN TWO AND THREE DIMENSIONS. Chapter
Overview. Vectors in Two Dimensions. The Dot Product.
Three –Dimensional Coordinate Geometry. Vectors in
Three Dimensions. The Cross Product. Equations of
Lines and Planes. Chapter 10 Review. Chapter 10 Test.
Focus on Modeling: Vector Fields. Cumulative Review
Test: Chapters 9 and 10. 11. SYSTEMS OF EQUATIONS
AND INEQUALITIES. Chapter Overview. Systems of
Linear Equations in Two Variables. Systems of Linear
Equations in Several Variables. Systems of Linear
Equations: Matrices. The Algebra of Matrices. Inverses
of Matrices and Matrix Equations. Determinants and
Cramer’s Rule. Partial Fractions. Systems of NonLinear Equations. Systems of Inequalities. Chapter 11
Review. Chapter 11 Test. Focus on Modeling: Linear
Programming. 12. ANALYTIC GEOMETRY. Overview.
Parabolas. Ellipses. Hyperbolas. Shifted Conics.
Rotation of Axes. Polar Equations of Conics. Chapter 12
Review. Chapter 12 Test. Focus on Modeling: Conics in
Architecture. Cumulative Review Test: Chapters 11 and
12. 13. SEQUENCES AND SERIES. Chapter Overview.
Sequences and Summation Notation. Arithmetic
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Sequences. Geometric Sequences. Mathematics
of Finance. Mathematical Induction. The Binomial
Theorem. Chapter 13 Review. Chapter 13 Test. Focus on
Modeling: Difference Equations. 14. COUNTING AND
PROBABILITY. Chapter Overview. Counting Principles.
Permutations and Combinations. Probability. Binomial
Probability. Expected Value. Chapter 14 Review. Chapter
14 Test. Focus on Modeling: The Monte Carlo Method.
Cumulative Review Test: Chapters 11 and 12. APPENDIX
Calculators and Calculations.
© 2012, 1152pp, Paperback, 9780840068637
innovation in the calculus market. It has been widely
its solid and effective pedagogy that addresses the
needs of a broad range of teaching and learning styles
and environments. Each title is just one component in a
comprehensive calculus course program that carefully
integrates and coordinates print, media, and technology
products for successful teaching and learning. Two
primary objectives guided the authors in writing
this book: to develop precise, readable materials for
and rules of calculus and to design comprehensive
pedagogical techniques and saves the instructor time.
NEW TO THIS EDITION
ALGEBRA AND TRIGONOMETRY,
LEVEL 1, 9E
© 2014, 976pp, Hardback, 9781133950967
omitted.
key topics.
of continuity.
exercise sets.
FEATURES
CALCULUS I WITH PRECALCULUS, 3E
CALCULUS I WITH PRECALCULUS, developed for
one-year courses, is ideal for instructors who wish to
successfully bring students up to speed algebraically
within precalculus and transition them into calculus.
The Larson Calculus program has a long history of
appropriately.
• Questions involving skills, writing, critical thinking,
problem-solving, applications, and real-data
applications are included throughout the text.
Exercises are presented in a variety of question
formats, including matching, free response, true/false,
modeling, and fill-in the blank.
• To address the changing needs of today’s instructors
and students and recognizing that the calculus course
is presented in a variety of teaching and learning
environments, the program resources are available
in print and online formats.
www.cengageasia.com
191
CONTENTS
Number.
© 2012, 1056pp, Hardback, 9780840068330
CALCULUS I WITH PRECALCULUS,
CALCULUS I WITH PRECALCULUS, 3e, International
Edition developed for one-year courses, is ideal for
instructors who wish to successfully bring students up
to speed algebraically within precalculus and transition
them into calculus. The Larson Calculus program has
a long history of innovation in the calculus market. It
has been widely praised by a generation of students
and professors for its solid and effective pedagogy
that addresses the needs of a broad range of teaching
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192
teaching and learning. Two primary objectives guided
the authors in writing this book: to develop precise,
readable materials for students that clearly define
and demonstrate concepts and rules of calculus and
to design comprehensive teaching resources for
and saves the instructor time.
NEW TO THIS EDITION
omitted.
key topics.
of continuity.
exercise sets.
FEATURES
appropriately.
appropriately.
• To address the changing needs of today’s instructors
and students and recognizing that the calculus course
is presented in a variety of teaching and learning
environments, the program resources are available
in print and online formats.
CONTENTS
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Number.
© 2012, 1056pp, Paperback, 9780840069207
COLLEGE ALGEBRA
A Make it Real Approach, International Edition
Frank Wilson, Chandler-Gilbert Community College ; Scott L.
Adamson, Chandler-Gilbert Community College; Trey Cox, ChandlerGilbert Community College; Alan E. O’Bryan, Arizona State University
This new text provides a contemporary approach
to college algebra, ideal for the many skeptical or
apprehensive students who ask, “When am I ever
going to use this?” The key phrase is “Make It Real”
since the goal is to make the material relevant and
understandable to today’s college students. But
many books make this claim—so how is COLLEGE
ALGEBRA: MAKE IT REAL, International Edition
different? In other texts, which simply wrap realworld situations around problems, the context isn’t
needed to do the mathematics. Written by skilled and
passionate teachers, this text uses real-world data sets
and situations to draw out mathematical concepts.
Students are immersed in familiar contexts—from
golf course ratings to Egyptian pyramids—from which
concepts emerge naturally, and then guided in using
their understanding of those ideas to make sense
of the mathematics. The real-world contexts are not
only helpful for understanding procedures—they’re
necessary. The concept of a function, the use of
modeling, and the thorough integration of real-world
applications are integral to the text. If there’s one new
college algebra text crafted to stand up to a “reality
check” comparison with your current book, this is it.
FEATURES
• Explanations and Examples: A conversational tone
and detailed explanations make the math come
alive for students. Intriguing, relevant photographs
and carefully rendered graphics pique students’
interest and capture their attention. Meaningful
real world contexts inform students about the world
and motivate them to investigate mathematical
concepts. Familiarity with these contexts, from
which ideas emerge intuitively, are not only helpful
for comprehending procedures—they’re necessary.
One student commented, “It’s like having the teacher
standing over my shoulder explaining things to me.”
• Variety of Homework Exercises: The overarching
philosophy of developing students’ mathematical
reasoning and persistent problem solving is evident
throughout the homework exercises, which are
divided into four sections: Concepts and Skills (for
practicing procedures and demonstrating a basic
understanding of key concepts), Show You Know
(requiring written explanations of big ideas), Make
It Real (real world contexts that help students
understand the world and make connections between
mathematics and their lives), and Stretch Your Mind
(requiring deep thought, creativity, and persistence).
• Study Sheets: The end-of-chapter Study Sheets
present a series of questions focused on the big
ideas of the chapter. As students reflect upon these
questions, they solidify their understanding of the
key mathematical concepts. The Study Sheets are an
ideal chapter review activity to help students prepare
for the end-of-chapter exam.
• Review Exercises: End-of-chapter review exercises
al low students to refine their conceptual
understanding and mathematical expertise. Grouped
by section number, these exercises make it easy to
focus on particular areas of study.
• Distinctive Treatment of Modeling and Graphs:
In keeping with the book’s approach, the authors
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194
promote student comprehension by presenting
modeling and graphs in familiar contextual situations;
that is, models and graphs describe the underlying
behavior that is embedded into the context. Modeling
and graphs are used extensively; for instance, Section
6.2 on Exponential Function Modeling and Graphs
features nine examples, all of which include a real
world context.
• Unique Make It Real Projects: These end-of-chapter
projects allow students to apply the concepts learned
in the chapter to data collected from an area of
personal interest. By allowing students to focus on a
real world context of their choosing, their motivation
and interest in doing the mathematics increases.
Additionally, the Make It Real Projects provide
learners another avenue for developing mathematical
reasoning and persistent problem solving as they
make sense of the mathematical ideas.
Using Matrices to Solve Linear Systems. Matrix
Operations and Applications. Using Inverse Matrices
to Solve Matrix Equations. Chapter 8 Review.
© 2013, 624pp, Paperback, 9781111988272
COLLEGE ALGEBRA, 6E
Real Mathematics, Real People, International Edition
CONTENTS
1. MATHEMATICAL MODELING, FUNCTIONS, AND
CHANGE. Mathematical Modeling. Functions and
Function Notation. Functions Represented by Tables and
Formulas. Functions Represented by Graphs. Functions
Represented by Words. Preview to Inverse Functions.
Chapter 1 Review. 2. LINEAR FUNCTIONS. Functions
with Constant Rates of Change. Modeling with Linear
Functions. Linear Regression. Systems of Linear
Equations. Systems of Linear Inequalities. Chapter 2
Review. 3. TRANSFORMATIONS AND FUNCTIONS.
Horizontal and Vertical Shifts. Horizontal and Vertical
Reflections. Vertical Stretches and Reflections.
Horizontal Stretches and Compressions. Chapter 3
Review. 4. QUADRATIC FUNCTIONS. Variable Rates of
Change. Modeling with Quadratic Functions. Quadratic
Functions, Graphs, and Forms. Chapter 4 Review. 5.
POLYNOMIAL, POWER, AND RATIONAL FUNCTIONS.
Higher-Order Polynomial Function Modeling. Power
Functions. Rational Functions. Chapter 5 Review. 6.
Percentage Change. Exponential Function Modeling
and Graphs. Compound Interest and Continuous
Growth. Solving Logarithmic and Exponential Equations.
Logarithmic Function Modeling. Chapter 6 Review. 7.
MODELING WITH OTHER TYPES OF FUNCTIONS.
Combinations of Functions. Piecewise Functions.
Composition of Functions. Logistic Functions. Choosing
a Mathematical Model. Chapter 7 Review. 8. MATRICES.
COLLEGE ALGEBRA: REAL MATHEMATICS, REAL
PEOPLE, 6e, International Edition is an ideal student
and instructor resource for courses that require the use
of a graphing calculator. The quality and quantity of the
through careful writing and design—including examples
NEW TO THIS EDITION
• With the extensive revision to create the Sixth Edition,
this book’s original subtitle, “A Graphing Approach,”
no longer represents the text’s essence (although
the graphing calculator is still required). The author’s
changes and the new title, “COLLEGE ALGEBRA: REAL
MATHEMATICS, REAL PEOPLE,” address a primary
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195
need in education today—relevance. The mathematics
in this text is both real and relevant, and the people
introduced are either already in or preparing for
careers in which they will use mathematics.
intuition.
can be solved in more than one way—and that
different methods yield the same result.
CONTENTS
Graphs of Rational Functions. Quadratic Models. 4.
Exponential Functions and Their Graphs. Logarithmic
Functions and Their Graphs. Properties of Logarithms.
Exponential and Logarithmic Models. Nonlinear
Models. Progressive Summary: Chapters P–4. 5.
LINEAR SYSTEMS AND MATRICES. Solving Systems
of Equations. Systems of Linear Equations in Two
Variables. Multivariable Linear Systems. Matrices and
Systems of Equations. Operations with Matrices. The
Inverse of a Square Matrix. The Determinant of a Square
Matrix. Applications of Matrices and Determinants.
Cumulative Test: Chapters 3–5. 6. SEQUENCES, SERIES,
Probability. 7. CONICS AND PARAMETRIC EQUATIONS.
Equations. Cumulative Test: Chapters 6–7. Progressive
Summary: Ch P–7. APPENDIX A: TECHNOLOGY
SUPPORT GUIDE. APPENDIX B: CONCEPTS IN
STATISTICS (Web only). Measures of Central Tendency
and Dispersion. Least Squares Regression. APPENDIX
C: VARIATION (Web only) APPENDIX D: SOLVING
LINEAR EQUATIONS AND INEQUALITIES (Web only).
APPENDIX E: SYSTEMS OF INEQUALITIES (Web only).
Solving Systems of Inequalities. Linear Programming.
APPENDIX F: MATHEMATICAL INDUCTION (Web only).
© 2012, 736pp, Paperback, 9781111575267
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196
COLLEGE ALGEBRA
Concepts and Contexts, International Edition
University, Long Beach; Phyllis Panman
This text bridges the gap between traditional and
reform approaches to algebra encouraging students
to see mathematics in context. It presents fewer
topics in greater depth, prioritizing data analysis
as a foundation for mathematical modeling, and
emphasizing the verbal, numerical, graphical and
symbolic representations of mathematical concepts as
well as connecting mathematics to real life situations
drawn from the students’ majors.
FEATURES
• The problems, the models and the real life data are
the three features of this book. They are used to relate
the mathematics to the students’ lives and to show
the usefulness and relevance of the mathematics to
the modern reality.
CONTENTS
1. DATA, FUNCTIONS, AND MODELS. Making Sense
of Data. Visualizing Relationships in Data. Equations:
Describing Relationships in Data. Functions: Describing
Change. Function Notation: The Concept of Function
as a Rule. Working with Functions: Graphs and
Graphing Calculators. Working with Functions: Getting
Information from the Graph. Working with Functions:
Modeling Real-World Relationships. Making and Using
Formulas. Concept Check and Review. EXPLORATION
1: Bias in Presenting Data. EXPLORATION 2: Collecting
and Analyzing Data. EXPLORATION 3: Every Graph
Tells a Story. 2. LINEAR FUNCTIONS AND MODELS.
Working with Functions: Average Rate of Change.
Linear Functions: Constant Rate of Change. Equations of
Lines: Making Linear Models. Varying the Coefficients:
Direct Proportionality. Linear Regression: Fitting
Lines to Data. Linear Equations: Getting Information
from a Model. Linear Equations: Where Lines Meet.
Concept Check and Review. EXPLORATION 1: When
Rates of Change. EXPLORATION 2: Linear Patterns.
EXPLORATION 3: Bridge Science. EXPLORATION 4:
Correlation and Causation. EXPLORATION 5: Fair
Division of Assets. 3. EXPONENTIAL FUNCTIONS AND
MODELS. Exponential Growth and Decay. Exponential
Models: Comparing Rates. Comparing Linear and
Exponential Growth. Graphs of Exponential Functions.
Fitting Exponential Curves to Data. Concept Check
and Review. EXPLORATION 1: Extreme Numbers:
Scientific Notation. EXPLORATION 2: So You Want
to be a Millionaire? EXPLORATION 3: Linear Patterns.
EXPLORATION 4: Modeling Radioactivity with Coins
and Dice. 4. LOGARITHMS AND EXPONENTIAL
MODELS. Logarithmic Functions. Laws of Logarithms.
Logarithmic Scales. The Natural Exponential and
Logarithmic Functions. Exponential Equations: Getting
Information from Model. Working With Functions:
Composition and Inverse. Concept Check and Review.
EXPLORATION 1: Super Origami. EXPLORATION 2:
Orders of Magnitude. EXPLORATION 3: Semi-Log
Graphs. EXPLORATION 4: The Even-Tempered Clavier. 5.
QUADRATIC FUNCTIONS AND MODELS. Working with
Functions: Shifting and Stretching. Quadratic Functions
and their Graphs. Maxima and Minima: Getting
Information from a Model. Quadratic Equations: Getting
Information from a Model. Fitting Quadratic Curves
to Data. Concept Check and Review. EXPLORATION
1: Transformation Stories. EXPLORATION 2: Toricelli’s
Law. EXPLORATION 2: Quadratic Patterns. 6. POWER,
POLYNOMIAL, AND RATIONAL FUNCTIONS. Working
with Functions: Algebraic Operations. Power Functions:
Positive Powers. Polynomial Functions: Combining
Power Functions. Fitting Power and Polynomial
Curves to Data. Power Functions: Negative Powers.
Rational Functions. Concept Check and Review.
EXPLORATION 1: Only in the Movies? EXPLORATION
2: Proportionality: Shape and Size. EXPLORATION 3:
Managing Traffic. EXPLORATION 4: Alcohol and the
Surge Function. 7. SYSTEMS OF EQUATIONS AND
CATEGORICAL DATA. Systems of Linear Equations in
Two Variables. Systems of Linear Equations in Several
Variables. Using Matrices to Solve Systems of Linear
Equations. Matrices and Categorical Data. Matrix
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Operations: Getting Information from Data. Matrix
Equations: Solving a Linear System. Concept Check and
Review. EXPLORATION 1: Collecting Categorical Data.
EXPLORATION 2: Will the Species Survive? ALGEBRA
TOOLKIT A: WORKING WITH NUMBERS. Numbers
and Their Properties. The Number Line and Intervals.
Integer Exponents. Radicals and Rational Exponents.
ALGEBRA TOOLKIT B: WORKING WITH EXPRESSIONS.
Combining Algebraic Expressions. Factoring Algebraic
Expressions. Rational Expressions. ALGEBRA TOOLKIT
C: WORKING WITH EQUATIONS. Solving Basic
Equations. Solving Quadratic Equations. Solving Basic
Inequalities. ALGEBRA TOOLKIT D: WORKING WITH
GRAPHS. The Coordinate Plane. Graphs of Two-Variable
Equations. Using a Graphing Calculator. Solving
Equations and Inequalities Graphically.
© 2011, 816pp, Paperback, 9780538733151
COLLEGE ALGEBRA, 8E
College
COLLEGE ALGEBRA, EIGHTH EDITION, incorporates
the dynamic link between concepts and applications
to bring mathematics to life. By integrating interactive
learning techniques, the Aufmann author team
helps students to better understand concepts, work
independently, and obtain greater mathematical
fluency. The Eighth Edition also includes technology
features to accommodate courses that allow the
option of using graphing calculators. Additional
program components that support student success
include tutorial practice, online homework, Live Online
Tutoring, and Instructional DVDs. The authors’ proven
Aufmann Interactive Method allows students to try a
skill as it is presented in example form. This interaction
between the examples and Try Exercises serves as
a checkpoint to students as they read the textbook,
do their homework, or study a section. In the Eighth
Edition, Review Notes are featured more prominently
throughout the text to help students recognize the key
prerequisite skills needed to understand new concepts.
NEW TO THIS EDITION
• NEW Concept Check Exercises - Each exercise set
starts with exercises that are designed to test your
students’ understanding of new concepts.
• NEW Enrichment Exercises - Each exercise set
concludes with an exercise or exercises that are
designed to extend the concepts presented in the
section or to provide exercises that challenge your
students’ problem solving abilities.
• NEW Interactive Demonstrations - New Interactive
Demonstrations allow you to adjust parameters
and immediately see the change produced by your
adjustment. These Interactive Demonstrations run
on computers and on mobile devices. Instructions
for using each of the demonstrations are provided.
You can access these Interactive Demonstrations by
scanning a QR code, with a QR reader app, or by using
the web address supplied in the directions.
• NEW An Interactive Technology Approach via
WolframAlpha - Several Integrating Technology
features show how WolframAlpha can be used to
perform computations, solve equations, graph
functions, and find regression functions. WolframAlpha
runs on computers and mobile devices. WolframAlpha
often provides an alternative to the use of a graphing
calculator. Access WolframAlpha by scanning a QR
code or by using the address: www.wolframalpha.com.
FEATURES
• Mid-Chapter Quizzes help you assess students’
understanding of the concepts studied earlier in the
chapter. The answers for all exercises in the MidChapter Quizzes are provided in the Answers to
Selected Exercises Appendix, along with a reference
to the section in which a particular concept was
presented.
• A Quantitative Reasoning feature demonstrates math
solutions to real-world problems and is compliant
with MAA Guidelines and AMATYC 2006 Crossroads
Revisited.
• Chapter Test Preps summarize the major concepts
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discussed in each chapter. These Test Preps help
students prepare for a chapter test. For each concept
there is a reference to a worked example illustrating
the concept and at least one exercise in the Chapter
Review Exercise Set relating to that concept.
• Visualize the Solution, available with both algebraic
and graphical solutions when appropriate, are
provided to help students visualize the mathematics
of the example and to create a link between the
algebraic and visual components of a solution.
• Exploring Concepts with Technology features appear
after the last section in each chapter and provide
you the option to use calculators or computers to
solve computationally difficult problems. In addition,
students are challenged to think about pitfalls that
can be produced when using technology to solve
• Integrating Technology boxes show how technology
can be used to illustrate concepts and solve many
mathematical problems. Examples and exercises that
require a calculator or a computer to find a solution
are identified by the graphing calculator icon.
CONTENTS
P. PRELIMINARY CONCEPTS. The Real Number
System. Integer and Rational Number Exponents.
Polynomials. Mid-Chapter P Quiz. Factoring. Rational
Expressions. Complex Numbers. Exploring Concepts
with Technology. Chapter P Test Prep. Chapter P
Review Exercises. Chapter P Test. 1. EQUATIONS AND
INEQUALITIES. Linear and Absolute Value Equations.
Formulas and Applications. Quadratic Equations. MidChapter 1 Quiz. Other Types of Equations. Inequalities.
Variation and Applications. Exploring Concepts with
2. FUNCTIONS AND GRAPHS. Two-Dimensional
Coordinate System and Graphs. Introduction to
Functions. Linear Functions. Mid-Chapter 2 Quiz.
Quadratic Functions. Properties of Graphs. Algebra of
Functions. Modeling Data using Regression. Exploring
Concepts with Technology. Chapter 2 Test Prep.
Chapter 2 Review Exercises. Chapter 2 Test. Chapter
2 Cumulative Review Exercises. 3. POLYNOMIAL
AND RATIONAL FUNCTIONS. Remainder Theorem
and Factor Theorem. Polynomial Functions of Higher
Degree. Zeros of Polynomial Functions. Mid-Chapter
3 Quiz. Fundamental Theorem of Algebra. Graphs of
Rational Functions and Their Applications. Exploring
Exercises. 4. EXPONENTIAL AND LOGARITHMIC
FUNCTIONS. Inverse Functions. Exponential Functions
and Their Applications. Logarithmic Functions and
Their Applications. Properties of Logarithms and
Logarithmic Scales. Mid-Chapter 4 Quiz. Exponential
and Logarithmic Equations. Exponential Growth and
Decay. Modeling Data with Exponential and Logarithmic
Functions. Exploring Concepts with Technology. Chapter
4 Test Prep. Chapter 4 Review Exercises. Chapter 4 Test.
Cumulative Review Exercises. 5. TOPICS IN ANALYTIC
GEOMETRY. Parabolas. Ellipses. Mid-Chapter 5 Quiz.
Hyperbolas. Exploring Concepts with Technology.
5 Test. Cumulative Review Exercises. 6. SYSTEMS OF
EQUATIONS AND INEQUALITIES. Systems of Linear
Equations in Two Variables. Systems of Linear Equations
in Three Variables. Nonlinear Systems of Equations.
Mid-Chapter 6 Quiz. Partial Fractions. Inequalities
in Two Variables and Systems of Inequalities. Linear
Programming. Exploring Concepts with Technology.
Chapter 6 Test. Cumulative Review Exercises. 7.
MATRICES. Gaussian Elimination Method. Algebra
of Matrices. Inverse of a Matrix. Mid-Chapter 7 Quiz.
Determinants. Exploring Concepts with Technology.
Chapter 7 Test. Cumulative Review Exercises. 8.
SEQUENCES, SERIES, AND PROBABILITY. Infinite
Sequences and Summation Notation. Arithmetic
Sequences and Series. Geometric Sequences and
Series. Mid-Chapter 8 Quiz. Mathematical Induction.
Binomial Theorem. Permutations and Combinations.
Introduction to Probability. Exploring Concepts with
SOLUTIONS TO THE TRY EXERCISES. ANSWERS TO
SELECTED EXERCISES. INSTRUCTOR ADDITIONAL
ANSWERS. INDEX.
© 2015, 784pp, Hardback, 9781285434773
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199
COLLEGE ALGEBRA AND CALCULUS, 2E
COLLEGE ALGEBRA AND CALCULUS: AN APPLIED
APPROACH, 2E, International Edition provides your
students a comprehensive resource for their college
algebra and applied calculus courses. The mathematical
concepts and applications are consistently presented
in the same tone and pedagogy to promote confidence
and a smooth transition from one course to the next.
The consolidation of content for two courses in a single
text saves you time in your course—and saves your
students the cost of an extra textbook.
NEW TO THIS EDITION
of key concepts.
FEATURES
chapter.
challenging, real-world applications—all of which can
choice.
CONTENTS
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200
of a Square Matrix. The Determinant of a Square Matrix.
Applications of Matrices and Determinants. 7. LIMITS
AND DERIVATIVES. Limits. Continuity. The Derivative
and the Slope of a Graph. Some Rules for Differentiation.
and Quotient Rules. The Chain Rule. 8. APPLICATIONS
OF THE DERIVATIVE. Higher-Order Derivatives.
Implicit Differentiation. Related Rates. Increasing
Test. 9. FURTHER APPLICATIONS OF THE DERIVATIVE.
Optimization Problems. Business and Economics
Applications. Asymptotes. Curve Sketching: A Summary.
Differentials and Marginal Analysis. 10. DERIVATIVES
OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Integrals. Integration by Substitution and The General
Power Rule. Exponential and Logarithmic Integrals.
Area and the Fundamental Theorem of Calculus. The
Area of a Region Bounded by Two Graphs. The Definite
Integral as the Limit of a Sum. 12. TECHNIQUES OF
INTEGRATION. Integration by Parts and Present Value.
Integration Tables. Numerical Integration. Improper
Integrals. 13. FUNCTIONS OF SEVERAL VARIABLES.
The Three-Dimensional Coordinate System. Surfaces
in Space. Functions of Several Variables. Partial
Derivatives. Extrema of Functions of Two Variables.
Lagrange Multipliers. Least Squares Regression Analysis.
Double Integrals and Area in the Plane. Applications of
Double Integrals. 14. TRIGONOMETRIC FUNCTIONS.
Radian Measure of Angles. The Trigonometric Functions.
Graphs of Trigonometric Functions. Derivatives of
Trigonometric Functions. Integrals of Trigonometric
Functions. ONLINE. 15. SERIES AND TAYLOR
POLYNOMIALS. Sequences and Summation Notation.
Sequences and Series. Series and Convergence.
p-Series and the Ratio Test. Power Series and Taylor’s
Theorem. Taylor Polynomials. Newton’s Method. 16.
PROBABILITY. Counting Principles. Probability. Discrete
and Continuous Random Variables. Expected Value
and Variance. Mathematical Induction. The Binomial
Theorem. Appendix A: An Introduction to Graphing
Utilities. Appendix B: Conic Sections. Conic Sections.
Conic Sections and Translations. Appendix C: Further
Appendix D: Precalculus Review. The Real Number
Polynomials. Fractions and Rationalization. Appendix E:
Alternate Introduction to the Fundamental Theorem of
Calculus. Appendix F: Differential Equations. Solutions
of Differential Equations. Separation of Variables.
First-Order Linear Differential Equations. Applications
of Differential Equations. Appendix G: Formulas.
Differentiation and Integration Formulas. Formulas
from Business and Finance. Appendix H: Properties
and Measurement. Review of Algebra, Geometry, and
Trigonometry. Units of Measurements. Appendix I:
Graphing Utility Programs. Appendix J: Mathematical
Induction. Supplements:
© 2013, 1136pp, Paperback, 9781133105183
COLLEGE ALGEBRA AND
TRIGONOMETRY, INTERNATIONAL
EDITION, 7E
Richard N. Aufmann, Palomar College; Vernon C. Barker, Palomar
College; Richard D. Nation, Palomar College
COLLEGE ALGEBRA AND TRIGONOMETRY, 7e,
International Edition, uses the dynamic link between
concepts and applications to bring mathematics to life.
By incorporating interactive learning techniques, the
Aufmann team helps students to better understand
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201
concepts, work independently, and obtain greater
mathematical fluency. The text also includes technology
features to accommodate courses that allow the option
of using graphing calculators. The authors’ proven
Aufmann Interactive Method allows students to try a
skill as it is presented in example form. This interaction
between the examples and Try Exercises serves as a
checkpoint to students as they read the textbook, do
their homework, or study a section. In the Seventh
Edition, Review Notes are featured more prominently
throughout the text to help students recognize the key
prerequisite skills needed to understand new concepts.
NEW TO THIS EDITION
• Mid-Chapter Quizzes New to this edition, these
quizzes help you assess your understanding of the
concepts studied earlier in the chapter. The answers
for all exercises in the Mid-Chapter Quizzes are
provided in the Answers to Selected Exercises
appendix, along with a reference to the section in
which a particular concept was presented.
• Chapter Test Preps The Chapter Test Preps summarize
the major concepts discussed in each chapter. These
Test Preps help you prepare for a chapter test. For
each concept there is a reference to a worked example
illustrating the concept and at least one exercise in the
Chapter Review Exercise Set relating to that concept.
FEATURES
• Visualize the Solution When appropriate, both
algebraic and graphical solutions are provided to
help you visualize the mathematics of the example
and to create a link between the algebraic and visual
components of a solution.
• Exploring Concepts with Technology The optional
Exploring Concepts with Technology feature appears
you the opportunity to use calculators or computers
to solve computationally difficult problems. In
addition, you are challenged to think about pitfalls
that can be produced when using technology to solve
• Integrating Technology Integrating Technology
boxes show how technology can be used to illustrate
concepts and solve many mathematical problems.
Examples and exercises that require a calculator or
a computer to find a solution are identified by the
• Chapter Review Exercise Sets and Chapter Tests
The Chapter Review Exercise Sets and the Chapter
Tests, at the end of each chapter, are designed to
provide you with another opportunity to assess your
understanding of the concepts presented in a chapter.
The answers for all exercises in the Chapter Review
Exercise Sets and the Chapter Tests are provided in
the Answers to Selected Exercises appendix along
with a reference to the section in which the concept
was presented.
CONTENTS
Each chapter concludes with Exploring Concepts with
Technology, Summary, Assessing Concepts, Review
Exercises, Quantitative Reasoning, Chapter Test,
and Cumulative Review Exercises. P. PRELIMINARY
CONCEPTS. The Real Number System. Integer and
Rational Number Exponents. Polynomials. Factoring.
Rational Expressions. Complex Numbers. 1. EQUATIONS
AND INEQUALITIES. Linear and Absolute Value
Equations. Formulas and Applications. Quadratic
Equations. Other Types of Equations. Inequalities.
Variation and Applications. 2. FUNCTIONS AND
GRAPHS. A Two Dimensional Coordinate System and
Graphs. Introduction to Functions. Linear Functions.
Quadratic Functions. Properties of Graphs. The
Algebra of Functions. Modeling Data Using Regression.
The Remainder Theorem and the Factor Theorem.
Polynomial Functions of Higher Degree. Zeros of
Polynomial Functions. The Fundamental Theorem
Applications. 4. EXPONENTIAL AND LOGARITHMIC
and Their Applications. Logarithmic Functions and
Their Applications. Properties of Logarithms and
Logarithmic Scales. Exponential and Logarithmic
Equations. Exponential Growth and Decay. Modeling
Data with Exponential and Logarithmic Functions. 5.
TRIGONOMETRIC FUNCTIONS. Angles and Arcs. Right
Triangle Trigonometry. Trigonometric Functions of
Any Angle. Trigonometric Functions of Real Numbers.
Graphs of the Sine and Cosine Functions. Graphs of the
Other Trigonometric Functions. Graphing Techniques.
Harmonic Motion—An Application of the Sine and
Cosine Functions. 6. TRIGONOMETRIC IDENTITIES AND
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202
EQUATIONS. Verification of Trigonometric Identities.
Sum, Difference, and Cofunction Identities. Doubleand Half-Angle Identities. Identities Involving the Sum
of Trigonometric Functions. Inverse Trigonometric
Functions. Trigonometric Equations. 7. APPLICATIONS
OF TRIGONOMETRY. The Law of Sines. The Law of
Cosines and Area. Vectors. Trigonometric Form of
Complex Numbers. De Moivre’s Theorem. 8. TOPICS IN
ANALYTIC GEOMETRY. Parabolas. Ellipses. Hyperbolas.
Rotation of Axes. Introduction to Polar Coordinates.
Polar Equations of the Conics. Parametric Equations.
Systems of Linear Equations in Two Variables. Systems of
Linear Equations in More than Two Variables. Nonlinear
Systems of Equations. Partial Fractions. Inequalities
Programming. 10. MATRICES. Gaussian Elimination
Method. The Algebra of Matrices. The Inverse of a
Matrix. Determinants. Cramer’s Rule. 11. SEQUENCES,
SERIES, AND PROBABILITY. Infinite Sequences and
Summation Notation. Arithmetic Sequences and
Series. Geometric Sequences and Series. Mathematical
Induction. The Binomial Theorem. Permutations and
Combinations. Introduction to Probability.
© 2011, 1072pp, Hardback, 9781439049396
in college or in their careers. The program addresses the
needs of students at all levels--and in particular those
who may have struggled in previous algebra courses-offering an abundance of examples and exercises that
reinforce concepts and make learning more dynamic.
The early introduction of functions in Chapter 1 ensures
compatibility with syllabi and provides a framework
for student learning. Instructors can also opt to use
graphing technology as a tool for problem solving and
for review or retention.
NEW TO THIS EDITION
of key concepts.
FEATURES
COLLEGE ALGEBRA WITH APPLICATIONS
FOR BUSINESS AND LIFE SCIENCES, 2E
COLLEGE ALGEBRA WITH APPLICATIONS FOR
BUSINESS AND LIFE SCIENCES, Second Edition, meets
the demand for courses that emphasize problem
solving, modeling, and real-world applications for
business and the life sciences. The authors provide
a firm foundation in algebraic concepts, and prompt
students to apply their understanding to relevant
examples and applications they are likely to encounter
chapter.
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203
• Revised! The Exercise Sets have been revised based
on actual student usage data to improve student
comprehension. Approximately 5,000 exercises
challenging, real-world applications--all of which can
choice.
• A wide variety of relevant examples--each of which is
titled for easy reference--includes solutions presented
graphically, analytically, and/or numerically to provide
further insight into mathematical concepts. Examples
that illustrate real-life situations are identified with
an icon.
and Summation Notation. Arithmetic Sequences and
Partial Sums. Geometric Sequences and Series. The
Binomial Theorem. Counting Principles. Probability.
Appendix A: An Introduction to Graphing Utilities.
Appendix B: Conic Sections. Conic Sections. Conic
Sections and Translations. Appendix C: Further
© 2013, 720pp, Hardback, 9781133108498
CONTENTS
of a Square Matrix. The Determinant of a Square
Matrix. Applications of Matrices and Determinants. 7.
SEQUENCES, SERIES, AND PROBABILITY. Sequences
COLLEGE ALGEBRA, HYBRID (WITH
text that engages students online! Do your students
attempt to memorize facts and mimic examples to
make it through algebra? James Stewart, author of the
worldwide, best-selling calculus texts, saw this scenario
time and again in his classes. So, along with longtime
coauthors Lothar Redlin and Saleem Watson, he wrote
COLLEGE ALGEBRA specifically to help students
learn to think mathematically and to develop genuine
problem-solving skills. Comprehensive and evenlypaced, the text has helped hundreds of thousands
of students. Incorporating technology, real-world
applications, and additional useful pedagogy, the sixth
edition promises to help more students than ever build
www.cengageasia.com
204
conceptual understanding and a core of fundamental
skills.
NEW TO THIS EDITION
• Early Chapter on Functions. The chapter on Functions
now appears earlier in the book--moving from Chapter
3 to Chapter 2. The review material (in Chapters P
and 1) has been streamlined and rewritten, allowing
Instructors to more quickly get to the key part of the
course—functions.
• Diagnostic Test. A diagnostic test, designed to test
preparedness for college algebra, is available at the
beginning of the book. This allows Instructors to
more easily determine if their students are ready for
the material they will encounter in college algebra
or if they should review some basic algebra skills. As
a result instructors can better schedule and organize
their lecture topics.
• Exercises. More than 30% of the exercises are new.
This includes new Concept Exercises and new Skills
exercises. Updated exercises provide more relevant
material that will engage students. Concept and Skill
exercises will improve their students’ ability to handle
application problems and allow instructors to spend
more time on more interesting applied problems.
• Book Companion Website. A new website www.
stewartmath.com contains Discovery Projects for
each chapter and Focus on Problem Solving sections
that highlight different problem-solving principles
outlined in the Prologue. Instructors can direct
students to this additional source for learning problem
solving skills.
• Chapter P Preliminaries. This chapter now contains a
section on basic equations, including linear equations
and power equations. Instructors have available to
them important review material which ultimately
will help in their students’ greater understanding of
graphing functions.
• Chapter 1 Equations and Graphs. This is a new chapter
that includes an introduction to the coordinate plane
and graphs of equations (in two variables), as well as
the material on solving equations. Including these
topics in one chapter highlights the relationship
between algebraic and graphical solutions of
equations. Instructors will now have more book
support in explaining the relationship between data
and its graphical representation and the algebraic
representation of that data.
FEATURES
• The new Get Ready feature at the beginning of a
section lets students know which previous sections
they need to have mastered before starting the
section.
• Concept exercises, in addition to drill/skill exercises,
vary from easy to difficult and help ensure that
students are truly grasping the algebraic theories.
• Cumulative Reviews appear after select groups of
chapters and help students gauge their progress and
gain experience in taking tests that cover a broad
range of concepts and skills.
CONTENTS
Preface. To the Student. Are You Ready for College
Algebra? Prologue: Principles of Problem Solving. P.
PREREQUISITES. Modeling the Real World with Algebra.
The Real Numbers. Integer Exponents and Scientific
Notation. Rational Exponents and Radicals. Algebraic
Expressions. Factoring. Rational Expressions. Solving
Basic Equations. Chapter P Review. Chapter P Test.
FOCUS ON MODELING: Making the Best Decisions.
1. EQUATIONS AND GRAPHS. The Coordinate Plane.
Graphs of Equations in Two Variables; Circles. Lines.
Solving Equations Graphically. Modeling with Equations.
Solving Quadratic Equations. Solving Other Types of
Equations. Solving Inequalities. Solving Absolute Value
Equations and Inequalities. Chapter 1 Review. Chapter 1
Test. FOCUS ON MODELING: Fitting Lines to Data. 2.
FUNCTIONS. Functions. Graphs of Functions. Getting
Information from the Graph of a Function. Average Rate
of Change of a Function. Transformations of Functions.
Combining Functions. One-to-One Functions and Their
Inverses. Chapter 2 Review. Chapter 2 Test. FOCUS ON
MODELING: Modeling with Functions. 3. POLYNOMIAL
AND RATIONAL FUNCTIONS. Quadratic Functions
and Models. Polynomial Functions and Their Graphs.
Dividing Polynomials. Real Zeros of Polynomials.
Complex Numbers. Complex Zeros and the Fundamental
Theorem of Algebra. Rational Functions. Modeling
Variation. Chapter 3 Review. Chapter 3 Test. FOCUS
ON MODELING: Fitting Polynomial Curves to Data.
Exponential Functions. The Natural Exponential
Function. Logarithmic Functions. Laws of Logarithms.
Exponential and Logarithmic Equations. Modeling
with Exponential and Logarithmic Functions. Chapter
4 Review. Chapter 4 Test. Cumulative Review Test:
Chapters 2, 3, and 4. FOCUS ON MODELING: Fitting
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205
Exponential and Power Curves to Data. 5. SYSTEMS OF
in Several Variables. Partial Fractions. Systems of
Nonlinear Equations. Systems of Inequalities. Chapter 5
Review. Chapter 5 Test. FOCUS ON MODELING: Linear
Programming. 6. MATRICES AND DETERMINANTS.
Matrices and Systems of Linear Equations. The Algebra
of Matrices. Inverses of Matrices and Matrix Equations.
Determinants and Cramer’s Rules. Chapter 6 Review.
Chapter 6 Test. FOCUS ON MODELING: Computer
Graphics. 7. CONIC SECTIONS. Parabolas. Ellipses.
Hyperbolas. Shifted Conics. Chapter 7 Review. Chapter
7 Test. Cumulative Review Test: Chapters 5, 6, and 7.
FOCUS ON MODELING: Conics in Architecture. 8.
SEQUENCES AND SERIES. Sequences and Summation
Mathematics of Finance. Mathematical Induction. The
Binomial Theorem. Chapter 8 Review. Chapter 8 Test.
FOCUS ON MODELING: Modeling with Recursive
Sequences. 9. PROBABILITY AND STATISTICS. Counting.
Probability. Binomial Probability. Expected Value.
Chapter 9 Review. Chapter 9 Test. Cumulative Review
Test: Chapters 8 and 9. FOCUS ON MODELING: The
Monte Carlo Method. APPENDIX A: Calculations and
Calculations. APPENDIX B: Graphing with a Graphing
Calculator. APPENDIX C: Using the TI-83/84 Graphing
Calculator.
© 2013, 576pp, Paperback, 9781133600435
COLLEGE ALGEBRA, HYBRID EDITION
(WITH ENHANCED WEBASSIGN - START
SMART GUIDE FOR STUDENTS), 9E
Larson’s COLLEGE ALGEBRA HYBRID, Ninth Edition,
delivers the same sound, consistently structured
explanations and exercises of mathematical concepts
to prepare students for further study in mathematics as
his market-leading hardcover text, COLLEGE ALGEBRA,
Ninth Edition, combined with a briefer paperback
format that engages students online with Enhanced
WebAssign®. The HYBRID demonstrates Larson’s
commitment to revolutionizing the way instructors
teach and students learn material by moving all the
end-of-section exercises from the text online as
well as incorporating more real-world applications,
ongoing review, and innovative technology. Each new
Larson HYBRID includes immediate student access
to Enhanced WebAssign®. The ninth edition features
“How Do You See It?” exercises that give students
practice applying the concepts, and new “Summarize”
features, “Checkpoint” problems, and a Companion
Website that reinforce understanding of the skill sets
to help students better prepare for tests. Enhanced
WebAssign® offers fully integrated content from the
text, with the addition of end-of-section problems
and chapter tests, as well as problem-specific videos,
animations, and lecture videos.
NEW TO THIS EDITION
• State-of-the-art package provides a cost-effective,
only, and each new HYBRID includes immediate
access to Enhanced WebAssign® and the Cengage
YouBook.
• Enhanced WebAssign® features fully integrated
content from the text, including all end-of-section
problems and chapter tests, as well as problemspecific videos, animations, and lecture videos. The
robust online homework solution allows instructors
to assign, collect, grade, and record homework
assignments online, minimizing workload and
streamlining the grading process. It also gives students
the ability to stay organized with assignments and
have up-to-date grade information.
• Fresh chapter openers highlight real-life problems
that connect to the examples and exercises presented
• Innovative “Summarize” features help students
of each section.
• Unprecedented “How Do You See It?” exercises in
every section present real-life problems that students
solve by visual inspection using the concepts in the
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206
lesson.
• Original “Checkpoint” problems encourage immediate
solutions, and more to support students outside the
text.
• Enhanced “Exercise Sets” deliver more rigor, relevancy,
and mastery of concepts.
• Expanded “Section Objectives” offer students the
upcoming section.
• Enriched remarks reinforce or expand on concepts
example.
CONTENTS
Test. Proofs in Mathematics. P.S. Problem Solving. 1
.EQUATIONS, INEQUALITIES, AND MATHEMATICAL
MODELING. Graphs of Equations. Linear Equations in
One Variable. Modeling with Linear Equations. Quadratic
Equations and Applications. Complex Numbers. Other
Types of Equations. Linear Inequalities in One Variable.
Other Types of Inequalities. Chapter Summary. Review
Problem Solving. 2. FUNCTIONS AND THEIR GRAPHS.
Linear Equations in Two Variables. Functions. Analyzing
Graphs of Functions. A Library of Parent Functions.
Transformations of Functions. Combinations of
Functions: Composite Functions. Inverse Functions.
Chapter Summary. Review Exercises. Chapter Test.
Cumulative Test for Chapters P-2. Proofs in Mathematics.
P.S. Problem Solving. 3. POLYNOMIAL FUNCTIONS.
Quadratic Functions and Models. Polynomial Functions
of Higher Degree. Polynomial and Synthetic Division.
Zeros of Polynomial Functions. Mathematical Modeling
and Variation. Chapter Summary. Review Exercises.
Solving. 4. RATIONAL FUNCTIONS AND CONICS.
Rational Functions and Asymptotes. Graphs of
Rational Functions. Conics. Translations of Conics.
Proofs in Mathematics. P.S. Problem Solving. 5.
and Logarithmic Models. Chapter Summary. Review
Exercises. Chapter Test. Cumulative Test for Chapters
3-5. Proofs in Mathematics. P.S. Problem Solving.
Linear and Nonlinear Systems of Equations. TwoVariable Linear Systems. Multivariable Linear Systems.
Partial Fractions. Systems of Inequalities. Linear
Programming. Chapter Summary. Review Exercises.
Solving. 7. MATRICES AND DETERMINANTS. Matrices
and Systems of Equations. Operations with Matrices.
The Inverse of a Square Matrix. The Determinant
of a Square Matrix. Applications of Matrices and
Determinants. Chapter Summary. Review Exercises.
Solving. 8. SEQUENCES, SERIES, AND PROBABILITY.
Sequences and Series. Arithmetic Sequences and Partial
Sums. Geometric Sequences and Series. Mathematical
Induction. The Binomial Theorem. Counting Principles.
Probability. Chapter Summary. Review Exercises.
in Mathematics. P.S. Problem Solving. APPENDIX A:
ERRORS AND THE ALGEBRA OF CALCULUS. APPENDIX
B CONCEPTS IN STATISTICS (WEB). Representing Data.
Measures of Central Tendency and Dispersion. Least
Squares Regression.
© 2014, 544pp, Hardback, 9781133950530
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207
Revisited.
• Chapter Test Preps The Chapter Test Preps summarize
the major concepts discussed in each chapter. These
Test Preps help you prepare for a chapter test. For
each concept there is a reference to a worked example
illustrating the concept and at least one exercise in the
Chapter Review Exercise Set relating to that concept.
FEATURES
COLLEGE ALGEBRA, INTERNATIONAL
EDITION, 7E
Richard N. Aufmann, Palomar College; Vernon C. Barker, Palomar
College; Richard D. Nation, Palomar College
COLLEGE ALGEBRA, 7e, International Edition uses the
dynamic link between concepts and applications to
bring mathematics to life. By incorporating interactive
learning techniques, the Aufmann team helps students
to better understand concepts, work independently,
and obtain greater mathematical fluency. The text also
includes technology features to accommodate courses
that allow the option of using graphing calculators.
Additional program components that support student
success include tutorial practice, online homework,
Live Online Tutoring, and Instructional DVDs. The
authors’ proven Aufmann Interactive Method allows
students to try a skill as it is presented in example
form. This interaction between the examples and
Try Exercises serves as a checkpoint to students as
they read the textbook, do their homework, or study
a section. In the Seventh Edition, Review Notes are
featured more prominently throughout the text to help
students recognize the key prerequisite skills needed
to understand new concepts.
NEW TO THIS EDITION
• Mid-Chapter Quizzes New to this edition, these
quizzes help you assess your understanding of the
concepts studied earlier in the chapter. The answers
for all exercises in the Mid-Chapter Quizzes are
provided in the Answers to Selected Exercises
appendix, page XX, along with a reference to the
section in which a particular concept was presented.
• A Quantitative Reasoning feature demonstrates math
solutions to real-world problems and is compliant
with MAA Guidelines and AMATYC 2006 Crossroads
• Visualize the Solution When appropriate, both
algebraic and graphical solutions are provided to
help you visualize the mathematics of the example
and to create a link between the algebraic and visual
components of a solution.
• Exploring Concepts with Technology The optional
Exploring Concepts with Technology feature appears
you the opportunity to use calculators or computers
to solve computationally difficult problems. In
addition, you are challenged to think about pitfalls
that can be produced when using technology to solve
• Integrating Technology Integrating Technology
boxes show how technology can be used to illustrate
concepts and solve many mathematical problems.
Examples and exercises that require a calculator or
a computer to find a solution are identified by the
• Chapter Review Exercise Sets and Chapter Tests
The Chapter Review Exercise Sets and the Chapter
Tests, at the end of each chapter, are designed to
provide you with another opportunity to assess your
understanding of the concepts presented in a chapter.
The answers for all exercises in the Chapter Review
Exercise Sets and the Chapter Tests are provided in
the Answers to Selected Exercises appendix along
with a reference to the section in which the concept
was presented.
CONTENTS
Table of Contents P. PRELIMINARY CONCEPTS.
The Real Number System. Integer and Rational
Number Exponents. Polynomials. Factoring. Rational
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208
Expressions. Complex Numbers. 1. EQUATIONS
AND INEQUALITIES. Linear and Absolute Value
Equations. Formulas and Applications. Quadratic
Equations. Other Types of Equations. Inequalities.
Variation and Applications. 2. FUNCTIONS AND
GRAPHS. A Two-Dimensional Coordinate System and
Graphs. Introduction to Functions. Linear Functions.
Quadratic Functions. Properties of Graphs. The
Algebra of Functions. Modeling Data Using Regression
3. POLYNOMIAL AND RATIONAL FUNCTIONS. The
Remainder of Theorem and the Factor Theorem.
Polynomial Functions of Higher Degree. Zeros of
Polynomial Functions. The Fundamental Theorem
Applications. 4. EXPONENTIAL AND LOGARITHMIC
and Their Applications. Logarithmic Functions and Their
Applications. Properties of Logarithms and Logarithmic
Scales. Exponential and Logarithmic Equations.
Exponential Growth and Decay. Modeling Data with
Exponential and Logarithmic Functions. 5. TOPICS IN
ANALYTIC GEOMETRY. Parabolas. Ellipses. Hyperbolas.
Systems of Linear Equations in Two Variables. Systems of
Linear Equations in More Than Two Variables. Nonlinear
Systems of Equations. Partial Fractions. Inequalities
Programming. 7. MATRICES. Gaussian Elimination
Method. The Algebra of Matrices. The Inverse of a
Matrix. Determinants. Cramer’s Rule. 8. SEQUENCES,
SERIES, AND PROBABILITY. Infinite Sequences and
Summation Notation. Arithmetic Sequences and
Series. Geometric Sequences and Series. Mathematical
Induction. The Binomial Theorem. Permutations and
Combinations. Introduction to Probability.
© 2011, 784pp, Paperback, 9781439049365
EDITION, 8E
Jerome E. Kaufmann, Western Illinois University (Retired); Karen L.
Schwitters, Seminole Community College
Known for a clear and concise exposition, numerous
examples, and plentiful problem sets, Jerome E.
Kaufmann and Karen L. Schwitters’s COLLEGE
ALGEBRA, 8E, International Edition is an easy-to-use
book that focuses on building technique and helping
students hone their problem-solving skills. The eighth
edition focuses on solving equations, inequalities, and
problems; and on developing graphing techniques and
using the concept of a function. Updated with new
application problems and examples throughout, the
eighth edition is accompanied by a robust collection
of teaching and learning resources, including Enhanced
WebAssign®, an easy-to-use online homework
management system for both instructors and students.
NEW TO THIS EDITION
• Classroom Examples: For every example in the text,
there is an associated classroom example problem
similar to the example problem. Answers to the
classroom example problems are furnished in the
Complete Solutions Manual but not in the Student’s
Edition. These classroom examples provide an
excellent source of an additional problem to further
the understanding of the example presented.
• Chapter summaries: Chapter Summaries have taken
on an entirely new look. The summaries are presented
in a grid fashion by objectives. Each row contains the
objective, pertinent information summarizing that
objective, and an example problem with solution for
that objective.
• Objectives. Each section begins with a numbered list
of objectives for that section. Then in the Problem
Set following that section, groups of problems are
www.cengageasia.com
209
identified by section objections.
FEATURES
• A Chapter test appears at the end of each chapter
to give students ample opportunity to prepare for
their exams.
• Cumulative Review Problem Sets appear at the ends
of Chapter 2-8 to ensure that students retain the
concepts of earlier chapters.
• Problems called “Thoughts into Words” are included
in all problems sets except the review exercises. These
problems are designed to encourage students to
express, in written form, their thoughts about various
mathematical ideas.
• Problem solving is an integral part of this text, as
is recommended by the standards produced by
NCTM and AMATYC. With problem solving as its
focus, Chapter 1 pulls together and expands on
a variety of approaches to solving equations and
inequalities. Polya’s four-phase plans is used as a basis
for developing various problem solving strategies.
Applications of radical equations are a part of
Section 1.5, and applications of slope are in Section
2.3. Functions are introduced in Chapter 3 and are
immediately used to solve problems. Exponential
and logarithmic functions become problem-solving
tools in Chapter 5. Systems of equations provide more
problem solving power in Chapter 6. Problem solving
is the unifying theme of Chapter 9.
• The Enhanced WebAssign component will include
approximately 2500 homework questions and a
YouBook.
CONTENTS
0. SOME BASIC CONCEPTS OF ALGEBRA: A REVIEW.
Some Basic Ideas. Exponents. Polynomials. Factoring
Polynomials. Rational Expressions. Radicals. Relationship
Between Exponents and Roots. Complex Numbers.
Chapter 0 Summary. Chapter 0 Review Problem Set.
Chapter 0 Test. 1. EQUATIONS, INEQUALITIES, AND
PROBLEM SOLVING. Linear Equations and Problem
Solving. More Equations and Applications. Quadratic
Equations. Applications of Linear and Quadratic
Equations. Miscellaneous Equations. Inequalities.
Quadratic and Rational Inequalities. Absolute Value
Equations and Inequalities. Chapter 1 Summary. Chapter
1 Review Problem Set. Chapter 1 Test. 2. COORDINATE
GEOMETRY AND GRAPHING TECHNIQUES. Coordinate
Geometry. Graphing Techniques: Linear Equations and
Inequalities. Determining the Equation of a Li ne. More
on Graphing. Circles, Ellipses, and Hyperbolas. Chapter
1 Summary. Chapter 1 Review Problem Set. Chapter
1 Test. Cumulative Review Problem Set (Chapters
0-2). 3. FUNCTIONS. Concept of a Function. Linear
Functions and Applications. Quadratic Equations.
Transformations of Some Basic Curves. Combining
Functions. Direct and Inverse Variation. Chapter 3
Summary. Chapter 3 Review Problem Set. Chapter 3
Test. Cumulative Review Problem Set (Chapters 0-3). 4.
POLYNOMIAL AND RATIONAL FUNCTIONS. Dividing
Polynomials and Synthetic Division. Remainder and
factor Theorems. Polynomial Equations. Graphing
Polynomial Functions. Graphing Rational Functions.
More on Graphing Rational Functions. Chapter 4
Summary. Chapter 4 Review Problem Set. Chapter 4
Test. Cumulative Review Problem Set (Chapters 0-4).
Exponents and Exponential Functions. Applications of
Exponential Functions. Inverse Functions. Logarithms.
Logarithmic Functions. Exponential Equations,
Logarithmic Equations, and Problem Solving. Chapter
5 Summary. Chapter 5 Review Problem Set. Chapter
5 Test. Cumulative Review Problem Set (Chapters
0-5). 6. SYSTEMS OF EQUATIONS. Systems of Two
Linear Equations in Two Variables. Systems of Three
Linear Equations in Three Variables. Matrix Approach
to Solving Linear Systems. Determinants. Cramer’s
Rule. Partial Fractions. Chapter 6 Summary. Chapter
6 Review Problem Set. Chapter 6 Test. Cumulative
Review Problem Set (Chapters 0-6). 7. ALGEBRA OF
MATRICES. Algebra of 2 × 2 Matrices. Multiplicative
Inverses. m x n Matrices. Systems of Linear Inequalities:
Linear Programming. Chapter 7 Summary. Chapter 7
Review Problem Set. Chapter 7 Test. Cumulative Review
Problem Set (Chapters 0-7). 8. CONIC SECTIONS.
Parabolas. Ellipses. Hyperbolas. Systems Involving
Nonlinear Equations. Chapter 8 Summary. Chapter 8
Review Problem Set. Chapter 8 Test. Cumulative Review
Problem Set (Chapters 0-8). 9. SEQUENCES AND
MATHEMATICAL INDUCTION. Arithmetic Sequences.
Geometric Sequences. Another Look at Problem Solving.
Mathematical Induction. Chapter 9 Summary. Chapter
9 Review Problem Set. Chapter 9 Test.
© 2013, 800pp, Paperback, 9781111990480
www.cengageasia.com
210
EDITION, 6E
Do your students attempt to memorize facts and mimic
examples to make it through algebra? James Stewart,
author of the worldwide, best-selling calculus texts, saw
this scenario time and again in his classes. So, along
with longtime coauthors Lothar Redlin and Saleem
Watson, he wrote COLLEGE ALGEBRA, 6E, International
Edition specifically to help students learn to think
mathematically and to develop genuine problemsolving skills. Comprehensive and evenly-paced, the
text has helped hundreds of thousands of students.
Incorporating technology, real-world applications, and
additional useful pedagogy, the sixth edition promises
to help more students than ever build conceptual
understanding and a core of fundamental skills.
NEW TO THIS EDITION
• Early Chapter on Functions. The chapter on Functions
now appears earlier in the book—moving from
Chapter 3 to Chapter 2. The review material (in
Chapters P and 1) has been streamlined and rewritten,
allowing Instructors to more quickly get to the key
part of the course—functions.
• Diagnostic Test. A diagnostic test, designed to test
preparedness for college algebra, is available at the
beginning of the book. This allows Instructors to
more easily determine if their students are ready for
the material they will encounter in college algebra
or if they should review some basic algebra skills. As
a result instructors can better schedule and organize
their lecture topics.
• Exercises. More than 30% of the exercises are new.
This includes new Concept Exercises and new Skills
exercises. Updated exercises provide more relevant
material that will engage students. Concept and Skill
exercises will improve their students’ ability to handle
application problems and allow instructors to spend
more time on more interesting applied problems.
• Book Companion Website. A new website, www.
stewartmath.com, contains Discovery Projects for
outlined in the Prologue. Instructors can direct
students to this additional source for learning problem
solving skills.
• Chapter P Preliminaries. This chapter now contains a
section on basic equations, including linear equations
and power equations. Instructors have available to
them important review material which ultimately
will help in their students’ greater understanding of
graphing functions.
• Chapter 1 Equations and Graphs. This is a new chapter
that includes an introduction to the coordinate plane
and graphs of equations (in two variables), as well as
the material on solving equations. Including these
topics in one chapter highlights the relationship
between algebraic and graphical solutions of
equations. Instructors will now have more book
support in explaining the relationship between data
and its graphical representation and the algebraic
representation of that data.
FEATURES
• The Get Ready feature at the beginning of a section
lets students know which previous sections they need
to have mastered before starting the section.
• Concept exercises, in addition to drill/skill exercises,
vary from easy to difficult and help ensure that
students are truly grasping the algebraic theories.
• Practice What You’ve Learned features at the end of
each example directs students to a similar problem in
the exercises, allowing them to immediately reinforce
the concept just covered.
• Cumulative Reviews appear after select groups of
chapters and help students gauge their progress and
gain experience in taking tests that cover a broad
range of concepts and skills.
CONTENTS
Preface. To the Student. Are You Ready for College
Algebra? Prologue: Principles of Problem Solving. P.
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PREREQUISITES. Modeling the Real World with Algebra.
The Real Numbers. Integer Exponents and Scientific
Notation. Rational Exponents and Radicals. Algebraic
Expressions. Factoring. Rational Expressions. Solving
Basic Equations. Chapter P Review. Chapter P Test.
FOCUS ON MODELING: Making the Best Decisions.
1. EQUATIONS AND GRAPHS. The Coordinate Plane.
Graphs of Equations in Two Variables; Circles. Lines.
Solving Equations Graphically. Modeling with Equations.
Solving Quadratic Equations. Solving Other Types of
Equations. Solving Inequalities. Solving Absolute Value
Equations and Inequalities. Chapter 1 Review. Chapter 1
Test. FOCUS ON MODELING: Fitting Lines to Data. 2.
FUNCTIONS. Functions. Graphs of Functions. Getting
Information from the Graph of a Function. Average Rate
of Change of a Function. Transformations of Functions.
Combining Functions. One-to-One Functions and Their
Inverses. Chapter 2 Review. Chapter 2 Test. FOCUS ON
MODELING: Modeling with Functions. 3. POLYNOMIAL
AND RATIONAL FUNCTIONS. Quadratic Functions
Theorem of Algebra. Rational Functions. Modeling
Variation. Chapter 3 Review. Chapter 3 Test. FOCUS
ON MODELING: Fitting Polynomial Curves to Data.
4 Review. Chapter 4 Test. Cumulative Review Test:
Chapters 2, 3, and 4. FOCUS ON MODELING: Fitting
Exponential and Power Curves to Data. 5. SYSTEMS OF
in Several Variables. Partial Fractions. Systems of
Nonlinear Equations. Systems of Inequalities. Chapter 5
Review. Chapter 5 Test. FOCUS ON MODELING: Linear
Programming. 6. MATRICES AND DETERMINANTS.
Matrices and Systems of Linear Equations. The Algebra
of Matrices. Inverses of Matrices and Matrix Equations.
Determinants and Cramer’s Rules. Chapter 6 Review.
Chapter 6 Test. FOCUS ON MODELING: Computer
Graphics. 7. CONIC SECTIONS. Parabolas. Ellipses.
Hyperbolas. Shifted Conics. Chapter 7 Review. Chapter
7 Test. Cumulative Review Test: Chapters 5, 6, and 7.
FOCUS ON MODELING: Conics in Architecture. 8.
SEQUENCES AND SERIES. Sequences and Summation
FOCUS ON MODELING: Modeling with Recursive
Sequences. 9. PROBABILITY AND STATISTICS. Counting.
Probability. Binomial Probability. Expected Value.
Chapter 9 Review. Chapter 9 Test. Cumulative Review
Test: Chapters 8 and 9. FOCUS ON MODELING: The
Monte Carlo Method. APPENDIX A: Calculations and
Calculations. APPENDIX B: Graphing with a Graphing
Calculator. APPENDIX C: Using the TI-83/84 Graphing
Calculator.
© 2013, 784pp, Paperback, 9781111990305
EDITION, 9E
Larson’s COLLEGE ALGEBRA, 9E, International Edition
is known for delivering sound, consistently structured
explanations and exercises of mathematical concepts to
prepare students for further study in mathematics. With
the ninth edition, Larson continues to revolutionize
the way students learn material by incorporating
innovative technology. “How Do You See It?” exercises
give students practice applying the concepts, and new
“Summarize” features, “Checkpoint” problems, and a
Companion Website reinforce understanding of the skill
sets to help students better prepare for tests. Enhanced
WebAssign® features fully integrated content from
the text, with the addition of end-of-section problems
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212
NEW TO THIS EDITION
of each section.
lesson.
text.
upcoming section.
example.
• Up-to-the-minute homework support through
CalcChat.com, an independent website, provides
students with free solutions to all odd-numbered
problems in the text.
FEATURES
• “Side-by-Side Examples” help students see not only
that a problem can be solved in more than one
way but also how different methods—algebraically,
graphically, and numerically—yield the same result.
The side-by-side format also addresses many different
learning styles.
CONTENTS
EQUATIONS, INEQUALITIES, AND MATHEMATICAL
MODELING. Graphs of Equations. Linear Equations in
One Variable. Modeling with Linear Equations. Quadratic
Equations and Applications. Complex Numbers. Other
Types of Equations. Linear Inequalities in One Variable.
Other Types of Inequalities. Chapter Summary. Review
Problem Solving. 2. FUNCTIONS AND THEIR GRAPHS.
Linear Equations in Two Variables. Functions. Analyzing
Graphs of Functions. A Library of Parent Functions.
Transformations of Functions. Combinations of
Functions: Composite Functions. Inverse Functions.
Cumulative Test for Chapters P-2. Proofs in Mathematics.
P.S. Problem Solving. 3. POLYNOMIAL FUNCTIONS.
Quadratic Functions and Models. Polynomial Functions
of Higher Degree. Polynomial and Synthetic Division.
Zeros of Polynomial Functions. Mathematical Modeling
Solving. 4. RATIONAL FUNCTIONS AND CONICS.
Rational Functions. Conics. Translations of Conics.
Linear and Nonlinear Systems of Equations. TwoVariable Linear Systems. Multivariable Linear Systems.
Partial Fractions. Systems of Inequalities. Linear
Programming. Chapter Summary. Review Exercises.
Solving. 7. MATRICES AND DETERMINANTS. Matrices
and Systems of Equations. Operations with Matrices.
The Inverse of a Square Matrix. The Determinant
of a Square Matrix. Applications of Matrices and
Determinants. Chapter Summary. Review Exercises.
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Solving. 8. SEQUENCES, SERIES, AND PROBABILITY.
Sequences and Series. Arithmetic Sequences and Partial
Sums. Geometric Sequences and Series. Mathematical
ERRORS AND THE ALGEBRA OF CALCULUS. APPENDIX
B: CONCEPTS IN STATISTICS (WEB). Representing Data.
Measures of Central Tendency and Dispersion. Least
Squares Regression.
© 2014, 624pp, Paperback, 9781133959700
EDITION, 11E
R. David Gustafson, Rock Valley College (Emeritus); Jeff Hughes,
Hinds Community College
Clearly written and comprehensive, Gustafson and
Hughes’ popular book, COLLEGE ALGEBRA, 11E,
International Edition provides in-depth and precise
coverage, incorporated into a framework of tested
teaching strategy. The authors combine carefully
selected pedagogical features and patient explanations
to give students a book that preserves the integrity
of mathematics, yet does not discourage them with
material that is confusing or too rigorous. Long
respected for its ability to help students quickly
master difficult problems, this book also helps them
develop the skills they’ll need in future courses and
in everyday life. Retaining the mathematical precision
instructors have come to expect, the authors have
focused on making this new edition more modern to
better illustrate to students the importance of math
in their world.
NEW TO THIS EDITION
• STRATEGY BOXES: To enable students to build on
their mathematical reasoning and approach problems
with confidence, Strategy boxes offer problem-solving
techniques and steps at appropriate points in the
material.
• CAUTION BOXES: Caution boxes appear throughout
the text to alert students to common errors
and misunderstandings, and reinforce correct
mathematics.
• NOW TRY EXERCISES: A reference to a Now Try
exercise follows all Examples and Self Check problems,
providing students an additional opportunity to assess
their understanding of the concept related to each
worked example. These references also show students
a correspondence between the examples in the book
and the exercise sets.
• TITLED EXAMPLES: Descriptive titles have been
added to clearly identify the topic and purpose of
each example.
• DESIGN: Color is used to highlight and differentiate
definition boxes, property and theorem boxes, and
strategy boxes—helping to categorize information
for students and making it easier to absorb and
remember.
FEATURES
• STUDENT-FRIENDLY WRITING STYLE: Clear, concise,
and friendly exposition helps to alleviate student
anxiety about reading a mathematics textbook.
The writing is informal yet accurate. Students
and instructors alike should find the reading both
interesting and inviting.
• CAREERS IN MATHEMATICS CHAPTER OPENERS:
To encourage students to explore careers that use
mathematics and make a connection between math
and real life, each chapter opens with Careers in
Mathematics. New, exciting careers are showcased
in this edition. Featuring information taken primarily
from the Occupational Outlook Handbook, these
snapshots include information on how professionals
use math in their work and who employs them. A web
address is provided, allowing students to learn more
about the career.
• SECTION OPENERS: To pique interest and motivate
students to read the material, each section begins
with a contemporary photo and a real-life application
that will appeal to students of varied interests.
• NUMBERED OBJECTIVES: Numbered learning
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214
objectives, which are listed at the beginning of each
section and appear as subheadings in the section,
keep students focused.
• EXAMPLE STRUCTURE: To help students gain a
deeper understanding of how to solve each problem,
solutions to examples begin with a stated approach.
The examples are engaging, and step-by-step
solutions with annotations are provided.
CONTENTS
0. A REVIEW OF BASIC ALGEBRA. Sets of Real Numbers.
Integer Exponents and Scientific Notation. Rational
Exponents and Radicals. Polynomials. Factoring
Polynomials. Rational Expressions. Chapter Review.
Chapter Test. 1. EQUATIONS AND INEQUALITIES.
Linear Equations and Rational Equations. Applications of
Linear Equations. Quadratic Equations. Applications of
Quadratic Equations. Complex Numbers. Polynomial and
Radical Equations. Inequalities. Absolute Value. Chapter
Review. Chapter Test. Cumulative Review Exercises.
2. THE RECTANGULAR COORDINATE SYSTEM AND
GRAPHS OF EQUATIONS. The Rectangular Coordinate
System. The Slope of a Nonvertical Line. Writing
Equations of Lines. Graphs of Equations. Proportion and
Variation. Chapter Review. Chapter Test. 3. FUNCTIONS.
Functions and Function Notation. Quadratic Functions.
Polynomial and Other Functions. Transformation of
Functions. Rational Functions. Operations on Functions.
Inverse Functions. Chapter Review. Chapter Test.
Cumulative Review Exercises. 4. EXPONENTIAL AND
and Their Graphs. Applications of Exponential Functions.
Logarithmic Functions and Their Graphs. Applications
of Logarithmic Functions. Properties of Logarithms.
Exponential and Logarithmic Equations. Chapter Review.
Chapter Test. 5. SOLVING POLYNOMIAL EQUATIONS.
The Remainder and Factor Theorems; Synthetic Division.
Descartes’ Rule of Signs and Bounds on Roots. Roots of
Polynomial Equations. Approximating Irrational Roots
of Polynomial Equations. Chapter Review. Chapter Test.
Cumulative Review Exercises. 6. LINEAR SYSTEMS.
Systems of Linear Equations. Gaussian Elimination
and Matrix Methods. Matrix Algebra. Matrix Inversion.
Determinants. Partial Fractions. Graphs of Linear
Inequalities. Linear Programming. Chapter Review.
Chapter Test. 7. CONIC SECTIONS AND QUADRATIC
SYSTEMS. The Circle and the Parabola. The Ellipse. The
Hyperbola. Solving Problems Using Nonlinear Systems
of Equations. Chapter Review. Chapter Test. Cumulative
Review Exercises. 8. NATURAL NUMBER FUNCTIONS
AND PROBABILITY. The Binomial Theorem. Sequences,
Series, and Summation Notation. Arithmetic Sequences.
Geometric Sequences. Mathematical Induction.
Permutations and Combinations. Probability. Chapter
Review. Chapter Test. 9. MATHEMATICS OF FINANCE
(online). Interest. Annuities and Future Value. Present
Value of an Annuity; Amortization. Linear Programming.
Chapter Review. Chapter Test. Cumulative Review
Exercises. Appendix I: A PROOF OF THE BINOMIAL
THEOREM. Appendix II: TABLES. Powers and Roots.
Base-10 Logarithms. Base-e Logarithms. Appendix III:
ANSWERS TO SELECTED EXERCISES (in Student Edition
only).
© 2013, 848pp, Paperback, 9781133103509
FUNCTIONS AND CHANGE, 5E
A Modeling Approach to College Algebra
Bruce Crauder, Oklahoma State University; Benny Evans, Oklahoma
State University; Alan Noell, Oklahoma State University
FUNCTIONS AND CHANGE: A MODELING APPROACH
TO COLLEGE ALGEBRA, Fifth Edition is optimal for
both non-traditional and terminal students taking
college algebra and those who may continue onto
calculus. The authors’ incorporate graphing utilities,
functions, modeling, real data, applications and projects
to develop skills, giving students the practice they
need to not only master basic mathematics but apply
it in future courses and careers. With a streamlined
presentation, fresh design and added features such as
“Test Your Understanding”, the fifth edition reinforces
the authors’ focus on connecting math in the real world
with added applications in business and social sciences,
promotes mastery of the material and fosters critical
thinking. Enhanced WebAssign now features increased
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215
exercise coverage, personalized study plans, lecture
videos and more that make it easier to get started with
online homework. Available with InfoTrac® Student
Collections http://gocengage.com/infotrac.
NEW TO THIS EDITION
• Fresh design with additional color and photographs
enhances the clarity and appeal of the exposition.
• Streamlined and updated layout allows for a greater
focus on the topics and presentations that work so
well in the classroom.
• Up-to-the-minute real-data invigorates the exercise
sets and connects to the real-world.
• New! Test Your Understanding feature follows
examples in the text and challenges students to solve
similar problems. Answers are provided to reinforce
correct work.
• New! Solving Inequalities section in Chapter 2
expands upon the fundamental ideas of solving
equations by the method of crossing graphs.
• New! Constant Percentage Change section in Chapter
4 allows for additional discussion and for students to
master its importance in applications of exponential
functions.
• Additional business and social sciences applications
strengthen the authors’ commitment to showing
students the importance of mathematics in the world
around them.
• Trimmed Algebraic Look sections are either grouped
together at the end of chapters or placed in the
appendix. Teachers may decide which of these
materials they wish to use.
• Reorganized Skill exercises are now located at the end
of the major exercises to emphasis the importance of
the major exercises and the many applications they
contain.
• Revised treatment of topics eliminates the use
of the logarithm in exponential regression and
power regression; and quadratics, higher-degree
polynomials, and rational functions is now in one
section.
Rates of Change with Formulas. A Further Look: Areas
Associated with Graphs. 2. GRAPHICAL AND TABULAR
ANALYSIS. Table and Trends. Graphs. Solving Linear
Equations. Solving Nonlinear Equations. Inequalities.
Optimization. Summary. Chapter Review Exercises.
A Further Look: Limits. A Further Look: Shifting and
Stretching. A Further Look: Optimizing with Parabolas.
3. STRAIGHT LINES AND LINEAR FUNCTIONS. The
Geometry of Lines. Linear Functions. Modeling Data
with Linear Functions. Linear Regression. Systems
of Equations. Summary. Chapter Review Exercises. A
Further Look: Parallel and Perpendicular Lines. A Further
Look: Secant Lines. 4. EXPONENTIAL FUNCTIONS.
Exponential Growth and Decay. Constant Percentage
Change. Modeling Exponential Data. Modeling Nearly
Exponential Data. Logarithmic Functions. Summary.
Chapter Review Exercises. A Further Look: Solving
Exponential Equations. 5. A SURVEY OF OTHER
COMMON FUNCTIONS. Logistic Functions. Power
Functions. Modeling Data with Power Functions.
Combining and Decomposing Functions. Polynomials
and Rational Functions. Summary. Chapter Review
Exercises. A Further Look: Fitting Logistic Data using
Rates of Change. A Further Look: Factoring Polynomials,
Behavior at Infinity. 6. RATES OF CHANGE. Velocity.
Rates of Change for Other Functions. Estimating Rates
of Change. Equations of Change: Linear and Exponential
Functions. Equations of Change: Graphical Solutions.
Summary. Chapter Review Exercises. APPENDIX. A.1
Order of Operations. A.2 Definition of a Function. A.3
Geometric Constructions. A.4 Inverse Function. A.5:
Solving Equations by Factoring. A.6 Equations of Lines.
A.7 Elementary Properties of Exponents. A.8 Quadratic
Functions and Complex Numbers. BRIEF ANSWERS TO
SELECTED EXERCISES.
© 2014, 560pp, Hardback, 9781133365556
CONTENTS
Prologue: Calculator Arithmetic. Summary. Chapter
Review Exercises. 1. FUNCTIONS. Functions Given by
Formulas. Functions Given by Tables. Functions Given
by Graphs. Functions Given by Words. Summary.
Chapter Review Exercises. A Further Look: Average
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216
FUNCTIONS AND CHANGE, 5E
College Algebra, International Edition
FUNCTIONS AND CHANGE: A MODELING APPROACH
TO COLLEGE ALGEBRA, 5E, International Edition is
optimal for both non-traditional and terminal students
taking college algebra and those who may continue onto
calculus. The authors’ incorporate graphing utilities,
functions, modeling, real data, applications and projects
to develop skills, giving students the practice they
need to not only master basic mathematics but apply
it in future courses and careers. With a streamlined
presentation, fresh design and added features such as
“Test Your Understanding”, the fifth edition reinforces
the authors’ focus on connecting math in the real world
with added applications in business and social sciences,
promotes mastery of the material and fosters critical
thinking. Enhanced WebAssign now features increased
exercise coverage, personalized study plans, lecture
videos and more that make it easier to get started with
online homework.
NEW TO THIS EDITION
• Fresh design with additional color and photographs
enhances the clarity and appeal of the exposition.
• Streamlined and updated layout allows for a greater
focus on the topics and presentations that work so
well in the classroom.
• Up-to-the-minute real-data invigorates the exercise
sets and connects to the real-world.
• New! Test Your Understanding feature follows
examples in the text and challenges students to solve
similar problems. Answers are provided to reinforce
correct work.
• New! Solving Inequalities section in Chapter 2
expands upon the fundamental ideas of solving
equations by the method of crossing graphs.
• New! Constant Percentage Change section in Chapter
4 allows for additional discussion and for students to
master its importance in applications of exponential
functions.
• Additional business and social sciences applications
strengthen the authors’ commitment to showing
students the importance of mathematics in the world
around them.
• Trimmed Algebraic Look sections are either grouped
together at the end of chapters or placed in the
appendix. Teachers may decide which of these
materials they wish to use.
• Reorganized Skill exercises are now located at the end
of the major exercises to emphasize the importance
of the major exercises and the many applications
they contain.
• Revised treatment of topics eliminates the use
of the logarithm in exponential regression and
power regression; and quadratics, higher-degree
polynomials, and rational functions is now in one
section.
CONTENTS
Prologue: Calculator Arithmetic. Summary. Chapter
Review Exercises. 1. FUNCTIONS. Functions Given by
Formulas. Functions Given by Tables. Functions Given
by Graphs. Functions Given by Words. Summary.
Chapter Review Exercises. A Further Look: Average
Rates of Change with Formulas. A Further Look: Areas
Associated with Graphs. 2. GRAPHICAL AND TABULAR
ANALYSIS. Table and Trends. Graphs. Solving Linear
Equations. Solving Nonlinear Equations. Inequalities.
Optimization. Summary. Chapter Review Exercises.
A Further Look: Limits. A Further Look: Shifting and
Stretching. A Further Look: Optimizing with Parabolas.
3. STRAIGHT LINES AND LINEAR FUNCTIONS. The
Geometry of Lines. Linear Functions. Modeling Data
with Linear Functions. Linear Regression. Systems
of Equations. Summary. Chapter Review Exercises. A
Further Look: Parallel and Perpendicular Lines. A Further
Look: Secant Lines. 4. EXPONENTIAL FUNCTIONS.
Exponential Growth and Decay. Constant Percentage
Change. Modeling Exponential Data. Modeling Nearly
Exponential Data. Logarithmic Functions. Summary.
Chapter Review Exercises. A Further Look: Solving
Exponential Equations. 5. A SURVEY OF OTHER
COMMON FUNCTIONS. Logistic Functions. Power
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Functions. Modeling Data with Power Functions.
Combining and Decomposing Functions. Polynomials
and Rational Functions. Summary. Chapter Review
Exercises. A Further Look: Fitting Logistic Data using
Rates of Change. A Further Look: Factoring Polynomials,
Behavior at Infinity. 6. RATES OF CHANGE. Velocity.
Rates of Change for Other Functions. Estimating Rates
of Change. Equations of Change: Linear and Exponential
Functions. Equations of Change: Graphical Solutions.
Summary. Chapter Review Exercises. APPENDIX. A.1
Order of Operations. A.2 Definition of a Function. A.3
Geometric Constructions. A.4 Inverse Function. A.5:
Solving Equations by Factoring. A.6 Equations of Lines.
A.7 Elementary Properties of Exponents. A.8 Quadratic
Functions and Complex Numbers. BRIEF ANSWERS TO
SELECTED EXERCISES.
© 2014, 560pp, Paperback, 9781133365594
AP/HS Edition
PRECALCULUS, 6E
Mathematics for Calculus High School Edition Level 1
© 2012, 1104pp, Hardback, 9781111428747
PRECALCULUS
A Make It Real Approach, International Edition
This new text provides a contemporary approach
to college algebra, ideal for the many skeptical or
apprehensive students who ask, “When am I ever
going to use this?” The key phrase is “Make It Real”
since the goal is to make the material relevant and
understandable to today’s college students. But many
books make this claim—so how is PRECALCULUS:
A MAKE IT REAL APPROACH, International Edition
different? In other texts, which simply wrap realworld situations around problems, the context isn’t
needed to do the mathematics. Written by skilled and
passionate teachers, this text uses real-world data sets
and situations to draw out mathematical concepts.
Students are immersed in familiar contexts—from
golf course ratings to Egyptian pyramids—from which
concepts emerge naturally, and then guided in using
their understanding of those ideas to make sense
of the mathematics. The real-world contexts are not
only helpful for understanding procedures—they’re
necessary. The concept of a function, the use of
modeling, and the thorough integration of real-world
applications are integral to the text. If there’s one new
precalculus text crafted to stand up to a “reality check”
comparison with your current book, this is it.
FEATURES
• Explanations and Examples: A conversational tone
and detailed explanations make the math come
alive for students. Intriguing, relevant photographs
and carefully rendered graphics pique students’
interest and capture their attention. Meaningful
real world contexts inform students about the world
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218
and motivate them to investigate mathematical
concepts. Familiarity with these contexts, from
which ideas emerge intuitively, are not only helpful
for comprehending procedures—they’re necessary.
One student commented, “It’s like having the teacher
standing over my shoulder explaining things to me.”
• Variety of Homework Exercises: The overarching
philosophy of developing students’ mathematical
reasoning and persistent problem solving is evident
throughout the homework exercises, which are
divided into four sections: Concepts and Skills (for
practicing procedures and demonstrating a basic
understanding of key concepts), Show You Know
(requiring written explanations of big ideas), Make
It Real (real world contexts that help students
understand the world and make connections between
mathematics and their lives), and Stretch Your Mind
(requiring deep thought, creativity, and persistence).
• Study Sheets: The end-of-chapter Study Sheets
present a series of questions focused on the big
ideas of the chapter. As students reflect upon these
questions, they solidify their understanding of the
key mathematical concepts. The Study Sheets are an
ideal chapter review activity to help students prepare
for the end-of-chapter exam.
• Review Exercises: End-of-chapter review exercises
al low students to refine their conceptual
understanding and mathematical expertise. Grouped
by section number, these exercises make it easy to
focus on particular areas of study.
• Distinctive Treatment of Modeling and Graphs:
In keeping with the book’s approach, the authors
promote student comprehension by presenting
modeling and graphs in familiar contextual situations;
that is, models and graphs describe the underlying
behavior that is embedded into the context. Modeling
and graphs are used extensively; for instance, Section
6.2 on Exponential Function Modeling and Graphs
features nine examples, all of which include a real
world context.
• Unique Make It Real Projects: These end-of-chapter
projects allow students to apply the concepts learned
in the chapter to data collected from an area of
personal interest. By allowing students to focus on a
real world context of their choosing, their motivation
and interest in doing the mathematics increases.
Additionally, the Make It Real Projects provide
learners another avenue for developing mathematical
reasoning and persistent problem solving as they
make sense of the mathematical ideas.
CONTENTS
1. MATHEMATICAL MODELING, FUNCTIONS, AND
CHANGE. Mathematical Modeling. Functions and
Function Notation. Functions Represented by Tables and
Formulas. Functions Represented by Graphs. Functions
Represented by Words. Preview to Inverse Functions.
Chapter 1 Review. 2. LINEAR FUNCTIONS. Functions
with Constant Rates of Change. Modeling with Linear
Functions. Linear Regression. Systems of Linear
Equations. Systems of Linear Inequalities. Chapter 2
Review. 3. TRANSFORMATIONS AND FUNCTIONS.
Horizontal and Vertical Shifts. Horizontal and Vertical
Reflections. Vertical Stretches and Reflections.
Horizontal Stretches and Compressions. Chapter 3
Review. 4. QUADRATIC FUNCTIONS. Variable Rates of
Change. Modeling with Quadratic Functions. Quadratic
Functions, Graphs, and Forms. Chapter 4 Review. 5.
POLYNOMIAL, POWER, AND RATIONAL FUNCTIONS.
Higher-Order Polynomial Function Modeling. Power
Functions. Rational Functions. Chapter 5 Review. 6.
Percentage Change. Exponential Function Modeling
and Graphs. Compound Interest and Continuous
Growth. Solving Logarithmic and Exponential Equations.
Logarithmic Function Modeling. Chapter 6 Review. 7.
MODELING WITH OTHER TYPES OF FUNCTIONS.
Combinations of Functions. Piecewise Functions.
Composition of Functions. Logistic Functions.
Choosing a Mathematical Model. Chapter 7 Review. 8.
TRIGONOMETRIC FUNCTIONS. Periodic Functions.
Angle Measure (Degrees and Radians). The Unit
Circle and Trigonometric Functions. Graphing Sine
and Cosine Functions. Modeling with Trigonometric
Functions. Other Trigonometric Functions. Inverse
Trigonometric Functions. Chapter 8 Review. 9.
TRIANGLE TRIGONOMETRY AND APPLICATIONS.
Right Triangle Trigonometry. Law of Cosines. Law of
Sines. Polar Coordinates. Vectors. Chapter 9 Review.
10. TRIGONOMETRIC IDENTITIES. Right Triangle
Trigonometry. Law of Cosines. Law of Sines. Chapter 10
Review. 11. CONIC SECTIONS. Slices of a Cone. Ellipses
and Circles. Parabolas. Hyperbolas. Chapter 11 Review.
12. SEQUENCES AND SERIES. Sequences. Arithmetic
and Geometric Sequences. Series. Chapter 12 Review.
© 2013, 944pp, Paperback, 9781111988289
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219
PRECALCULUS, 12E
Functions and Graphs, International Edition
Earl Swokowski, late of Marquette University; Jeffery Cole, AnokaRamsey Community College
The latest edition of Swokowski and Cole’s
PRECALCULUS: FUNCTIONS AND GRAPHS, 12e,
International Edition retains the elements that have
made it so popular with instructors and students alike:
clear exposition, an appealing and uncluttered layout,
and applications-rich exercise sets. The excellent, timetested problems have been widely praised for their
consistency and their appropriate level of difficulty
for precalculus students. The book also provides
calculator examples, including specific keystrokes that
show students how to use various graphing calculators
to solve problems more quickly. The Twelfth Edition
features updated topical references and data, and
continues to be supported by outstanding technology
resources. Mathematically sound, this book effectively
prepares students for further courses in mathematics.
NEW TO THIS EDITION
• New Chapter Tests at the end of each chapter
provide an additional source of exam questions and
great practice for students. The new items include
straightforward questions based on exercises in the
sections as well as questions that require students
to stretch their thinking a bit and expand their use of
the basic concepts.
• Arrow notation is introduced earlier (Section 2.2)
and revisited more often in this edition, bolstering
precalculus content to more effectively prepare
students for calculus topics.
• Approximately 20% of the exercises are new or
revised, including many featuring updated real data
and new applications.
• New Examples illustrate numerous topics: find
the inverse of a rational function (Section 4.1, with
the method for checking presented in a marginal
note); predict a quantity using the decay formula
(Section 4.3); how to show that an equation is not
an identity (Section 6.1); use the subtraction formula
for the cosine to find an exact value when given an
exact trigonometric value and the sign of another
trigonometric function (Section 6.3); and how to find
double angle values of other trigonometric functions
given that the tangent of an angle is a constant
(Section 6.4).
• Other new examples: solve a polynomial equation by
using the theorem on nth roots (Section 7.6); substitute
to aid in solving a system of equations (Section 8.2);
find terms of a sequence that is recursively defined in
terms of two preceding terms (Section 9.1); given two
terms of an arithmetic sequence, find another term
using a new formula (Section 9.2); given two terms
of a geometric sequence, find another term using
a new formula (Section 9.3); and graph a system of
inequalities using parametric equations (Section 10.4).
FEATURES
this text to encourage the practice that’s critical for
concept mastery.
• Many exercises have online tutorials associated with
them. These exercises are easily identified in the text
with icons, making it simple for students to get extra
practice as needed. The exercises are also assignable
through Enhanced WebAssign®.
• Each concept is explained with great care, including
step-by-step comments in the solutions of the
examples. Graphs, figures, charts, and tables help
students interpret graphical data, and accompany
many examples.
• The text provides many topical examples showing how
mathematical concepts have real-life applications.
• Each exercise set begins with drill problems and then
progresses to more challenging problems. Some
exercises ask students to produce and examine a
table of values as an aid to solve a problem. Others
ask students to interpret some aspect of a given table
of values. Many involve graphical solutions.
CONTENTS
Each chapter ends with Review Exercises, Discussion
Exercises, and a Chapter Test. 1. TOPICS FROM
ALGEBRA. Real Numbers. Exponents and Radicals.
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220
Algebraic Expressions. Equations. Complex Numbers.
Inequalities. 2. FUNCTIONS AND GRAPHS. Rectangular
Coordinate Systems. Graphs of Equations. Lines.
Definition of Function. Graphs of Functions. Quadratic
Functions. Operations on Functions. 3. POLYNOMIAL
AND RATIONAL FUNCTIONS. Polynomial Functions
of Degree Greater Than 2. Properties of Division.
Zeros of Polynomials. Complex and Rational Zeros of
Polynomials. Rational Functions. Variation. 4. INVERSE,
EXPONENTIAL, AND LOGARITHMIC FUNCTIONS.
Inverse Functions. Exponential Functions. The Natural
Exponential Function. Logarithmic Functions. Properties
of Logarithms. Exponential and Logarithmic Equations. 5.
TRIGONOMETRIC FUNCTIONS. Angles. Trigonometric
Functions of Angles. Trigonometric Functions of Real
Numbers. Values of the Trigonometric Functions.
Trigonometric Graphs. Additional Trigonometric Graphs.
Applied Problems. 6. ANALYTIC TRIGONOMETRY.
Verifying Trigonometric Identities. Trigonometric
Equations. The Additions and Subtraction of Formulas.
Multiple-Angle Formulas. Product-To-Sum and SumTo-Product Formulas. The Inverse Trigonometric
Functions. 7. APPLICATIONS OF TRIGONOMETRY.
The Law of Sines. The Law of Cosines. Vectors.
The Dot Product. Trigonometric Form for Complex
Numbers. De Moivre’s Theorem and nth Roots of
Complex Numbers. 8. SYSTEMS OF EQUATIONS AND
INEQUALITIES. Systems of Equations. Systems of Linear
Equations in Two Variables. Systems of Inequalities.
Linear Programming. Systems of Linear Equations in
More Than Two Variables. The Algebra of Matrices.
The Inverse of a Matrix. Determinants. Properties
of Determinants. Partial Fractions. 9. SEQUENCES,
SERIES, AND PROBABILITY. Infinite Sequences
and Summation Notation. Arithmetic Sequences.
Geometric Sequences. Mathematical Induction. The
Binomial Theorem. Permutations. Distinguishable
Permutations and Combinations. Probability. 10.
TOPICS FROM ANALYTICAL GEOMETRY. Parabolas.
Ellipses. Hyperbolas. Plane Curves and Parametric
Equations. Polar Coordinates. Polar Equations of Conics.
Appendix I: Common Graphs and Their Equations.
Appendix II: A Summary of Graph Transformations.
Appendix III: Graphs of the Trigonometric Functions and
Their Inverses. Appendix IV: Values of the Trigonometric
Functions of Special Angles on a Unit Circle.
© 2012, 912pp, Paperback, 9780840068903
PRECALCULUS, 6E
Real Mathematics, Real People, International Edition
PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE,
6e, International Edition is an ideal student and
through careful writing and design—including examples
NEW TO THIS EDITION
• With the extensive revision to create the Sixth Edition,
this book’s original subtitle, “A Graphing Approach,”
no longer represents the text’s essence (although
the graphing calculator is still required). The author’s
changes and the new title, “PRECALCULUS: REAL
MATHEMATICS, REAL PEOPLE, International Edition
,” address a primary need in education today—
relevance. The mathematics in this text is both real
and relevant, and the people introduced are either
already in or preparing for careers in which they will
use mathematics.
www.cengageasia.com
221
intuition.
can be solved in more than one way—and that
different methods yield the same result.
CONTENTS
Each chapter concludes with a summary, review
exercises, a chapter test, and proofs in mathematics.
1. FUNCTIONS AND THEIR GRAPHS. Introduction to
Library of Functions. Lines in the Plane. Functions.
Graphs of Functions. Shifting, Reflecting, and
Stretching Graphs. Combinations of Functions.
Inverse Functions. Linear Models and Scatter Plots.
Quadratic Functions. Polynomial Functions of Higher
Degree. Real Zeros of Polynomial Functions. Complex
Numbers. The Fundamental Theorem of Algebra.
Rational Functions. Quadratic Models. Progressive
Summary (Chapters 1 and 2). 3. EXPONENTIAL
Test: Chapters 1–3. Progressive Summary (Chapters
1–3). 4. TRIGONOMETRIC FUNCTIONS. Radian and
Summary (Chapters 1–6). 7. LINEAR SYSTEMS AND
Probability. 9. TOPICS IN ANALYTIC GEOMETRY. Circles
and Parabolas. Ellipses. Hyperbolas and Rotation of
Conics. Parametric Equations. Polar Coordinates.
Graphs of Polar Equations. Polar Equations of Conics.
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222
Cumulative Test: Chapters 7–9. Progressive Summary
(Chapters 3–9). 10. ANALYTIC GEOMETRY IN THREE
DIMENSIONS. The Three-Dimensional Coordinate
System. Vectors in Space. The Cross Product of Two
Vectors. Lines and Planes in Space. APPENDIX A:
TECHNOLOGY SUPPORT GUIDE. APPENDIX B: REVIEW
OF GRAPHS, EQUATIONS, AND INEQUALITIES (WEB
ONLY). The Cartesian Plane. Graphs of Equations.
Solving Equations Algebraically and Graphically. Solving
Inequalities Algebraically and Graphically. Representing
Data Graphically. APPENDIX C: CONCEPTS IN
STATISTICS (WEB ONLY). Measures of Central Tendency
and Dispersion. Least Squares Regression. APPENDIX
D: VARIATION (WEB ONLY). APPENDIX E: SOLVING
LINEAR EQUATIONS AND INEQUALITIES (WEB ONLY).
APPENDIX F: SYSTEMS OF INEQUALITIES (WEB ONLY).
Solving Systems of Inequalities. Linear Programming.
APPENDIX G: MATHEMATICAL INDUCTION (WEB
ONLY).
© 2012, 896pp, Paperback, 9781111572419
PRECALCULUS, 3E
A Concise Course, International Edition
Larson’s PRECALCULUS: A CONCISE COURSE, 3E,
International Edition is known for delivering the
same sound, consistently structured explanations and
exercises of mathematical concepts as his marketleading PRECALCULUS, 9E, International Edition. In
PRECALCULUS: A CONCISE COURSE, 3E, International
Edition, the author offers instructors a streamlined
presentation to precalculus that is a perfect onesemester alternative to traditional textbooks. With
the third edition, Larson continues to revolutionize
the way students learn material by incorporating
innovative technology. How Do You See It? exercises
give students practice applying the concepts, and
new summarize features, checkpoint problems, and a
companion website reinforce understanding of the skill
the text, with the addition of end-of-section problems
NEW TO THIS EDITION
of each section.
text.
• Enhanced Exercise Sets deliver more rigor, relevancy,
upcoming section.
• Enriched Remarks reinforce or expand on concepts
example.
FEATURES
• Side-By-Side Examples help students see not only that
a problem can be solved in more than one way but also
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223
CONTENTS
1. FUNCTIONS AND THEIR GRAPHS. Rectangular
Coordinates. Graphs of Equations. Linear Equations in
Two Variables. Functions. Analyzing Graphs of Functions.
A Library of Parent Functions. Transformations of
Solving. 2. POLYNOMIAL AND RATIONAL FUNCTIONS.
Functions of Higher Degree. Polynomial and Synthetic
Division. Complex Numbers. Zeros of Polynomial
Functions. Rational Functions. Nonlinear Inequalities.
4. TRIGONOMETRY. Radian and Degree Measure.
Trigonometric Functions: The Unit Circle. Right Triangle
Trigonometry. Trigonometric Functions of Any Angle.
Graphs of Sine and Cosine Functions. Graphs of
Other Trigonometric Functions. Inverse Trigonometric
Difference Formulas. Multiple-Angle and Product-toSum Formulas. Law of Sines. Law of Cosines. Chapter
Summary. Review Exercises. Chapter Test. Proofs
in Mathematics. P.S. Problem Solving. 6. TOPICS IN
ANALYTIC GEOMETRY. Lines. Introduction to Conics:
Parabolas. Ellipses. Hyperbolas. Parametric Equations.
Polar Coordinates. Graphs of Polar Equations. Polar
Equations of Conics. Chapter Summary. Review Exercises.
in Mathematics. P.S. Problem Solving. APPENDIX A: A
REVIEW OF FUNDAMENTAL CONCEPTS OF ALGEBRA
(WEB). Real Numbers and Their Properties. Exponents
and Radicals. Polynomials and Factoring. Rational
Expressions. Solving Equations. Linear Inequalities
in One Variable. Errors and the Algebra of Calculus.
APPENDIX B: CONCEPTS IN STATISTICS (WEB).
© 2014, 592pp, Paperback, 9781285051314
PRECALCULUS, 6E
Mathematics for Calculus, International Edition
This best selling author team explains concepts simply
and clearly, without glossing over difficult points.
Problem solving and mathematical modeling are
introduced early and reinforced throughout, providing
mathematical thinking. Comprehensive and evenly
paced, the book provides complete coverage of the
function concept, and integrates a significant amount
of graphing calculator material to help students
develop insight into mathematical ideas. The authors’
attention to detail and clarity, the same as found in
James Stewart’s market-leading Calculus text, is what
makes this text the market leader.
NEW TO THIS EDITION
• More than 20% of the exercises in the text are new. In
addition, each exercise set has been restructured to
begin with new Concept exercises, and reorganized
to more closely follow the exposition in the
corresponding section. Cummulative Review Tests,
which follow chapters 4, 7, 9, 11, and 13, are new to
this edition as well.
www.cengageasia.com
224
• The section entitled “Principles of Problem Solving” is
now a Prologue to the book. Problem Solving sections,
each highlighting a particular problem solving
principle, are now posted on the Book Companion
Website.
• Discovery Projects, which encourage and motivate
students to further explore chapter topics, are now
Now Try Exercise, allowing students to reinforce
just memorize.
functions.
trigonometric functions and their graphs (Section
5.5) to better segue into the section that follows (on
harmonic motion).
trigonometric functions and right triangles (Section
6.4), which is needed in applying the Laws of Sines and
Cosines in the following section, as well as for solving
trigonometric equations in Chapter 7.
• Chapter 7 has been completely revised, including two
new sections on trigonometric equations (Sections 7.4
and 7.5) that expand coverage of this topic.
• Chapter 8 is completely revised, and now features a
sharper focus on the concept of coordinate systems
and a new section on parametric equations.
CONTENTS
Prologue: Principles of Problem Solving. 1.
FUNDAMENTALS. Chapter Overview. Real Numbers.
Exponents and Radicals. Algebraic Expressions.
Fractional Expressions. Equations. Modeling with
Equations. Inequalities. Coordinate Geometry. Solving
Equations and Inequalities Graphically. Lines. Modeling
Variation. 2. FUNCTIONS. Chapter Overview. What Is
a Function?. Graphs of Functions. Getting Information
from the Graph of a Function. Average Rate of Change
of a Function. Transformations of Functions. Combining
Functions. One-to-One Functions and Their Inverses.
Functions as Models. 3. POLYNOMIAL AND RATIONAL
FUNCTIONS. Chapter Overview. Quadratic Functions
Theorem of Algebra. Rational Functions. Chapter 3
Review. Chapter 3 Test. Focus on Modeling: Fitting
Polynomial Curves to Data. 4. EXPONENTIAL AND
LOGARITHMIC FUNCTIONS. Chapter Overview.
4 Review. Chapter 4 Test. Focus on Modeling: Fitting
Exponential and Power Curves to Data. Cumulative
Review Test: Chapters 2, 3, and 4. 5. TRIGONOMETRIC
FUNCTIONS: UNIT CIRCLE APPROACH. Chapter
Overview. The Unit Circle. Trigonometric Functions
of Real Numbers. Trigonometric Graphs. More
Trigonometric Graphs. Inverse Trigonometric Functions
and Their Graphs. Modeling Harmonic Motion. Chapter
Sinusoidal Curves to Data. 6. TRIGONOMETRIC
FUNCTIONS: RIGHT TRIANGLE APPROACH. Chapter
Overview. Angle Measure. Trigonometry of Right
Triangles. Trigonometric Functions of Angles. Inverse
Trigonometric Functions and Triangles. The Law of
Sines. The Law of Cosines. Chapter 6 Review. Chapter
6 Test. Focus on Modeling: Surveying. 7. ANALYTIC
TRIGONOMETRY. Chapter Overview. Trigonometric
Identities. Addition and Subtraction Formulas. DoubleAngle, Half-Angle, and Sum-Product Identities. Basic
Trigonometric Equations. More Trigonometric Equations.
Traveling and Standing Waves. Cumulative Review Test:
Chapters 5, 6, and 7. 8. POLAR COORDINATES AND
PARAMETRIC EQUATIONS. Chapter Overview. Polar
Coordinates. Graphs of Polar Equations. Polar Form of
Complex Numbers; DeMoivre’s Theorem. Plane Curves
and Parametric Equations. Chapter 8 Review. Chapter
8 Test. Focus on Modeling: The Path of a Projectile. 9.
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225
Three Dimensions. The Cross Product. Equations of Lines
and Planes. Chapter 9 Review. Chapter 9 Test. Focus
on Modeling: Vector Fields. Cumulative Review Test:
Chapters 8 and 9. 10. SYSTEMS OF EQUATIONS AND
INEQUALITIES. Chapter Overview. Systems of Linear
in Several Variables. Systems of Linear Equations:
Matrices. The Algebra of Matrices. Inverses of Matrices
and Matrix Equations. Determinants and Cramer’s Rule.
Partial Fractions. Systems of Non-Linear Equations.
Systems of Inequalities. Chapter 10 Review. Chapter
10 Test. Focus on Modeling: Linear Programming. 11.
CONIC SECTIONS. Overview. Parabolas. Ellipses.
Hyperbolas. Shifted Conics. Rotation of Axes. Polar
Equations of Conics. Chapter 11 Review. Chapter 11 Test.
Focus on Modeling: Conics in Architecture. Cumulative
Review Test: Chapters 10 and 11. 12. SEQUENCES AND
SERIES. Chapter Overview. Sequences and Summation
Focus on Modeling: Difference Equations. 13. LIMITS: A
PREVIEW OF CALCULUS. Chapter Overview. Finding
Limits Numerically and Graphically. Finding Limits
Algebraically. Tangent Lines and Derivatives. Limits
at Infinity: Limits of Sequences. Areas. Chapter 13
Review. Chapter 13 Test. APPENDIX: Calculators and
Calculations.
© 2012, 1008pp, Paperback, 9780840068866
PRECALCULUS, 6E
Real Mathematics, Real People, Alternate International
Edition
PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE,
6e, International Edition is an ideal student and
through careful writing and design--including examples
NEW TO THIS EDITION
• With the extensive revision to create the Sixth
Edition, this book’s original subtitle, “A Graphing
Approach,” no longer represents the text’s essence
(although the graphing calculator is still required).
The author’s changes and the new title, “ ALGEBRA
AND TRIGONOMETRY: REAL MATHEMATICS, REAL
PEOPLE, 6e, International Edition,” address a primary
need in education today--relevance. The mathematics
in this text is both real and relevant, and the people
introduced are either already in or preparing for
careers in which they will use mathematics.
intuition.
www.cengageasia.com
226
can be solved in more than one way--and that different
methods yield the same result.
CONTENTS
Graphs of Rational Functions. Quadratic Models.
Cumulative Test: Chapters 1-3. 4. EXPONENTIAL
Test: Chapters 3–4. Progressive Summary: Chapters P–4.
5. TRIGONOMETRIC FUNCTIONS. Angles and Their
Measure. Right Triangle Trigonometry. Trigonometric
Summary: Chapters P–7. 8. LINEAR SYSTEMS AND
Probability. 10. TOPICS IN ANALYTIC GEOMETRY.
Polar Equations of Conics. Cumulative Test: Chapters
8–10. Progressive Summary: Ch P–10. APPENDIX
A: TECHNOLOGY SUPPORT GUIDE. APPENDIX B:
CONCEPTS IN STATISTICS (Web only). Measures
of Central Tendency and Dispersion. Least Squares
Regression. APPENDIX C: VARIATION (Web only)
APPENDIX D: SOLVING LINEAR EQUATIONS AND
INEQUALITIES (Web only). APPENDIX E: SYSTEMS
OF INEQUALITIES (Web only). Solving Systems of
Inequalities. Linear Programming. APPENDIX F:
MATHEMATICAL INDUCTION (Web only).
© 2012, 1008pp, Paperback, 9781111430269
www.cengageasia.com
227
PRECALCULUS WITH LIMITS,
Larson’s PRECALCULUS WITH LIMITS, 3E, International
Edition is known for delivering the same sound,
consistently structured explanations and exercises
of mathematical concepts as the market-leading
PRECALCULUS, 9E, International Edition with a
laser focus on preparing students for calculus. In
PRECALCULUS WITH LIMITS, 3E, International Edition,
the author includes a brief algebra review to the core
precalculus topics along with coverage of analytic
geometry in three dimensions and an introduction
to concepts covered in calculus. With the third
edition, Larson continues to revolutionize the way
students learn material by incorporating more realworld applications, ongoing review, and innovative
technology. How Do You See It? exercises give students
practice applying the concepts, and new Summarize
features, Checkpoint problems, and a Companion
Website reinforce understanding of the skill sets
the text, with the addition of End-of-Section problems
and Chapter Tests, as well as problem-specific videos,
NEW TO THIS EDITION
of each section.
text.
upcoming section.
example.
FEATURES
CONTENTS
www.cengageasia.com
228
in Mathematics. P.S. Problem Solving. 8. MATRICES
AND DETERMINANTS. Matrices and Systems of
Equations. Operations with Matrices. The Inverse
of a Square Matrix. The Determinant of a Square
Matrix. Applications of Matrices and Determinants.
SEQUENCES, SERIES, AND PROBABILITY. Sequences
and Series. Arithmetic Sequences and Partial Sums.
Geometric Sequences and Series. Mathematical
in Mathematics. P.S. Problem Solving. 10. TOPICS IN
ANALYTIC GEOMETRY. Lines. Introduction to Conics:
Parabolas. Ellipses. Hyperbolas. Rotation of Conics.
Parametric Equations. Polar Coordinates. Graphs of
Polar Equations. Polar Equations of Conics. Chapter
in Mathematics. P.S. Problem Solving. 11. ANALYTIC
GEOMETRY IN THREE DIMENSIONS. The ThreeDimensional Coordinate System. Vectors in Space.
The Cross Product of Two Vectors. Lines and Planes in
Space. Chapter Summary. Review Exercises. Chapter
LIMITS AND AN INTRODUCTION TO CALCULUS.
Introduction to Limits. Techniques for Evaluating Limits.
The Tangent Line Problem. Limits at Infinity and Limits
of Sequences. The Area Problem. Chapter Summary.
Chapters. Proofs in Mathematics. P.S. Problem Solving.
APPENDIX A. Review of Fundamental Concepts of
Algebra. A.1 Real Numbers and Their Properties. A.2
Exponents and Radicals. A.3 Polynomials and Factoring.
A.4 Rational Expressions. A.5 Solving Equations. A.6
Linear Inequalities in One Variable. A.7 Errors and the
Algebra of Calculus. APPENDIX B. Concepts in Statistics
(web). B.1 Representing Data. B.2 Measures of Central
Tendency and Dispersion. B.3 Least Squares Regression.
© 2014, 1088pp, Paperback, 9781133954606
PRECALCULUS WITH LIMITS,
With the same design and feature sets as the
market leading Precalculus, 8/e, this addition to the
Larson Precalculus series provides both students
and instructors with sound, consistently structured
explanations of the mathematical concepts. Designed
for a two-term course, this text contains the features
that have made Precalculus a complete solution for
www.cengageasia.com
229
both students and instructors: interesting applications,
cutting-edge design, and innovative technology
combined with an abundance of carefully written
exercises. In addition to a brief algebra review and the
core precalculus topics, PRECALCULUS WITH LIMITS,
International Edition, covers analytic geometry in
three dimensions and introduces concepts covered in
calculus.
NEW TO THIS EDITION
• NEW Cap Stone Exercises – the Cap Stone exercises
assesses students understanding of all concepts
covered in the section’s material.
• NEW detailed Chapter Review – The new edition now
includes explanations and/or examples for all learning
objectives. This will further promote students’
understanding of the material.
• NEW Caution/Warning boxes – The warnings cautions
students away from common errors and pitfalls.
• NEW Algebra Helps – the author provides appropriate
caution boxes, study tips and algebra helps to guide
the student through difficult concepts.
• Improved Examples (graphical solution side by side
with algebraic solution). This is intended to improve
the students graphical understanding of algebra.
• New/Revised End of section exercises.
• Enhanced WebAssign.
FEATURES
• Side-by-side Example Solutions for select examples
include multiple problem solving approaches—such
as algebraic, graphical, and numerical—to appeal to
a variety of teaching and learning styles.
• Checkpoints after each Example/Solution refer
students to similar drills in the Section Exercises,
allowing students to practice and reinforce the
concepts they just learned. Answers to Checkpoints
are included at the back of the book.
• Vocabulary Checks open every set of Section
Exercises. This review of mathematical terms,
formulas, and theorems provides regular assessment
and reinforcement of students’ understanding of
algebraic language and concepts.
CONTENTS
Coordinates. Graphs of Equations. Linear Equations
in Two Variables. Functions. Analyzing Graphs of
Functions. A Library of Functions. Transformations
of Functions. Combinations of Functions: Composite
Exercises. Chapter Test. Cumulative Test: Chapters
1-3. Proofs in Mathematics. P.S. Problem Solving. 4.
TRIGONOMETRY. Radian and Degree Measure.
Chapter Test. Cumulative Test: Chapters 4-6. Proofs
Mathematics. P.S. Problem Solving. 8. MATRICES
AND DETERMINANTS. Matrices and Systems of
Equations. Operations with Matrices. The Inverse of
a Square Matrix. The Determinant of a Square Matrix.
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230
Applications of Matrices and Determinants. Chapter
Mathematics. P.S. Problem Solving. 9. SEQUENCES,
SERIES, AND PROBABILITY. Sequences and Series.
Sequences and Series. Mathematical Induction. The
Binomial Theorem. Counting Principles. Probability.
Cumulative Test: Chapters 7-9. Proofs in Mathematics.
P.S. Problem Solving. 10. TOPICS IN ANALYTIC
GEOMETRY. Lines. Introduction to Conics: Parabolas.
Ellipses. Hyperbolas. Rotation of Conics. Parametric
Polar Equations of Conics. Chapter Summary. Review
Problem Solving. 11. ANALYTIC GEOMETRY IN THREE
DIMENSIONS. The Three-Dimensional Coordinate
System. Vectors in Space. The Cross Product of
Two Vectors. Lines and Planes in Space. Chapter
Mathematics. P.S. Problem Solving. 12. LIMITS AND
AN INTRODUCTION TO CALCULUS. Introduction to
Limits. Techniques for Evaluating Limits. The Tangent
Line Problem. Limits at Infinity and Limits of Sequences.
The Area Problem. Chapter Summary. Review Exercises.
Chapter Test. Cumulative Test: Chapters 10-12. Proofs
REVIEW OF FUNDAMENTAL CONCEPTS OF ALGEBRA.
Real Numbers and Their Properties. Exponents
and Radicals. Polynomials and Factoring. Rational
Expressions. Solving Equations. Linear Inequalities
in One Variable. Errors and the Algebra of Calculus.
APPENDIX B: CONCEPTS IN STATISTICS (WEB).
© 2011, 1152pp, Paperback, 9780538735483
PRECALCULUS WITH LIMITS, LEVEL 4, 3E
© 2014, 1120pp, Hardback, 9781133962885
PRECALCULUS, ENHANCED WEBASSIGN
EDITION (WITH ENHANCED WEBASSIGN
WITH EBOOK PRINTED ACCESS CARD
FOR MATH AND SCIENCE, 1-TERM), 6E
The market leading textbook in precalculus is
now available in a cost-saving paperback format.
PRECALCULUS, ENHANCED WEBASSIGN EDITION
contains the same sound mathematics found in the
authors’ original text, PRECALCULUS: MATHEMATICS
FOR CALCULUS, Sixth Edition plus full support
of Cengage Learning’s powerful online homework
program, Enhanced WebAssign. Each new Enhanced
WebAssign Edition features the Start Smart Guide for
Students, a simple step-by-step how-to booklet for
getting started with online homework. The result is a
customized resource that will better prepare students
for future courses in mathematics and sciences. In
PRECALCULUS: MATHEMATICS FOR CALCULUS,
www.cengageasia.com
231
Sixth Edition best-selling authors, James Stewart,
Lothar Redlin and Saleem Watson refine their focus on
problem solving and mathematical modeling to provide
mathematical thinking. The author team explains
critical concepts simply and clearly, without glossing
over difficult points to provide complete coverage
of the function concept, and integrates a significant
amount of graphing calculator material to help students
develop insight into mathematical ideas.
NEW TO THIS EDITION
• New paperback format gives your students a costsaving choice without sacrificing any of the highquality content you expect from this marketingleading text.
• Enhanced WebAssign, used by over one million
students at more than 1,100 institutions, allows
you to assign, collect, grade, and record homework
assignments via the web. This proven and
reliable homework system includes thousands of
algorithmically generated homework problems,
links to relevant textbook sections, lecture videos,
problem-specific tutorials, and more.
• The Enhanced WebAssign Start Smart Guide for
Students_ gets your students up and running quickly
with Enhanced WebAssign so they can study smarter
and improve their performance in class.
• New and updated exercises. More than 20% of
the exercises in the text are new. In addition, each
exercise set has been restructured to begin with new
“Concept” exercises, and reorganized to more closely
follow the exposition in the corresponding section.
“Cumulative Review Tests” , which follow chapters 4,
7, 9, 11, and 13, are new to this edition as well.
• New “Principles of Problem Solving” Prolugue ties
to the Problem Solving sections, each highlighting a
particular problem solving principle which are now
avaialble Book Companion Website.
• Discovery Projects encourage and motivate students
to further explore chapter topics, and are now
Now Try Exercise XX, allowing students to reinforce
just memorize.
functions.
trigonometric functions and their graphs (Section
5.5) to better segue into the section that follows (on
harmonic motion).
CONTENTS
Prologue: Principles of Problem Solving. 1.
FUNDAMENTALS. Chapter Overview. Real Numbers.
Exponents and Radicals. Algebraic Expressions.
Fractional Expressions. Equations. Modeling with
Equations. Inequalities. Coordinate Geometry. Solving
Equations and Inequalities Graphically. Lines. Modeling
Variation. 2. FUNCTIONS. Chapter Overview. What Is
a Function?. Graphs of Functions. Getting Information
from the Graph of a Function. Average Rate of Change
of a Function. Transformations of Functions. Combining
Functions. One-to-One Functions and Their Inverses.
Functions as Models. 3. POLYNOMIAL AND RATIONAL
FUNCTIONS. Chapter Overview. Quadratic Functions
Theorem of Algebra. Rational Functions. Chapter 3
Review. Chapter 3 Test. Focus on Modeling: Fitting
Polynomial Curves to Data. 4. EXPONENTIAL AND
LOGARITHMIC FUNCTIONS. Chapter Overview.
Exponential and Power Curves to Data. Cumulative
Review Test: Chapters 2, 3, and 4. 5. TRIGONOMETRIC
FUNCTIONS: UNIT CIRCLE APPROACH. Chapter
Overview. The Unit Circle. Trigonometric Functions
of Real Numbers. Trigonometric Graphs. More
Trigonometric Graphs. Inverse Trigonometric Functions
and Their Graphs. Modeling Harmonic Motion. Chapter
www.cengageasia.com
232
Sinusoidal Curves to Data. 6. TRIGONOMETRIC
FUNCTIONS: RIGHT TRIANGLE APPROACH. Chapter
Overview. Angle Measure. Trigonometry of Right
Triangles. Trigonometric Functions of Angles. Inverse
Trigonometric Functions and Triangles. The Law of
Sines. The Law of Cosines. Chapter 6 Review. Chapter
6 Test. Focus on Modeling: Surveying. 7. ANALYTIC
TRIGONOMETRY. Chapter Overview. Trigonometric
Identities. Addition and Subtraction Formulas. DoubleAngle, Half-Angle, and Sum-Product Identities. Basic
Trigonometric Equations. More Trigonometric Equations.
Traveling and Standing Waves. Cumulative Review Test:
Chapters 5, 6, and 7. 8. POLAR COORDINATES AND
PARAMETRIC EQUATIONS. Chapter Overview. Polar
Coordinates. Graphs of Polar Equations. Polar Form of
Complex Numbers; DeMoivre’s Theorem. Plane Curves
and Parametric Equations. Chapter 8 Review. Chapter
8 Test. Focus on Modeling: The Path of a Projectile. 9.
Three Dimensions. The Cross Product. Equations of Lines
and Planes. Chapter 9 Review. Chapter 9 Test. Focus
on Modeling: Vector Fields. Cumulative Review Test:
Chapters 8 and 9. 10. SYSTEMS OF EQUATIONS AND
INEQUALITIES. Chapter Overview. Systems of Linear
in Several Variables. Systems of Linear Equations:
Matrices. The Algebra of Matrices. Inverses of Matrices
and Matrix Equations. Determinants and Cramer’s Rule.
Partial Fractions. Systems of Non-Linear Equations.
Systems of Inequalities. Chapter 10 Review. Chapter
10 Test. Focus on Modeling: Linear Programming. 11.
ANALYTIC GEOMETRY. Overview. Parabolas. Ellipses.
Hyperbolas. Shifted Conics. Rotation of Axes. Polar
Equations of Conics. Chapter 11 Review. Chapter 11 Test.
Focus on Modeling: Conics in Architecture. Cumulative
Review Test: Chapters 10 and 11. 12. SEQUENCES AND
SERIES. Chapter Overview. Sequences and Summation
Focus on Modeling: Difference Equations. 13. LIMITS: A
PREVIEW OF CALCULUS. Chapter Overview. Finding
Limits Numerically and Graphically. Finding Limits
Algebraically. Tangent Lines and Derivatives. Limits at
Infinity: Limits of Sequences. Areas. Chapter 13 Review.
Chapter 13 Test.
© 2014, 1040pp, Paperback, 9781133594765,
PRECALCULUS, HYBRID EDITION (WITH
PRINTED ACCESS CARD AND START
SMART GUIDE FOR STUDENTS), 9E
Larson’s PRECALCULUS HYBRID, Ninth Edition,
delivers the same sound, consistently structured
explanations and exercises of mathematical concepts
as his market-leading hardcover text, PRECALCULUS,
Ninth Edition, combined with a briefer paperback
format that engages students online with Enhanced
WebAssign®. The HYBRID demonstrates Larson’s
commitment to revolutionizing the way instructors
teach and students learn material by moving all the
end-of-section exercises from the text online as
well as incorporating more real-world applications,
ongoing review, and innovative technology. Each new
Larson HYBRID includes immediate student access
to Enhanced WebAssign®. The ninth edition features
“How Do You See It?” exercises that give students
practice applying the concepts, and new “Summarize”
features, “Checkpoint” problems, and a Companion
Website reinforce understanding of the skill sets
WebAssign® offers fully integrated content from the
text, with the addition of end-of-section problems
NEW TO THIS EDITION
• State-of-the-art package provides a cost-effective,
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233
only and each new HYBRID includes immediate access
to Enhanced WebAssign® and the Cengage YouBook.
• Enhanced WebAssign® features fully integrated
content from the text, including all end-of-section
problems and chapter tests, as well as problemspecific videos, animations, and lecture videos. The
robust online homework solution allows instructors
to assign, collect, grade, and record homework
assignments online, minimizing workload and
streamlining the grading process. It also gives students
the ability to stay organized with assignments and
have up-to-date grade information.
of each section.
lesson.
text.
upcoming section.
example.
CONTENTS
1. FUNCTIONS AND THEIR GRAHS. Rectangular
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Sequences and Partial Sums. Geometric Sequences and
Series. Mathematical Induction. The Binomial Theorem.
Counting Principles. Probability. Chapter Summary.
Solving. 10. TOPICS IN ANALYTIC GEOMETRY. Lines.
Introduction to Conics: Parabolas. Ellipses. Hyperbolas.
Rotation of Conics. Parametric Equations. Polar
Coordinates. Graphs of Polar Equations. Polar Equations
of Conics. Chapter Summary. Review Exercises. Chapter
Test. Proofs in Mathematics. P.S. Problem Solving.
© 2014, 688pp, Hardback, 9781133950547
Coming Soon!
PRECALCULUS, INTERNATIONAL
EDITION, 9E
Larson’s PRECALCULUS, 9E, International Edition is
known for delivering sound, consistently structured
explanations and exercises of mathematical concepts to
expertly prepare students for the study of calculus. With
the ninth edition, the author continues to revolutionize
the way students learn the material by incorporating
innovative technology. How Do You See It? exercises
give students practice applying the concepts, and
new Summarize features, Checkpoint problems, and a
Companion Website reinforce understanding of the skill
the text, with the addition of End-of-Section problems
and Chapter Tests, as well as problem-specific videos,
NEW TO THIS EDITION
of each section.
text.
upcoming section.
example.
FEATURES
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235
CONTENTS
1. FUNCTIONS AND THEIR GRAHS. Rectangular
Sequences and Partial Sums. Geometric Sequences and
Series. Mathematical Induction. The Binomial Theorem.
Counting Principles. Probability. Chapter Summary.
Solving. 10. TOPICS IN ANALYTIC GEOMETRY. Lines.
Introduction to Conics: Parabolas. Ellipses. Hyperbolas.
Rotation of Conics. Parametric Equations. Polar
Coordinates. Graphs of Polar Equations. Polar Equations
of Conics. Chapter Summary. Review Exercises. Chapter
Test. Proofs in Mathematics. P.S. Problem Solving.
© 2014, 976pp, Paperback, 9781133954576
EDITION
Karla Neal, Louisiana State University; R. David Gustafson, Rock
Valley College (Emeritus); Jeff Hughes, Hinds Community College
PRECALCULUS, International Edition prepares students
for calculus and the rigors of that course, having been
written by teachers who have taught the courses and
seen where students need help—and where other
texts have come up short. The text features precise
definitions and exposition, carefully crafted pedagogy,
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and a strong emphasis on algebraic, transcendental,
and trigonometric functions. To show students how
important and relevant precalculus topics are to their
future coursework, an optional Looking Ahead to
Calculus feature appears in each chapter. The varied
examples and exercises include many that encourage
students to use and understand graphs, as opposed
to simply draw them, providing additional sound
preparation for calculus.
FEATURES
• LOOKING AHEAD TO CALCULUS: Offering an
interesting glimpse into calculus, this feature
demonstrates the relevance of precalculus topics to
students’ future success. Each feature (placed at the
end of the chapter to allow instructional flexibility)
includes objectives referencing the related chapter
material, discussion of the topics, and “Connect
to Calculus” exercises. References to this optional
material (highlighted so that instructors may teach
or skip it at their discretion) appear throughout each
chapter, reinforcing the connection between the
topics at hand and future courses.
• ACCENTS ON TECHNOLOGY AND CALCULATORS:
Accents on Technology appear throughout the
textbook to encourage students to become intelligent
users of technology and grasp concepts graphically.
They illustrate and guide the use of a TI-84 graphing
calculator for specific problems. Although graphing
calculators are incorporated into the book, their use
is not required. All graphing topics are fully discussed
in traditional ways.
• CAREERS IN MATHEMATICS CHAPTER OPENERS:
To encourage students to explore careers that use
mathematics and make a connection between math
and real life, each chapter opens with Careers in
Mathematics. New, exciting careers are showcased
in this edition. Featuring information taken primarily
from the Occupational Outlook Handbook, these
snapshots include information on how professionals
use math in their work and who employs them. A web
address is provided, allowing students to learn more
about the career.
• SECTION OPENERS: Each section begins with a
contemporary photo and a real-life application that
will appeal to students of varied interests, piquing
interest and motivating students to read the material.
• NUMBERED OBJECTIVES: Numbered learning
objectives, which are listed at the beginning of each
section and appear as subheadings in the section,
keep students focused.
• STUDENT-FRIENDLY WRITING STYLE: Clear, concise,
and friendly exposition helps to alleviate student
anxiety about reading a mathematics textbook.
The writing is informal yet accurate. Students
and instructors alike should find the reading both
interesting and inviting.
• STRATEGY BOXES: To enable students to build on
their mathematical reasoning and approach problems
with confidence, Strategy boxes offer problem-solving
techniques and steps at appropriate points in the
material.
• CAUTION BOXES: Caution boxes appear throughout
the text to alert students to common errors
and misunderstandings, and reinforce correct
mathematics.
• COMMENTS: Comment boxes appear throughout the
textbook, providing additional insights; for instance,
clarification on a specific step or concept in an
example, or a tip for studying the material.
• TITLED EXAMPLES: Descriptive titles have been
added to clearly identify the topic and purpose of
each example.
CONTENTS
R. BASIC CONCEPTS. Linear Equations and
Applications. Complex Numbers. Quadratic Equations
and Applications. Other Types of Equations. Inequalities.
The Rectangular Coordinate System. Equations of
Lines. Chapter Summary. Chapter Test. Looking Ahead
to Calculus. 1. GRAPHS AND FUNCTIONS. Graphs of
Equations. Functions and Function Notation. Graphs
of Functions. Basic Graphs. Transformations of Graphs.
Operations on Functions. Inverse Functions. Chapter
Summary. Chapter Test. Looking Ahead to Calculus
Quadratic Functions. Polynomial Functions. Rational
Zeros of Polynomial Functions. Roots of Polynomial
Equations. Rational Functions. Polynomial and
Rational Inequalities. Chapter Summary. Chapter Test.
Looking Ahead to Calculus. 3. EXPONENTIAL AND
LOGARITHMIC FUNCTIONS. Exponential Functions,
Graphs, and Applications. Applications of Exponential
Functions. Logarithmic Functions and Their Graphs.
Applications of Logarithmic Functions. Properties of
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Chapter Summary. Chapter Test. Looking Ahead to
Calculus. 4. TRIGONOMETRIC FUNCTIONS. Angles and
Their Measurement. The Unit Circle and Trigonometric
Functions. Trigonometric Functions of Any Angle;
Fundamental Identities. Graphs of the Sine and Cosine
Functions. Graphs of the Tangent, Cotangent, Secant
and Cosecant Functions. Regression and Other Graphs
Involving Trigonometric Functions. Chapter Summary.
Chapter Test. Looking Ahead to Calculus. 5. ANALYTIC
TRIGONOMETRY. Inverse Trigonometric Functions.
Inverse Cotangent, Secant, and Cosecant Functions
(Optional). Verifying Trigonometric Identities. Sum
and Difference Formulas. Double-Angle, PowerReduction, Half-Angle Formulas. Product-to-Sum and
Sum-to-Product Formulas. Trigonometric Equations I.
Trigonometric Equations II. Chapter Summary. Chapter
Test. Looking Ahead to Calculus. 6. APPLICATIONS;
OBLIQUE TRIANGLES. Solving Right Triangles. More
Right Triangle Applications. Law of Sines. Law of Cosines.
Area of Triangles. Angular and Linear Velocity—Circular
Motion. Chapter Summary. Chapter Test. Looking Ahead
to Calculus. 7. POLAR COORDINATES; VECTORS.
Polar Coordinates. Polar Equations and Graphs.
Complex Plane; Polar Form of Complex Numbers;
DeMoivre’s Theorem. Vectors. Dot Product. Chapter
Summary. Chapter Test. Looking Ahead to Calculus. 8.
LINEAR SYSTEMS AND MATRICES. Systems of Linear
Equations. Gaussian Elimination and Matrix Methods.
Matrix Algebra. Matrix Inversion. Determinants.
Partial Fractions. Graphs of Linear Inequalities. Linear
Programming (available on website). Chapter Summary.
Chapter Test. Looking Ahead to Calculus. 9. CONIC
SECTIONS AND QUADRATIC SYSTEMS. The Circle and
the Parabola. The Ellipse. The Hyperbola. Solving Nonlinear Systems of Equations. Plane Curves and Parametric
Equations. Conic Sections in Polar Coordinates. Chapter
Summary. Chapter Test. Looking Ahead to Calculus. 10.
NATURAL NUMBER FUNCTIONS AND PROBABILITY.
The Binomial Theorem. Sequences, Series, and
Summation Notation. Arithmetic Sequences. Geometric
Sequences. Mathematical Induction. Permutations
and Combinations (available on website). Probability
(available on website). Chapter Summary. Chapter Test.
Looking Ahead to Calculus. 11. INTRODUCTION TO
CALCULUS (available on website). Limits. Properties of
Limits. Limits and Continuity. Average Rate of Change.
Tangents and Derivatives. Area and Integrals. Chapter
Summary. Chapter Test. APPENDIX. Sets of Real
Numbers. Integer Exponents and Scientific Notation.
Radicals and Rational Exponents. Polynomials. Factoring
Polynomials. Rational Expressions.
© 2013, 1024pp, Paperback, 9780495826675
EDITION, 7E
David Cohen, late of University of California, Los Angeles; Theodore
B. Lee, City College of San Francisco; David Sklar, San Francisco State
University
Written by David Cohen and co-authors Theodore B.
Lee and David Sklar, PRECALCULUS, 7e, International
Edition focuses on the use of a graphical perspective to
provide a visual understanding of college algebra and
trigonometry. Cohen’s texts are known for their clear
writing style and outstanding, graded exercises and
applications, including many examples and exercises
involving applications and real-life data. Graphs,
visualization of data, and functions are introduced and
emphasized early on to aid student understanding.
Although the text provides thorough treatment of the
graphing calculator, the material is arranged to allow
instructors to teach the course with as much or as little
graphing utility work as they wish.
NEW TO THIS EDITION
• In addition to being honed in numerous sections
to improve clarity, this edition combines material
from PRECALCULUS: A PROBLEMS-ORIENTED
APPROACH, International Edition with that of
PRECALCULUS: WITH UNIT-CIRCLE TRIGONOMETRY,
4e, International Edition—creating a single book that
accommodates the introduction of trigonometry
with either a right triangle approach or a unit-circle
approach.
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• This edition’s broader content allows instructors
wishing to introduce trigonometry via right triangles
to do so by covering Chapters 6 through 10. Instructors
wishing to introduce trigonometry via the unit circle
may do so by skipping Chapter 6 and then covering
Chapters 7 through 10.
• Section 1.7 presents rewritten coverage of symmetry
that features an increased emphasis on geometry.
• In Section 2.4, the “table” presentation of non-linear
inequalities is complemented with a sign chart on a
number line.
• In Section 3.4, “Techniques in Graphing,” material on
graphing techniques has been rewritten to include
coverage of vertical and horizontal scaling of graphs.
• Section 3.5, ‘Methods of Combining Functions,”
includes new material of an abstract nature in
discussing combinations of two even functions, two
odd functions, or an even function and an odd function
to determine whether properties are “preserved.”
• In Section 3.6, the presentation of inverse functions
has been rewritten to emphasize the connection
between a one-to-one function and its inverse
function.
• Section 4.6 includes a more detailed discussion
and analysis of limiting behavior without using
limits or limit notation. Enhanced discussion of
limiting behavior (developed in Sections 4.6 and 4.7)
continues in Sections 5.1 through 5.3 with the analysis
of asymptote and other end behavior of graphs of
exponential and logarithmic functions.
• A new Section 14.6 on limits at infinity helps students
in the transition to a calculus course.
• To keep the text at a manageable length, many
“Projects” are now referenced but not included in the
book. Instead, they are accessible online at http://
www.cengage.com/international.
CONTENTS
1. FUNDAMENTALS. Sets of Real Numbers. Absolute
Value. Solving Equations (Review and Preview).
Rectangular Coordinates. Visualizing Data. Graphs and
Graphing Utilities. Equations of Lines. Symmetry and
Graphs. Circles. 2. EQUATIONS AND INEQUALITIES.
Quadratic Equations: Theory and Examples. Other
Types of Equations. Inequalities. More on Inequalities.
3. FUNCTIONS. The Definition of a Function. The
Graph of a Function. Shapes of Graphs. Average
Rate of Change. Techniques in Graphing. Methods of
Combining Functions. Iteration. Inverse Functions.
4. POLYNOMIAL AND RATIONAL FUNCTIONS:
APPLICATIONS TO OPTIMIZATION. Linear Functions.
Quadratic Functions. Using Iteration to Model
Populations Growth (Optional Section). Setting Up
Equations That Devine Functions. Maximum and
Minimum Problems. Polynomial Functions. Rational
FUNCTIONS. Exponential Functions. The Exponential
Function y = ex. Logarithmic Functions. Properties of
Logarithms. Equations and Inequalities with Logs and
Exponents. Compound Interest. Exponential Growth and
Decay. 6. AN INTRODUCTION TO TRIGONOMETRY VIA
RIGHT TRIANGLES. Trigonometric Functions of Acute
Angles. Right-Triangle Applications. Trigonometric
Functions of Angles. Trigonometric Identities. 7. THE
TRIGONOMETRIC FUNCTIONS. Radian Measure.
Trigonometric Functions of Angles. Evaluating the
Trigonometric Functions. Algebra and the Trigonometric
Functions. Right-Triangle Trigonometry. 8. GRAPHS
OF TRIGONOMETRIC FUNCTIONS. Trigonometric
Functions of Real Numbers. Graphs of the Sine and
Cosine Functions. Graphs of y = A sin(Bx-C) and y =
A cos(Bx-C). Simple Harmonic Motion. Graphs of the
Tangent and the Reciprocal Functions. 9. ANALYTICAL
TRIGONOMETRY. The Addition Formulas. The DoubleAngle Formulas. The Product-to-Sum and Sum-toProduct Formulas. Trigonometric Equations. The Inverse
Trigonometric Functions. 10. ADDITIONAL TOPICS IN
TRIGONOMETRY. Right-Triangle Applications. The
Law of Sines and the Law of Cosines. Vectors in the
Plane: A Geometric Approach. Vectors in the Plane: An
Algebraic Approach. Parametric Equations. Introduction
to Polar Coordinates. Curves in Polar Coordinates.
DeMoivre’s Theorem. 11. SYSTEMS OF EQUATIONS.
Systems of Two Linear Equations in Two Unknowns.
Gaussian Elimination. Matrices. The Inverse of a Square
Matrix. Determinants and Cramer’s Rule. Nonlinear
Systems of Equations. Systems of Inequalities. 12.
THE CONIC SECTIONS. The Basic Equations. The
Parabola. Tangents to Parabolas (Optional Section). The
Ellipse. The Hyperbola. The Focus-Directrix Property
of Conics. The Conics in Polar Coordinates. Rotation
of Axes. 13. ROOTS OF POLYNOMIAL EQUATIONS.
Division of Polynomials. The Remainder Theorem
and the Factor Theorem. The Fundamental Theorem
of Algebra. Rational and Irrational Roots. Conjugate
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Roots and Descartes’s Rule of Signs. Introduction to
Partial Fractions. More About Partial Fractions. 14.
ADDITIONAL TOPICS IN ALGEBRA. Mathematical
Induction. The Binomial Theorem. Introduction to
Sequences and Series. Arithmetic Sequences and Series.
Geometric Sequences and Series. Introduction to Limits.
Appendix A.1: Significant Digits. Appendix A.2: √2 is
Irrational. Appendix A.3: The Complex Number System.
Answers. Index.
© 2012, 1184pp, Paperback, 9781111428778
EDITION, 5E
J. Douglas Faires, Youngstown State University; James DeFranza, St.
Lawrence University
PRECALCULUS, 5e, International Edition, focuses on
teaching the essentials that students need to both
fulfill their precalculus requirement and be fully
prepared to succeed in calculus. The text presents an
integrated review of algebra and trigonometry while
covering fundamental calculus concepts, and providing
the solid grounding in analysis and graphing that is
necessary to make a successful transition to calculus.
This streamlined text provides all the mathematics that
students need—without bogging them down in review
material or overwhelming them with too much, too
soon. The authors have purposely kept this book, unlike
many available Precalculus books, at a length that can
be covered in one term.
NEW TO THIS EDITION
• A large number of carefully designed applications
that emphasize the importance and relevance of
precalculus and calculus have been added to the
examples and exercise sets. They cover a wide range
of areas, including biology, ecology, medicine, physics,
economics, geometry, engineering, archeology,
optimization, social science, ﬁnance, space science,
and mathematics. Highlighted and placed at the ends
of sections, the applications can be included or not at
the instructor’s discretion.
• All exercise sets have been reviewed to ensure
that the material covered in the section, and the
techniques presented in the examples, are sufficient
to permit students to work the problems. As in
previous editions, exercises vary in level from routine
to those that offer applications and extend the
theory presented. Approximately 30% of the routine
exercises, purposely similar in design to those in the
previous edition, are new.
• Chapter 4, “Trigonometric Functions,” now reviews
right triangle trigonometry (likely to be most familiar
to students) earlier in the chapter so that students
feel more comfortable with the subject before they
are exposed to the unit circle definition needed for
calculus. This approach facilitates an easier transition
for students, while still emphasizing the need to give
trigonometry a functional approach consistent with
the other topics in the text.
• New “Principles of Problem Solving” comments,
which highlight key techniques, augment the book’s
problem-solving focus. The comments—provided
when a technique is presented initially and then
explicitly used later when needed—are designed to
help students develop systematic procedures for
setting up and solving routine as well as application
problems.
• The authors conducted an exhaustive check of every
example, exercise, explanation, and essentially every
line of the text, honing as needed to clarify, assure
accuracy, and further emphasize the relevance
of mathematics—without altering the compact
“essentials” presentation.
FEATURES
• The terminology in the text parallels that used in
calculus texts, and the examples and exercises are
presented in the way students will encounter them
in calculus—preparing students for their next course
and providing them with a good head start.
• To maintain the text’s brevity while allowing
instructors greater flexibility in assigning content,
the Book Companion Website includes coverage of
useful, yet not fundamental, material on such topics
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240
as Descartes’ Rule of Signs, Rotation of Axes for conic
sections, and solving systems of equations.
• The authors weave an algebra and trigonometry
review throughout the text to help students see where
the gaps in their background must be filled before
they take calculus.
• Explanations in the margin alert students to material
that applies directly to calculus to help them prioritize
their study.
• New concepts are presented using relevant
applications, reinforced first with examples and then
with the exercises.
CONTENTS
Chapter 1 Functions. 1.1 Introduction. 1.2 The Real Line.
1.3 The Coordinate Plane. 1.4 Equations and Graphs. 1.5
Using Technology to Graph Functions. 1.6 Functions.
1.7 Linear Functions. 1.8 Quadratic Functions. Review
Exercises. Exercises for Calculus. Chapter Test. Chapter
2 New Functions From Old. 2.1 Introduction. 2.2 Other
Common Functions. 2.3 Arithmetic Combinations of
Functions. 2.4 Composition of Functions. 2.5 Inverse
Functions. Review Exercises. Exercises for Calculus.
Chapter Test. Chapter 3 Algebraic Functions. 3.1
Introduction. 3.2 Polynomial Functions. 3.3 Finding
Factors and Zeros of Polynomials. 3.4 Rational Functions.
3.5 Other Algebraic Functions. 3.6 Complex Roots of
Polynomials. Review Exercises. Exercises for Calculus.
Chapter Test. Chapter 4 Trigonometric Functions. 4.1
Introduction. 4.2 Measuring Angles. 4.3 Right-Triangle
Trigonometry. 4.4 The Sine and Cosine Functions. 4.5
Graphs of the Since and Cosine Functions. 4.6 Other
Trigonometric Functions. 4.7 Trigonometric Identities.
4.8 Inverse Trigonometric Functions. 4.9 Additional
Trigonometric Applications. Review Exercises. Exercises
for Calculus. Chapter Test. Chapter 5 Exponential and
Logarithm Functions. 5.1 Introduction. 5.2 The Natural
Exponential Function. 5.3 Logarithm Functions. 5.4
Exponential Growth and Decay. Review Exercises.
Exercises for Calculus. Chapter Test. Chapter 6 Conic
Sections, Polar Coordinates, and Parametric Equations.
6.1 Introduction. 6.2 Parabolas. 6.3 Ellipses. 6.4
Hyperbolas. 6.5 Polar Coordinates. 6.6 Conic Sections
in Polar Coordinates. 6.7 Parametric Equations. Review
Exercises. Exercises for Calculus . Chapter Test.
© 2012, 464pp, Paperback, 9780840068880
COHEN/LEE/SKLAR’S PRECALCULUS,
7TH, 7E
David Cohen, late of University of California, Los Angeles
© 2012, 768pp, Paperback, 9781111428242
CRAUDER/EVANS/NOELL’S FUNCTIONS
AND CHANGE: A MODELING APPROACH
TO COLLEGE ALGEBRA, 5TH, 5E
INTRODUCTION, 9th Edition, this manual shows you
how to approach and solve problems using the same
step-by-step explanations found in your textbook
examples.
© 2014, 344pp, Paperback, 9781133365587
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241
KAUFMANN/SCHWITTERS’ COLLEGE
ALGEBRA, 8TH, 8E
MCKEAGUE/TURNER’S TRIGONOMETRY,
7TH, 7E
Jerome E. Kaufmann, Western Illinois University (Retired); Karen L.
Schwitters, Seminole Community College
Charles P. McKeague, Cuesta Community College; Mark Turner,
Cuesta College
© 2013, 368pp, Paperback, 9781111990459
© 2013, 320pp, Paperback, 9781111989767
LARSON’S COLLEGE ALGEBRA, 9TH, 9E
FOR NEAL/GUSTAFSON/HUGHES’
PRECALCULUS
This guide offers step-by-step solutions for all oddnumbered text exercises, Chapter and Cumulative
Tests, and Practice Tests with solutions.
© 2014, 528pp, Paperback, 9781133962946
Karla Neal, Louisiana State University; R. David Gustafson, Rock
Valley College (Emeritus)
© 2013, 392pp, Paperback, 9780495826668
www.cengageasia.com
242
WILSON’S PRECALCULUS: MAKE IT REAL
STUDENT STUDY AND SOLUTIONS
MANUAL FOR LARSON’S PRECALCULUS
WITH LIMITS, 3E
© 2014, 752pp, Paperback, 9781285177694
© 2013, 448pp, NonBook-Disk, 9781111988388
MANUAL FOR LARSON’S PRECALCULUS
WITH LIMITS, 3RD, 3E
MANUAL FOR LARSON’S ALGEBRA &
TRIGONOMETRY, 9TH, 9E
© 2014, 752pp, Paperback, 9781133947219
© 2014, 776pp, Paperback, 9781133954415
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243
MANUAL FOR LARSON’S PRECALCULUS:
A CONCISE COURSE, 3RD, 3E
© 2014, 416pp, Paperback, 9781133954491
STUDENT STUDY GUIDE FOR WILSON’S
PRECALCULUS: MAKE IT REAL
Written by the text authors, this Study Guide includes
review material for each section of the text. It includes
section objectives, concepts, vocabulary, exercises,
worked out examples, and practice chapter tests with
solutions.
© 2013, 256pp, Paperback, 9781111988340
STUDENT STUDY GUIDE AND
SOLUTIONS MANUAL FOR LARSON’S
TRIGONOMETRY, 9E
© 2014, 416pp, Paperback, 9781133954293
STUDY GUIDE WITH SOLUTIONS FOR
FAIRES/DEFRANZA’S PRECALCULUS, 5TH,
5E
J. Douglas Faires, Youngstown State University; James DeFranza, St.
Lawrence University
Written by the authors of the core text, this Student
Study Guide with Solutions reinforces student
understanding with detailed explanations, worked-out
examples, and practice problems.
© 2012, 448pp, Paperback, 9781111427368
www.cengageasia.com
244
STUDY GUIDE WITH STUDENT
SOLUTIONS MANUAL FOR AUFMANN’S
ALGEBRA AND TRIGONOMETRY, 8TH, 8E
College
Reinforces student understanding and aids in test
preparation with detailed explanations, worked-out
examples, and practice problems. Lists key ideas to
master and builds problem-solving skills. Includes
worked solutions to the odd-numbered problems in
the text.
© 2015, 1056pp, Paperback, 9781285451121
STUDY GUIDE WITH STUDENT
SOLUTIONS MANUAL FOR AUFMANN’S
COLLEGE ALGEBRA, 8TH, 8E
College
Reinforces student understanding and aids in test
preparation with detailed explanations, worked-out
examples, and practice problems. Lists key ideas to
master and builds problem-solving skills. Includes
worked solutions to the odd-numbered problems in
the text.
© 2015, 768pp, Paperback, 9781285454962
TRIGONOMETRY, HYBRID (WITH
Enhanced WebAssign®. The result: a briefer printed
text that engages students online! James Stewart,
author of the best-selling calculus textbook series, and
his coauthors Lothar Redlin and Saleem Watson, wrote
TRIGONOMETRY to address a problem they frequently
saw in their classrooms: Students who attempted to
memorize facts and mimic examples—and who were
not prepared to “think mathematically.” With this
text, Stewart, Redlin and Watson help students learn
to think mathematically and develop true, lasting
problem-solving skills. Patient, clear, and accurate,
TRIGONOMETRY consistently illustrates how useful
and applicable trigonometry is to real life.
NEW TO THIS EDITION
• Exercise Sets: More than 20% of the exercises are new,
including new Concept Exercises for each section.
Key exercises are now linked to examples in the text
to help students better understand the concepts
involved as they do their homework.
• Book Companion Website: A new website, www.
stewartmath.com, contains Discovery Projects for
outlined in the Prologue. Though the book itself
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245
introduces the notion of problem solving to the
student, the website provides reinforcement of that
skill.
• Chapter 1 Functions and Graphs: This chapter has been
rewritten to focus more sharply on the fundamental
and crucial concept of function. A new section
entitled “Getting Information from the Graph of a
Function” encourages students to think of the graph
of a function as a tool for understanding the behavior
of the function.
• Chapter 2 Trigonometric Functions: Unit Circle
Approach This chapter includes a new section on
inverse trigonometric functions and their graphs.
Introducing this topic here reinforces the “function”
concept in the context of trigonometry.
• Chapter 3 Trigonometric Functions: Right Triangle
inverse trigonometric functions and right triangles
(Section 6.4), which is needed for applying the Laws
of Sines and Cosines in the following section, as well
as for solving trigonometric equations in Chapter 4.
Whether or not you cover inverse trig functions in
your course, complete content on this important topic
is provided, better preparing students for calculus.
• Chapter 4 Analytic Trigonometry: This chapter has
been completely revised. There are two new sections
on trigonometric equations (Sections 4.4 and 4.5).
The material on this topic (formerly in Section 4.5)
has been expanded and revised, and the addition
of more examples helps students better grasp this
difficult topic.
• Chapter 5 Polar Coordinates and Parametric
Equations: This chapter is now more sharply focused
on the concept of a coordinate system. The section
on parametric equations is new to this chapter.
The material on vectors is now in its own chapter.
Separating the parametric equations from vectors
better distinguishes these topics for students. This is
of particular importance since both topics are likely
to be new to students in Trigonometry.
• Chapter 6 Vectors in Two and Three Dimensions:
This is a new chapter with a new Focus on Modeling
section. By isolating the vectors coverage, students
are provided with more examples and more detailed
coverage of vectors—an exciting topic that they may
be covering concurrently in physics classes.
• Chapter 7 Analytic Geometry: This chapter is
now more closely devoted to the topic of analytic
geometry, especially the conic sections; the section
on parametric equations has been moved to Chapter
5. Students likely did not cover conics in the college
algebra course they took prior to trigonometry, so
the expanded conics coverage provides them with
the visual understanding of often-abstract geometric
forms.
• Chapter 8 Exponential and Logarithmic Functions: The
material on the natural exponential function is now in
a separate section. Expanded coverage provides the
students with more examples for help with homework
exercise.
CONTENTS
1. FUNCTIONS AND GRAPHS. Coordinate Geometry.
Lines. What is a Function? Graphs of Functions.
Transformations of Functions. Combining Functions.
One-to-One Functions and Their Inverses. Focus on
Modeling: Fitting Lines to Data. 2. TRIGONOMETRIC
FUNCTIONS: UNIT CIRCLE APPROACH. The Unit
Modeling Harmonic Motion. Focus on Modeling:
Fitting Sinusoidal Curves to Data. 3. TRIGONOMETRIC
FUNCTIONS: RIGHT TRIANGLE APPROACH. Angle
Measure. Trigonometry of Right Triangles. Trigonometric
and Triangles. The Law of Sines. The Law of Cosines. Focus
on Modeling: Surveying. 4. ANALYTIC TRIGONOMETRY.
Trigonometric Identities. Addition and Subtraction
Formulas. Double-Angle, Half-Angle, and ProductSum Formulas. Basic Trigonometric Equations. More
Trigonometric Equations. Focus on Modeling: Traveling
and Standing Waves. 5. POLAR COORDINATES AND
PARAMETRIC EQUATIONS. Polar Coordinates. Graphs
of Polar Equations. Polar Form of Complex Numbers;
DeMoivre’s Theorem. Plane Curves and Parametric
Equations. Focus on Modeling: The Path of a Projectile. 6.
VECTORS IN TWO AND THREE DIMENSIONS. Vectors
in Two Dimensions. The Dot Product. Three-Dimensional
Coordinate Geometry. Vectors in Three Dimensions. The
Cross Product. Equations of Lines and Planes. Focus on
Modeling: Vector Fields. 7. CONIC SECTIONS. Parabolas.
Ellipses. Hyperbolas. Shifted Conics. Rotation of Axes.
Polar Equations of Conics. Focus on Modeling: Conics
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246
in Architecture. 8. EXPONENTIAL AND LOGARITHMIC
FUNCTIONS. Exponential Functions. The Natural
Damped Harmonic Motion. Focus on Modeling: Fitting
Exponential and Power Curves to Data. APPENDIX
A: Algebra Review. Real Numbers. Exponents and
Radicals. Algebraic Expressions. Equations. Inequalities.
APPENDIX B: Geometry Review. Congruence and
Similarity of Triangles. The Pythagorean Theorem.
APPENDIX C: Graphing Calculators. Using a Graphing
Calculator. Solving Equations and Inequalities
Graphically.
© 2013, 480pp, Paperback, 9781111574475
EDITION, 2E
James Stewart, author of the best-selling calculus
textbook series, and his coauthors Lothar Redlin
and Saleem Watson, wrote TRIGONOMETRY, 2E,
International Edition to address a problem they
frequently saw in their classrooms: Students who
attempted to memorize facts and mimic examples—and
who were not prepared to “think mathematically.” With
this text, Stewart, Redlin and Watson help students
learn to think mathematically and develop true, lasting
problem-solving skills. Patient, clear, and accurate,
TRIGONOMETRY, 2E, International Edition consistently
illustrates how useful and applicable trigonometry is
to real life.
NEW TO THIS EDITION
• Exercise Sets: More than 20% of the exercises are new,
including new Concept Exercises for each section.
Key exercises are now linked to examples in the text
to help students better understand the concepts
involved as they do their homework.
• Book Companion Website: A new website contains
Discovery Projects for each chapter and Focus on
Problem Solving sections that highlight different
problem-solving principles outlined in the Prologue.
Though the book itself introduces the notion of
problem solving to the student, the website provides
reinforcement of that skill.
• Chapter 1 Functions and Graphs: This chapter has been
rewritten to focus more sharply on the fundamental
and crucial concept of function. A new section
entitled “Getting Information from the Graph of a
Function” encourages students to think of the graph
of a function as a tool for understanding the behavior
of the function.
• Chapter 2 Trigonometric Functions: Unit Circle
inverse trigonometric functions and their graphs.
Introducing this topic here reinforces the “function”
concept in the context of trigonometry.
• Chapter 3 Trigonometric Functions: Right Triangle
inverse trigonometric functions and right triangles
(Section 6.4), which is needed for applying the Laws
of Sines and Cosines in the following section, as well
as for solving trigonometric equations in Chapter 4.
Whether or not you cover inverse trig functions in
your course, complete content on this important topic
is provided, better preparing students for calculus.
• Chapter 4 Analytic Trigonometry: This chapter has
been completely revised. There are two new sections
on trigonometric equations (Sections 4.4 and 4.5).
The material on this topic (formerly in Section 4.5)
has been expanded and revised, and the addition
of more examples helps students better grasp this
difficult topic.
• Chapter 5 Polar Coordinates and Parametric
Equations: This chapter is now more sharply focused
on the concept of a coordinate system. The section
on parametric equations is new to this chapter.
The material on vectors is now in its own chapter.
Separating the parametric equations from vectors
www.cengageasia.com
247
better distinguishes these topics for students. This is
of particular importance since both topics are likely
to be new to students in Trigonometry.
• Chapter 6 Vectors in Two and Three Dimensions:
This is a new chapter with a new Focus on Modeling
section. By isolating the vectors coverage, students
are provided with more examples and more detailed
coverage of vectors—an exciting topic that they may
be covering concurrently in physics classes.
• Chapter 7 Analytic Geometry: This chapter is
now more closely devoted to the topic of analytic
geometry, especially the conic sections; the section
on parametric equations has been moved to Chapter
5. Students likely did not cover conics in the college
algebra course they took prior to trigonometry, so
the expanded conics coverage provides them with
the visual understanding of often-abstract geometric
forms.
• Chapter 8 Exponential and Logarithmic Functions: The
material on the natural exponential function is now in
a separate section. Expanded coverage provides the
students with more examples for help with homework
exercise.
CONTENTS
1. FUNCTIONS AND GRAPHS. Coordinate Geometry.
Lines. What is a Function? Graphs of Functions.
Transformations of Functions. Combining Functions.
One-to-One Functions and Their Inverses. Focus on
Modeling: Fitting Lines to Data. 2. TRIGONOMETRIC
FUNCTIONS: UNIT CIRCLE APPROACH. The Unit
Modeling Harmonic Motion. Focus on Modeling:
Fitting Sinusoidal Curves to Data. 3. TRIGONOMETRIC
FUNCTIONS: RIGHT TRIANGLE APPROACH. Angle
Measure. Trigonometry of Right Triangles. Trigonometric
and Triangles. The Law of Sines. The Law of Cosines. Focus
on Modeling: Surveying. 4. ANALYTIC TRIGONOMETRY.
Trigonometric Identities. Addition and Subtraction
Formulas. Double-Angle, Half-Angle, and ProductSum Formulas. Basic Trigonometric Equations. More
Trigonometric Equations. Focus on Modeling: Traveling
and Standing Waves. 5. POLAR COORDINATES AND
PARAMETRIC EQUATIONS. Polar Coordinates. Graphs
of Polar Equations. Polar Form of Complex Numbers;
DeMoivre’s Theorem. Plane Curves and Parametric
Equations. Focus on Modeling: The Path of a Projectile. 6.
VECTORS IN TWO AND THREE DIMENSIONS. Vectors
in Two Dimensions. The Dot Product. Three-Dimensional
Coordinate Geometry. Vectors in Three Dimensions. The
Cross Product. Equations of Lines and Planes. Focus on
Modeling: Vector Fields. 7. CONIC SECTIONS. Parabolas.
Ellipses. Hyperbolas. Shifted Conics. Rotation of Axes.
Polar Equations of Conics. Focus on Modeling: Conics
in Architecture. 8. EXPONENTIAL AND LOGARITHMIC
FUNCTIONS. Exponential Functions. The Natural
Damped Harmonic Motion. Focus on Modeling: Fitting
Exponential and Power Curves to Data. APPENDIX
A: Algebra Review. Real Numbers. Exponents and
Radicals. Algebraic Expressions. Equations. Inequalities.
APPENDIX B: Geometry Review. Congruence and
Similarity of Triangles. The Pythagorean Theorem.
APPENDIX C: Graphing Calculators. Using a Graphing
Calculator. Solving Equations and Inequalities
Graphically.
© 2013, 624pp, Paperback, 9781133110743
EDITION, 9E
Larson’s TRIGONOMETRY, 9E, International Edition is
known for delivering sound, consistently structured
explanations and exercises of mathematical concepts.
With the ninth edition, the author continues to
revolutionize the way students learn material by
incorporating more real-world applications, ongoing
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248
review, and innovative technology. How Do You See It?
exercises give students practice applying the concepts,
and new Summarize features, Checkpoint problems,
and a Companion Website reinforce understanding
of the skill sets to help students better prepare for
tests. Enhanced WebAssign® features fully integrated
content from the text, with the addition of End-ofSection problems and Chapter Tests, as well as problemspecific videos, animations, and lecture videos.
NEW TO THIS EDITION
of each section.
text.
upcoming section.
example.
FEATURES
CONTENTS
Properties. Solving Equations. The Cartesian Plane and
Functions. Analyzing Graphs of Functions. A Library
of Parent Functions. Transformations of Functions.
Combinations of Functions: Composite Functions.
Inverse Functions. Chapter Summary. Review Exercises.
Solving. 1. TRIGONOMETRY. Radian and Degree
Measure. Trigonometric Functions: The Unit Circle. Right
Triangle Trigonometry. Trigonometric Functions of Any
Angle. Graphs of Sine and Cosine Functions. Graphs of
Vectors and Dot Products. Chapter Summary. Review
1-3. Proofs in Mathematics. P.S. Problem Solving. 4.
COMPLEX NUMBERS. Complex Numbers. Complex
Solutions of Equations. Trigonometric Form of a
Complex Number. DeMoivre’s Theorem. Chapter
Mathematics. P.S. Problem Solving. 5. EXPONENTIAL
Functions and Their Graphs. Logarithmic Functions and
Their Graphs. Properties of Logarithms. Exponential and
Logarithmic Equations. Exponential and Logarithmic
Models. Chapter Summary. Review Exercises. Chapter
TOPICS IN ANALYTIC GEOMETRY. Lines. Introduction
to Conics: Parabolas. Ellipses. Hyperbolas. Rotation of
Conics. Parametric Equations. Polar Coordinates. Graphs
of Polar Equations. Polar Equations of Conics. Chapter
Summary. Review Exercises. Chapter Test. Cumulative
Test for Chapters 4-6. Proofs in Mathematics. P.S.
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249
Problem Solving. APPENDIX A Concepts in Statistics
(web). A.1 Representing Data. A.2 Measures of Central
Tendency and Dispersion. A.3 Least Squares Regression.
© 2014, 592pp, Paperback, 9781133954248
EDITION, 7E
Charles P. McKeague, Cuesta Community College; Mark Turner,
Cuesta College
Choose the book written for the way you teach with
McKeague/Turner’s best-selling TRIGONOMETRY, 7E,
International Edition. This trusted edition presents
contemporary concepts in short, manageable sections
using the most current, detailed examples and
high-interest applications. Captivating illustrations
of trigonometry concepts in action, such as Lance
Armstrong’s cycling success, the Ferris wheel, and even
the human cannonball, as well as unique Historical
Vignettes help motivate and keep students’ interest
throughout your course. TRIGONOMETRY, 7E,
International Edition continues to use a standard rightangle approach to trigonometry with an unmatched
emphasis on study skills that prepares students for
future success in advanced courses, such as calculus.
The book’s proven blend of exercises, fresh applications,
and projects is now combined with a simplified
approach to graphing and the convenience of Enhanced
WebAssign®—a leading, time-saving online homework
tool for instructors and students that’s correlated with
your Instructor’s Edition for cohesive support.
NEW TO THIS EDITION
• Student Learning Objectives: Each section begins
with a list of student learning objectives that describe
the specific, measurable knowledge and skills that
students are expected to achieve. Learning objectives
help the student to identify and focus on the
important concepts in each section and increase the
likelihood of their success by having established and
clear goals. For instructors, learning objectives can
help in organizing class lessons and learning activities
and in creating student assessments.
• Learning Objectives Assessments: Multiple choice
questions have been added at the end of every
problem set, and are designed to be used in class
or outside of class to assess student learning. Each
question directly corresponds to one of the student
learning objectives for that section. Answers to
these questions are not available to students, but are
provided for instructors in the Instructor’s Solutions
Manual. These problems can be especially useful
for schools and institutions required to provide
documentation and data relating to assessment of
student learning outcomes.
• Matched Practice Problems: In every section of this
book, each example is now paired with a matched
practice problem that is similar to the example. These
problems give students an opportunity to practice
what they have just learned before moving on to the
next example. Instructors may want to use them as inclass examples or to provide guided practice activities
in class. Answers are given in the answers section in
the back of the book.
• Concepts and Vocabulary: Each problem set begins
with a new set of questions that focus on grasping
the main ideas and understanding the vocabulary/
terminology presented in that particular section. Most
of these questions are short-answer, but in some cases
also include matching or other formats.
• Cumulative Tests: To help students review previous
learning and better retain information, three
cumulative tests have been added to the book.
These are similar to the chapter tests, except that
the questions pertain to all of the sections in the
book up to that point. The Cumulative Tests are good
resources for students studying for a midterm exam or
final exam. Answers to both odd and even problems
for cumulative tests are given in the back of the book.
• New Exercises and Applications: New exercises and
applications have been added in some sections to help
students gain a better grasp of key concepts and to
help motivate students and stimulate their interest
in trigonometry.
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250
FEATURES
• A simplified, step-by-step approach to graphing
introduces the sine and cosine functions first to make
graphing as accessible as possible for your students. A
step-by-step framing approach simplifies the graphing
process throughout Chapter 4.
• Captivating themes throughout the text highlight
trigonometry concepts in action with illustrations
such as the human cannonball, cycling, the Ferris
wheel, sports, navigation systems, and cable cars.
These intriguing themes, clearly marked with icons
in the examples and problem sets, help students
correlate one lesson with another throughout the
course.
• Enhanced WebAssign®: This revision is accompanied
by a significant increase in the number of exercises
that are included within Enhanced WebAssign®. All
of the odd problems in each problem set, and in some
cases a number of even problems, are now available
in electronic form. This proven homework system is
enhanced to include links to textbook sections, video
examples, and problem-specific tutorials that clarify
learning.
• Additional unique Historical Vignettes in this
edition intrigue students by providing background
on the ways in which many of the central ideas in
trigonometry originated.
Identities. Sum and Difference Formulas. Double-Angle
Formulas. Half-Angle Formulas. Additional Identities.
Summary. Test. Projects. 6. EQUATIONS. Solving
Trigonometric Equations. More on Trigonometric
Equations. Trigonometric Equations Involving Multiple
Angles. Parametric Equations and Further Graphing.
Summary. Test. Projects. Cumulative Test. 7. TRIANGLES.
The Law of Sines. The Law of Cosines. The Ambiguous
Case. The Area of a Triangle. Vectors: An Algebraic
Approach. Vectors: The Dot Product. Summary.
Test. Projects. 8. COMPLEX NUMBERS AND POLAR
COORDINATES. Complex Numbers. Trigonometric
Form for Complex Numbers. Products and Quotients
in Trigonometric Form. Roots of a Complex Number.
Polar Coordinates. Equations in Polar Coordinates and
Their Graphs. Summary. Test. Projects. Cumulative Test.
Appendix A: REVIEW OF FUNCTIONS. Introduction
to Functions. The Inverse of a Function. Answers to
Selected Exercises. Index.
© 2013, 592pp, Paperback, 9781111989811
CONTENTS
1. THE SIX TRIGNONMETRIC FUNCTIONS. Angles,
Degrees, and Special Triangles. The Rectangular
Coordinate System. Definition I: Trigonometric
Functions. Introduction to Identities. More on
Identities. Summary. Test. Projects. 2. RIGHT ANGLE
TRIGONOMETRY. Definition II: Right Triangle
Trigonometry. Calculators and Trigonometric Functions
of an Acute Angle. Solving Right Triangles. Applications.
Vectors: A Geometric Approach. Summary. Test. Projects.
3. RADIAN MEASURE. Reference Angle. Radians
and Degrees. Definition III: Circular Functions. Arc
Length and Area of a Sector. Velocities. Summary. Test.
Projects. Cumulative Test. 4. GRAPHING AND INVERSE
FUNCTIONS. Basic Graphs. Amplitude, Reflection,
and Period. Vertical and Horizontal Translations. The
Other Trigonometric Functions. Finding an Equation
From its Graph. Graphing Combinations of Functions.
Inverse Trigonometric Functions. Summary. Test.
Projects. 5. IDENTITIES AND FORMULAS. Proving
TRIGONOMETRY, LEVEL 1, 9E
© 2014, 592pp, Hardback, 9781133954323
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251
Combined Author/Title Index
A
A First Course in Differential Equations with Modeling
Applications, International Edition, 10e, p.159
A First Course in Mathematical Modeling, International Edition,
5e, p.161
A Transition to Advanced Mathematics, International Edition,
7e, p.162
Abstract Algebra, 3e, p.163
Adler, Modeling the Dynamics of Life, 3e, p.32
Algebra & Trigonometry, 9e, p.182
Algebra and Trigonometry with Analytic Geometry,
International Edition, 13e, p.187
Algebra and Trigonometry, 6e, p.184
Algebra and Trigonometry, 8e, p.185
Algebra and Trigonometry, International Edition, 3e, p.189
Algebra and Trigonometry, Level 1, 9e, p.191
Applied CALC (with CourseMate Printed Access Card), 2e, p.66
Applied CALC (with Mathematics CourseMate with eBook
Printed Access Card), p.67
Applied Calculus for the Managerial, Life, and Social Sciences,
10e, p.72
9e, p.68/p.70
Hybrid Edition, 9e, p.73
Applied Calculus, Brief Hybrid (with Enhanced WebAssign with
eBook LOE Printed Access Card for One-Term Math and
Science), 6e, p.75
Applied Calculus, Hybrid Edition (with Enhanced WebAssign
with eBook LOE Printed Access Card for One-Term Math and
Science), 6e, p.78
Applied Calculus, Hybrid, 6e, p.77
Applied Calculus, International Edition, 6e, p.80/p.81
Applied Mathematics for the Managerial, Life, and Social
Sciences, Hybrid (with Enhanced WebAssign with eBook LOE
Printed Access Card for One-Term Math and Science), 6e,
p.83
Sciences, International Edition, 6e, p.85
Aufmann/Barker/Nation, College Algebra and Trigonometry,
Aufmann/Barker/Nation, College Algebra, International
Edition, 7e, p.208
Aufmann/Lockwood/Nation/Clegg, Mathematical Excursions,
Enhanced Edition, 3rd, 3e, p.127
Aufmann/Lockwood/Nation/Clegg, Mathematical Excursions,
Aufmann/Lockwood/Nation/Clegg, Student Solutions Manual
for Aufmann/Lockwood/Nation/Clegg’s Mathematical
Excursions, 3rd, 3e, p.137
Aufmann/Nation, Algebra and Trigonometry, 8e, p.185
Aufmann/Nation, College Algebra, 8e, p.198
Aufmann/Nation, Study Guide with Student Solutions Manual
for Aufmann’s Algebra and Trigonometry, 8th, 8e, p.245
Aufmann/Nation, Study Guide with Student Solutions Manual
for Aufmann’s College Algebra, 8th, 8e, p.245
B
Bassarear, Mathematics for Elementary School Teachers,
Bello/Kaul/Britton, Student Solutions Manual for Bello/Kaul/
Britton’s Topics in Contemporary Mathematics, 10th, 10e,
p.138
Bello/Kaul/Britton, Topics in Contemporary Mathematics,
Berresford/Rockett, Applied Calculus, Brief Hybrid (with
Enhanced WebAssign with eBook LOE Printed Access Card
for One-Term Math and Science), 6e, p.75
Berresford/Rockett, Applied Calculus, Hybrid Edition (with
Berresford/Rockett, Brief Applied Calculus, International
Edition, 6e, p.88
Berresford/Rockett, FINITE (with Mathematics CourseMate
with eBook Printed Access Card), p.101
Berresford/Rockett, Student Solutions Manual for Berresford/
Rockett’s Applied Calculus, 6th, 6e, p.124
Blanchard/Devaney/Hall, Differential Equations, International
Edition (with DE Tools Printed Access Card), 4e, p.167
Bracken/Miller, Intermediate Algebra, International Edition,
p.59
Brief Applied Calculus, International Edition, 6e, p.88
Brief Applied Calculus, Hybrid (with Enhanced WebAssign with
Science), p.89
Brief Applied Calculus, International Edition, p.90
Brief Calculus, 9e, p.92/p.93
Burden/Faires, Numerical Analysis, International Edition, 9e,
p.176
C
Calculus Concepts, 5e, p.97
Calculus I with Precalculus, 3e, p.191
Calculus I with Precalculus, International Edition, 3e, p.3/p.192
Calculus Single Variable with Vector Functions, AP*, 7e, p.14
Calculus of a Single Variable, 10e, p.6
Calculus of a Single Variable, Hybrid (with Enhanced
WebAssign Homework and eBook LOE Printed Access Card
for Multi Term Math and Science), 10e, p.10
Calculus of a Single Variable, Hybrid, 6e, p.8
Calculus of a Single Variable, International Edition, 10e, p.12
Calculus with CB CourseSmart eBook, 10e, p.14
Calculus, 5e, p.2/p.3
Calculus, 9e, p.94/p.96
Calculus, Hybrid (with Enhanced WebAssign Homework and
eBook LOE Printed Access Card for Multi Term Math and
Science), 10e, p.19
Calculus, Hybrid Edition (with Enhanced WebAssign with eBook
for Multi Term Math and Science), 7e, p.22
Calculus, Hybrid, 6e, p.17
Calculus, International Metric Edition, 7e, p.24
Calculus: Concepts & Contexts, Hybrid with Enhanced
WebAssign Printed Access Card, 3 Semester, 4e, p.27
Campbell, Introduction to Advanced Mathematics, p.171
Cheney/Kincaid, Numerical Mathematics and Computing,
Cheney/Kincaid, Student Solutions Manual for Cheney/
Kincaid’s Numerical Mathematics and Computing, 7th, 7e,
p.181
252
www.cengageasia.com
Cohen, Student Solutions Manual for Cohen/Lee/Sklar’s
Precalculus, 7th, 7e, p.241
Cohen/Lee/Sklar, Precalculus, International Edition, 7e, p.238
College Algebra, p.194/p.197
College Algebra and Calculus, 2e, p.99/p.200
College Algebra and Trigonometry, International Edition, 7e,
p.201
College Algebra with Applications for Business and Life
Sciences, 2e, p.203
College Algebra, 6e, p.195
College Algebra, 8e, p.198
College Algebra, Hybrid (with Enhanced WebAssign with eBook
LOE Printed Access Card for One-Term Math and Science),
6e, p.204
College Algebra, Hybrid Edition (with Enhanced WebAssign Start Smart Guide for Students), 9e, p.206
College Algebra, International Edition, 11e, p.214
Contemporary Abstract Algebra, International Edition, 8e, p.163
Crauder/Evans/Noell, Functions and Change, 5e, p.215/p.217
Crauder/Evans/Noell, Student Solutions Manual for Crauder/
Evans/Noell’s Functions and Change: A Modeling Approach
to College Algebra, 5th, 5e, p.241
Finite Mathematics and Applied Calculus, International Edition,
6e, p.105
Finite Mathematics for the Managerial, Life, and Social
Sciences, 11e, p.107
Finite Mathematics for the Managerial, Life, and Social
Finite Mathematics, Enhanced Edition (with Enhanced
WebAssign with eBook for One Term Math and Science
Printed Access Card), 7e, p.110
Finite Mathematics, Hybrid (with Enhanced WebAssign with
Science), 6e, p.113
Finite Mathematics, Hybrid (with Enhanced WebAssign with
Science), 8e, p.112
Finite Mathematics, International Edition, 6e, p.115
Finite Mathematics, International Edition, 8e, p.116
Fox, Mathematical Modeling with Maple, International Edition,
p.175
Freitag, Mathematics for Elementary School Teachers, p.150
Freitag, Mathematics for Elementary Teachers, p.133
Freitag, Student Solutions Manual for Freitag’s Mathematics
for Elementary School Teachers: A Process Approach, p.138
Functions and Change, 5e, p.215/p.217
Fundamentals of Algebraic Modeling, International Edition, 6e,
p.125
D
G
Differential Equations with Boundary-Value Problems,
Differential Equations, International Edition (with DE Tools
Discrete Mathematics, p.62/p.63
Discrete Mathematics with Applications, International Edition,
4e, p.63
Gallian, Contemporary Abstract Algebra, International Edition,
8e, p.163
Gallian, Student Solutions Manual for Gallian’s Contemporary
Abstract Algebra, 8th, 8e, p.181
Gilbert, Elements of Modern Algebra, 8e, p.169
Giordano/Fox/Horton, A First Course in Mathematical
Modeling, International Edition, 5e, p.161
Gustafson/Hughes, College Algebra, International Edition, 11e,
p.214
E
Elementary Linear Algebra, International Edition, 7e, p.168
Elementary Technical Mathematics, 11e, p.57
Elements of Modern Algebra, 8e, p.169
Epp, Discrete Mathematics with Applications, International
Edition, 4e, p.63
Essential Calculus, International Metric Edition, 2e, p.29
Essential Calculus: Early Transcendentals, 2e, p.30
Ewen/Nelson, Elementary Technical Mathematics, 11e, p.57
F
FINITE (with Mathematics CourseMate with eBook Printed
Access Card), p.101
Faires/Burden, Numerical Methods, International Edition, 4e,
p.179
Faires/Burden, Student Solutions Manual for Faires/Burden’s
Numerical Methods, 4th, 4e, p.181
Faires/DeFranza, Precalculus, International Edition, 5e, p.240
Faires/DeFranza, Study Guide with Solutions for Faires/
Defranza’s Precalculus, 5th, 5e, p.244
Fierro, Mathematics for Elementary School Teachers,
International Edition, p.155
Finite Math and Applied Calculus, Hybrid, 6e, p.103
H
Harshbarger, MATH APPS (with Math CourseMate with eBook
Harshbarger/Reynolds, Mathematical Applications for
the Management, Life, and Social Sciences, Hybrid (with
Harshbarger/Reynolds, Mathematical Applications for the
Management, Life, and Social Sciences, International Edition,
10e, p.122
Hungerford, Abstract Algebra, 3e, p.163
I
Intermediate Algebra, International Edition, p.59
Introduction to Advanced Mathematics, p.171
J
Johnson/Mowry, Mathematics, 7e, p.131
Ju/Xing/Lin/Hu, Linear Algebra, p.174
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Kaufmann/Schwitters, College Algebra, International Edition,
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Kaufmann/Schwitters, Student Solutions Manual for
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LaTorre/Kenelly/Biggers/Carpenter, Calculus Concepts, 5e,
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Larson, Algebra & Trigonometry, 9e, p.182
Larson, Algebra and Trigonometry, 6e, p.184
Larson, Algebra and Trigonometry, Level 1, 9e, p.191
Larson, Brief Calculus, 9e, p.92/p.93
Larson, Calculus I with Precalculus, 3e, p.191
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p.148
Larson, Precalculus with Limits, International Edition, 2e, p.229
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Larson/Falvo, Student Solutions Manual for Larson/Falvo’s
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Edition, 5e, p.152
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McKeague/Turner, Student Solutions Manual for McKeague/
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Multivariable Calculus, Hybrid (with Enhanced WebAssign
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Nature of Mathematics, 12e, p.136
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Poole, Linear Algebra, 3e, p.171
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Student Study and Solutions Manual for Larson’s Algebra &
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Student Study and Solutions Manual for Larson’s Precalculus
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Tan, Applied Calculus for the Managerial, Life, and Social
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Tan, Single Variable Calculus: Early Transcendentals, p.38
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Timmons/Johnson/McCook, Fundamentals of Algebraic
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Waner/Costenoble, Student Solutions Manual for Waner/
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Wilson, Applied CALC (with CourseMate Printed Access Card),
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Zill/Wright, Differential Equations with Boundary-Value
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