- McGraw

Transcription

- McGraw

NEW TITLES
DEVELOPMENT MATHEMATICS
2009
Author
ISBN-13
MHID
Introductory Algebra, 3e
Bello
9780073533438
0073533432
11
Algebra For College Students, 5e
Dugopolski
9780073533520
0073533521
34
Elementary Algebra, 6e
Dugopolski
9780077224790
0077224795
12
Elementary And Intermediate Algebra, 3e
Dugopolski
9780077224820
0077224825
16
Intermediate Algebra, 6e
Dugopolski
9780077224813
0077224817
27
Beginning And Intermediate Algebra, 2e
Messersmith
9780077224837
0077224833
18
Hall
9780073229713
0073229717
20
Basic Mathematical Skills With Geometry, 7e
Hutchison
9780073309590
0073309591
5
Beginning Algebra, 7e
Hutchison
9780073309606
0073309605
13
Hutchison
9780073048239
0073048232
21
Elementary And Intermediate Algebra, Hutchinson
9780073309316
0073309311
23
Intermediate Algebra
Hutchison
9780073309309
0073309303
29
Miller
9780073312675
0073312673
14
Miller
9780073312699
007331269X
24
Miller
9780073312682
0073312681
31
9780070131651
0070131651
46
Page
2008
Alternate Hardcover Edition, 3e
Mathematics Service Courses
2007
Mathematics For Technicians, 6e
Alldis
i
HED_08 Math&Statistics_NewTitles.indd 1
1/21/2008 5:22:23 PM
NEW TITLES
NEW TITLES
Precalculus
Statistics and Probability
2009
Author
ISBN-13
MHID
College Algebra: Graphs And Models, 3e
Barnett
9780073051956
0073051950
Precalculus: Graphs And Models, 3e
Barnett
9780077221294
007722129X
2009
Author
ISBN-13
MHID
51
Complete Business Statistics With Student CD, 7e
Aczel
9780077239695
0077239695
119
58
Business Statistics In Practice, 5e
Bowerman
9780073373591
0073373591
119
Page
Page
2008
2008
College Algebra, 8e
Barnett
9780073312620
0073312622
52
Elementary Statistics: A Brief Version, 4e
Bluman
9780073534961
007353496X
109
College Algebra With Trigonometry, 8e
Barnett
9780073312644
0073312649
56
Essentials Of Business Statistics With Student CD, 2e
Bowerman
9780073319889
0073319880
119
Precalculus With Limits, 6e
Barnett
9780073365800
0073365807
60
Basic Statistics For Business And Economics With Lind
9780077230968
0077230965
120
Precalculus With Mathzone, 6e
Barnett
9780073312637
0073312630
61
Trigonometry With Mathzone
Coburn
9780073312668
0073312665
54
Basic Statistics Using Excel To Accompany Statistical
Lind
9780073030265
0073030260
120
Statistical Techniques In Business And Economics, 3e
Lind
9780073272962
0073272965
120
Statistics For Engineers And Scientists, 2e
Navidi
9780073309491
0073309494
117
calculus
2008
Calculus: Late Transcendental Functions, 3e
Smith
9780073312705
0073312703
69
Calculus: Multivariable: Late Transcendental Functions, 3e
Smith
9780073314204
007331420X
80
Calculus, Single Variable: Late Transcendental Functions, 3e
Smith
9780073314198
0073314196
74
Brown
9780073051949
0073051942
101
Brown
9780073051932
0073051934
88
Student CD, 6e
Techniques In Business And Economics, 13e
Higher Mathematics
2009
Complex Variables And Applications, 8e
2008
Fourier Series And Boundary Value Problems, 7e
ii
HED_08 Math&Statistics_NewTitles.indd 2-3
iii
1/21/2008 5:22:24 PM
CONTENTS
Developmental Mathematics Higher Mathematics
Algrebra For College Students . . . . . . . . . . . . . . . . . . . . . 34
Abstract Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Arithmetic/Basic Math. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Advanced Engineering Mathematics. . . . . . . . . . . . . . . . . 94
Beginning Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Advanced Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Beginning/Intermediate Algebra Combined. . . . . . . . . . . . 16
Combinatorics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Intermediate Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Complex Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Prealgebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Differential Equations With Boundary Value Problems. . . 87
Dynamical System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
********************
Graph Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
History Of Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Mathematics Service
Courses
Introductory Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Business Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . .41
Mathematical References. . . . . . . . . . . . . . . . . . . . . . . . 105
Discrete Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Number Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Finite Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Numerical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Partial Differential Equations. . . . . . . . . . . . . . . . . . . . . . . 88
Liberal Arts Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . 41
Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Mathematics For Elementary Teachers. . . . . . . . . . . . . . . 43
Transition To Higher Math/Foundations Of Higher
Linear Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Technical Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Math. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
********************
********************
Precalculus
Statistics & Probability
College Algebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Advanced Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
College Algebra With Trigonometry. . . . . . . . . . . . . . . . . . 56
Applied Statistics – Engineering . . . . . . . . . . . . . . . . . . . 117
Precalculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Applied Statistics – Eduction, Psychology And Soical
Trigonometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Applied Statistics – Science, Health And Biostatistics. . . 115
Business Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
********************
Statistics And Probability (Calculus) . . . . . . . . . . . . . . . . 114
Statistics And Probability (Non-Calculus) . . . . . . . . . . . . 109
Calculus
Applied/Business Calculus . . . . . . . . . . . . . . . . . . . . . . . . 67
Calculus and Analytic Geometry. . . . . . . . . . . . . . . . . . . . 69
Multi-Variable Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Single Variable Calculus. . . . . . . . . . . . . . . . . . . . . . . . . . 74
********************
1
3
DEVELOPMENTAL
MATHEMATICS
Algrebra for College Students.............................................................................34
Arithmetic/Basic Math............................................................................................5
Beginning Algebra...............................................................................................11
Beginning/Intermediate Algebra Combined.........................................................16
Intermediate Algebra...........................................................................................27
PreAlgebra............................................................................................................9
NEW TITLES
DEVELOPMENT MATHEMATICS
2009
Author
ISBN-13
MHID
Bello
9780073533438
0073533432
11
Algebra For College Students, 5e
Dugopolski
9780073533520
0073533521
34
Dugopolski
9780077224790
0077224795
12
Dugopolski
9780077224820
0077224825
16
Dugopolski
9780077224813
0077224817
27
Messersmith
9780077224837
0077224833
18
Hall
9780073229713
0073229717
20
Basic Mathematical Skills With Geometry, 7e
Hutchison
9780073309590
0073309591
5
Hutchison
9780073309606
0073309605
13
Hutchison
9780073048239
0073048232
21
Elementary And Intermediate Algebra, Hutchinson
9780073309316
0073309311
23
Hutchison
9780073309309
0073309303
29
Miller
9780073312675
0073312673
14
Miller
9780073312699
007331269X
24
Miller
9780073312682
0073312681
31
Page
2008
Alternate Hardcover Edition, 3e
4
DEVELOPMENTAL MATHEMATICS
Arithmetic/Basic Math
for each section. The application exercises that are now integrated
into every section are a crucial component of this organization.
Contents
1 Operations on Whole Numbers
1.1 The Decimal Place-Value System
1.2 Addition
1.3 Subtraction
1.4 Rounding, Estimation, and Order
1.5 Multiplication
1.6 Division
1.7 Exponential Notation and the Order of Operations
2 Multiplying and Dividing Fractions
2.1 Prime Numbers and Divisibility
2.2 Factoring Whole Numbers
2.3 Fraction Basics
2.4 Simplifying Fractions
2.5 Multiplying Fractions
2.6 Dividing Fractions
3 Adding and Subtracting Fractions
3.1 Adding and Subtracting Fractions with Like Denominators
3.2 Common Multiples
3.3 Adding and Subtracting Fractions with Unlike Denominators
3.4 Adding and Subtracting Mixed Numbers
3.5 Order of Operations with Fractions
3.6 Estimation Applications
4 Decimals
4.1 Place Value and Rounding
4.2 Converting Between Fractions and Decimals
4.3 Adding and Subtracting Decimals
4.4 Multiplying Decimals
4.5 Dividing Decimals
5 Ratios and Proportions
5.1 Ratios
5.2 Rates and Unit Pricing
5.3 Proportions
5.4 Solving Proportions
6 Percents
6.1 Writing Percents as Fractions and Decimals
6.2 Writing Decimals and Fractions as Percents
6.3 Identifying the Parts of a Percent Problem
6.4 Solving Percent Problems
7 Measurement
7.1 The Units of the English System
7.2 Metric Units of Length
7.3 Metric Units of Weight and Volume
7.4 Converting Between the English and Metric Systems
8 Geometry
8.1 Area and Circumference
8.2 Lines and Angles
8.3 Triangles
8.4 Square Roots and the Pythagorean Theorem
9 Data Analysis and Statistics
9.1 Means, Medians, and Modes
9.2 Tables, Pictographs, and Bar Graphs
9.3 Line Graphs and Predictions
9.4 Creating Bar Graphs and Pie Charts
9.5 Describing and Summarizing Data Sets
10 The Real Number System
10.1 Real Numbers and Order
10.2 Adding Real Numbers
10.3 Subtracting Real Numbers
10.4 Multiplying Real Numbers
10.5 Dividing Real Numbers and the Order of Operations
11 An Introduction to Algebra
11.1 From Arithmetic to Algebra
11.2 Evaluating Algebraic Expressions
11.3 Adding and Subtracting Algebraic Expressions
11.4 Using the Addition Property to Solve an Equation
11.5 Using the Multiplication Property to Solve an Equation
11.6 Combining the Properties to Solve Equations
New
International Edition
BASIC MATHEMATICAL
SKILLS WITH GEOMETRY
Seventh Edition
By Donald Hutchison, Stefan Baratto and Barry
Bergman of Clackamas Community College
2008 (November 2006)
ISBN-13: 978-0-07-330959-0 / MHID: 0-07-330959-1
ISBN-13: 978-0-07-110191-2 / MHID: 0-07-110191-8 [IE]
Browse http://www.mhhe.com/baratto
Basic Mathematical Skills with Geometry, 7/e by Baratto/Bergman
is part of the latest offerings in the successful Streeter-Hutchison
Series in Mathematics. The seventh edition continues the hallmark
approach of encouraging the learning of mathematics by focusing its
coverage on mastering math through practice. This worktext seeks to
provide carefully detailed explanations and accessible pedagogy to
introduce basic mathematical skills and put the content in context. The
authors use a three-pronged approach (I. Communication, II. Pattern
Recognition, and III. Problem Solving) to present the material and
stimulate critical thinking skills. Items such as Math Anxiety boxes,
Check Yourself exercises, and Activities represent this approach and
the underlying philosophy of mastering math through practice. The
exercise sets have been expanded, organized, and clearly labeled.
Vocational and professional-technical exercises have been added
throughout. Repeated exposure to this consistent structure should
help advance the student’s skills in relating to mathematics. The book
is designed for a one-semester basic math course and is appropriate
for lecture, learning center, laboratory, or self-paced courses. It is
accompanied by numerous useful supplements, including McGrawHill’s online homework management system, MathZone.
New to this edition
CHANGES TO GEOMETRY COVERAGE--Geometry and
measurement have been split into two chapters, with some of the
geometry material now being presented earlier in the book. In
Chapter 7, which now focuses on measurements, material has been
added on temperature conversions, including additional examples.
Chapter 8 now focuses on geometric topics and includes more precise
vocabulary terms.
“MAKE THE CONNECTION”--Chapter-Opening Vignettes
were substantially revised to provide students interesting, relevant
scenarios that will capture their attention and engage them in the
upcoming material. Furthermore, exercises and Activities related to
the Opening Vignettes were added or updated in each chapter. These
exercises are marked with a special icon next to them.
“READING YOUR TEXT”--This new feature is a set of quick
exercises presented at the end of each section meant to quiz students
vocabulary knowledge. These exercises are designed to encourage
careful reading of the text. Answers to these exercises are provided
at the end of the book.
RESTRUCTURING OF END-OF-SECTION EXERCISES--The
comprehensive End-of-Section exercises have been reorganized to
more clearly identify the different types of exercises being presented.
This structure highlights the progression in level and type of exercise
5
By Julie Miller, Daytona Beach Cc-Daytona Beach, Molly O’Neill,
Daytona Beach Cc-Daytona Beach, and Nancy Hyde, Broward
Community College
ISBN-13: 978-0-07-322970-6 / MHID: 0-07-322970-9
(with MathZone)
ISBN-13: 978-0-07-330548-6 / MHID: 0-07-330548-0 (softcover)
Browse: http:www.mhhe.com/moh
Basic College Mathematics offers a refreshing approach to the
traditional content of the course. Presented in worktext format, Basic
College Mathematics focuses on basic number skills: operations and
problem-solving with whole numbers, fractions, and decimals. Other
topics include geometry, measurement, ratios, proportions, percents,
and the real number system (with an introduction to algebra). The text
reflects the compassion and insight of its experienced author team with
features developed to address the specific needs of developmental
level students.
Contents
1 Whole Numbers
2 Fractions: Multiplication and Division
3 Fractions: Addition and Subtraction
4 Decimals
5 Ratio and Proportion
6 Percents
7 Measurement
8 Geometry
9 Introduction to Statistics
10 Real Numbers
11 Solving Equations
BASIC COLLEGE MATHEMATICS
Second Edition
By Ignacio Bello, University of South Florida, Tampa
2006 / Hardcover with CD
ISBN-13: 978-0-07-330499-1 / MHID: 0-07-330499-9
ISBN-13: 978-0-07-299098-0 / MHID: 0-07-299098-8
(with MathZone)
http://www.mhhe.com/bello
Basic College Mathematics will be a review of fundamental math
concepts for some students and may break new ground for others.
Nevertheless, students of all backgrounds will be delighted to find a
refreshing book that appeals to all learning styles and reaches out to
diverse demographics. Through down-to-earth explanations, patient
skill-building, and exceptionally interesting and realistic applications,
this worktext will empower students to learn and master mathematics
in the real world.
2.5 Addition and Subtraction of Mixed Numbers
2.6 Order of Operations and Grouping Symbols
2.7 Equations and Problem Solving
3. DECIMALS
3.1 Addition and Subtraction of Decimals
3.2 Multiplication and Division of Decimals
3.3 Fractions and Decimals
3.4 Decimals, Fractions, and Order
3.5 Solving Equations and Word Problems
4. RATIO, RATE, AND PROPORTION
4.1 Ratio and Proportion
4.2 Rates
4.3 Word Problems Involving Proportion
5. PERCENT
5.1 Percent Notation
5.2 Percent Problems
5.3 Solving Percent Problems using Proportions
5.4 Taxes, Interest, Commissions, and Discounts
5.5 Applications: Percent of Increase and Decrease
5.6 Consumer Credit
6. STATISTICS AND GRAPHS
6.1 Tables and Pictographs
6.2 Bar and Line Graphs
6.3 Circle Graphs
6.4 Mean, Median, and Mode
7. MEASUREMENT AND THE METRIC SYSTEM
7.1 Length
7.2 The Metric System
7.3 Converting Between American and Metric Units
7.4 Converting Units of Area
7.5 Capacity
7.6 Weight and Temperature
8. GEOMETRY
8.1 Finding Perimeters
8.2 Finding Areas
8.3 Volume of Solids
8.4 Angles and Triangles
8.5 Square Roots and Pythagoras’ Theorem
9. THE REAL NUMBERS
9.1 Addition and Subtraction of Integers
9.2 Multiplication and Division of Integers
9.3 The Rational Numbers
9.4 Order of Operations
10. INTRODUCTION TO ALGEBRA
10.1 Introduction to Algebra
10.2 The Algebra of Exponents
10.3 Scientific Notation
10.4 Solving Linear Equations
10.5 Applications: Word Problems
INVITATION TO PUBLISH
BASIC COLLEGE MATHEMATICS
Contents
1. WHOLE NUMBERS
1.1 Standard Numerals
1.2 Ordering and Rounding Whole Numbers
1.3 Addition
1.4 Subtraction
1.5 Multiplication
1.6 Division
1.7 Primes, Factors, and Exponents
1.8 Order of Operations and Grouping Symbols
1.9 Equations and Problem Solving
2. FRACTIONS AND MIXED NUMBERS
2.1 Fractions and Mixed Numbers
2.2 Equivalent Fractions
2.3 Multiplication and Division of Fractions and Mixed Numbers
2.4 Addition and Subtraction of Fractions
6
McGraw-Hill is interested in
reviewing manuscript for
publication. Please contact your
local McGraw-Hill office or email to
[email protected]
Visit McGraw-Hill Education (Asia)
Website: www.mcgraw-hill.com.sg
MATH FOR THE ANXIOUS
11 Moving Beyond Math Anxiety
Math Memories. Taking the Next Step. Strategies for Success.
Exercises
By Rosanne Proga
2005 / 176 pages
ISBN-13: 978-0-07-288584-2 / MHID: 0-07-288584-X
Contents
1 The Misery of Math Anxiety
Math Memories. Math Anxiety: What Causes it? To Succeed in
Math... Why Learn Math? How We Learn Math. Problem Solving.
Math Anxiety: Why Must It Be Addressed? Strategies for Success.
Exercises.
2 Strategies for Conquering Math Anxiety
Math Memories. Choosing the Righ Math Course. Getting the Most
Out of a Math Class. Your Attitued Toward Mathematics. Strategies
for Effective Studying. Estimation. How to “Read” a Math Book. Using
Additional Resources. Test Preparation. Test-Taking Strategies. How
to Measure Results. Strategies for Success. Exercises.
3 Becoming Nimble with Numbers
Math Memories. Common Problems. Hints for Studying Numbers.
Symbols Used in Mathematics. Addition of Whole Numbers. Addition in
Daily Life: Total Mileage. Subtraction of Whole Numbers. Subtraction
in Daily Life: Population Expansion. Subtraction in Daily Life: Bank
Deposit. Multiplication of Whole Numbers. Multiplication in Daily Life:
Buying Stock. Division of Whole Numbers. Division in Daily Life:
Rows in a Lecture Hall. Division in Daily Life: Lottery Prize. Word
Problems. Word Problems in Daily Life: Sales Profits. Strategies for
Success. Exercises.
4 Fighting Fear of Fractions
Math Memories. Common Problems. Hints for Studying Fractions.
What Is A Fraction? Properties of Fractions. Types of Fractions.
Converting Between Mixed Numbers and Improper Fractions.
Equivalent Fractions. Reducing to Lowest Terms. Lowest Common
Denominator. Addition and Subtraction of Fractions. Multiplication
of Fractions. Division of Fractions. Fractions in Daily Life: Moving
Furniture. Fractions in Daily Life: Measuring Fabric. Strategies for
Success. Exercises.
5 Daring to Do Decimals
Math Memories. Common Problems. Hints for Studying Decimals.
Naming Decimals. Estimation. Addition and Subtraction of Decimals.
Multiplication of Decimals. Decimals in Daily Life: Calculating Cost.
Division of Decimals. Decimals in Daily Life: Calculating Mileage.
Strategies for Success. Exercises.
6 Gaining Proficiency with Percents
Math Memories. Common Problems. Hints for Studying Percents.
Converting Percents to Fractions. Converting Percents to Decimals.
Converting Decimals to Percents. Converting Fractions to Percents.
Percents in Daily Life: Discounts. Percents in Daily Life: Interest.
Percents in Daily Life: Tipping. Percents in Daily Life: Taxes. Strategies
for Success. Exercises.
7 Getting the Most out of Graphs
Math Memories. Commong Problems. Hints for Studying Graphs. Bar
Graphs in Daily Life. Pictographs in Daily Life. Line Graphs in Daily
Life. Pie Charts in Daily Life. Strategies for Success. Exercises.
8 Succeeding with Signed Numbers
Math Memories. Common Problems. Hints for Studying Signed
Numbers. Addition of Signed Numbers. Subtraction of Signed
Numbers. Multiplication of Signed Numbers. Division of Signed
Numbers. Signed Numbers in Daily Life: Bank Account Balance.
Signed Numbers in Daily Life: Elevation. Strategies for Success.
Exercises.
9 Mastering Measurement
Math Memories. Common Problems. Hints for Studying Measurement.
Units of Time. Units of Length. Units of Weight. Units of Volume. The
Metric System. Estimating Conversions Between English and Metric
Units. Measurement in Daily Life: Unit Price. Strategies for Success.
Exercises. 10 Grasping Geometry: Math Memories. Commong
Problems. Hints for Studying Geometry. Perimeter. Geometry in
Daily Life: Perimeter. Area. Geometry in Daily Life: Area. Circles.
Geometry in Daily Life: Circles. Volume. Geometry in Daily Life:
Volume. Strategies for Success. Exercises.
7
MATHEMATICS FOR TECHNICIANS
Fifth Edition
By Blair Alldis, former Head Teacher of Mathematics, Randwick College
of TAFE, Australia
2002 / 304 pages
ISBN-13: 978-0-07-471157- 6 / MHID: 0-07-471157-1 (with CD)
McGraw-Hill Australia Title
Contents
Preface
Chapter 1 Fractions and Decimals
Chapter 2 Ratio, Proportion and Percentage
Chapter 3 Measurement and Mensuration
Chapter 4 Introduction to Algebra
Chapter 5 Formulae: evaluation and transposition
Chapter 6 Introduction to Geometry
Chapter 7 Geometry of Triangles and Quadrilaterals
Chapter 8 Geometry of the Circle
Chapter 9 Straight Line Coordinate Geometry
Chapter 10 Introduction to Trigonometry
Chapter 11 Indices and Radicals
Chapter 12 Polynomials
Chapter 13 Functions and their Graphs
Chapter 14 Logarithms and Exponential Equations
Chapter 15 Non-Linear Empirical Equations
Chapter 16 Compound Interest: exponential growth and decay
Chapter 17 Circular Functions
Chapter 18 Phase Angles: more graphs of trigonometrical functions
Chapter 19 Trigonometry of Oblique Triangles
Chapter 20 Trigonometrical Identities
Chapter 21 Introduction to Vectors. Answers to chapter exercises
and self-test problems.
SCHAUM’S A-Z MATHEMATICS
By John Berry; Ted Graham and Elizabeth Berry
2004 / 288 pages
ISBN-13: 978-0-07-141936-9 / MHID: 0-07-141936-5
A Schaum’s Publication
Schaum’s A-Z handbooks make excellent complements to course
textbooks and test preparation guides. Ideal for ambitious high school
seniors—especially AP students—and college freshmen, they feature
concise, thoroughly cross-referenced definitions of hundreds of key
terms and phrases that help students quickly break through the
jargon barrier. Clear explanations of key concepts, supplemented
with lucid illustrations, help build mastery of theory and provide a
ready reference to supplement class work.
EVERYDAY MATH DEMYSTIFIED
How to Solve Word Problems in
Mathematics
By Stan Gibilisco
2004 / Softcover / 440 pages
ISBN-13: 978-0-07-143119-4 / MHID: 0-07-143119-5
A Professional Publication
By David Wayne, NJ Public Schools
2001 / 176 pages
ISBN-13: 978-0-07-136272-6 / MHID: 0-07-136272-X
Contents
PART ONE: EXPRESSING QUANTITIES
Chapter 1. Numbers and Arithmetic
Chapter 2. How Variables Relate
Chapter 3. Extreme Numbers
Chapter 4. How Things Are Measured
Test: Part One
PART TWO: FINDING UNKNOWNS
Chapter 5. Basic Algebra
Chapter 6. More Algebra
Chapter 7. A Statistics Sampler
Chapter 8. Taking Chances
Test: Part Two
PART THREE: SHAPES AND PLACES
Chapter 9. Geometry on the Flats
Chapter 10. Geometry in Space
Chapter 11. Graphing It
Chapter 12. A Taste of Trigonometry
Test: Part Three
PART FOUR: MATH IN SCIENCE
Chapter 13. Vectors and 3D
Chapter 14. Growth and Decay
Chapter 15. How Things Move
Test: Part Four. Final Exam. Answers to Quiz, Test, and Exam
Questions. Suggested Additional References. Index
Contents
Chapter 1: Measurement, Estimation, and Using Formulas
Chapter 2: Using Algebraic Equations to Solve Problems
Chapter 3: Word Problems Involving Ratio, Proportion, and
Percentage
Chapter 4: Word Problems Involving Geometry and Trignometry
Chapter 5: Word Problems Involving Statistics, Counting, and
Probability
Chapter 6: Miscellaneous Problem Drill. Appendix: A Brief Review of
Solving Equations.
SCHAUM’S OUTLINE OF REVIEW OF
ELEMENTARY MATHEMATICS
Second Edition
By Barnett Rich (deceased), Philip Schmidt, State University College—
New Paltz
1997 / 288 pages
ISBN-13: 978-0-07-052279-4 / MHID: 0-07-052279-0
http://books.mcgraw-hill.com/cgi-bin/getbook.pl?isbn=0070522790&
adkey=W02003
Contents
Fundamentals of Arithmetic: Number
Fundamentals of Arithmetic and Introduction to Calculators
Fractions
Decimals
Percents
Signed Numbers
Fundamentals of Algebra: Laws and Operations
Fundamentals of Algebra: Equations and Formulas
Ratios, Proportions, and Rates. Fundamentals of Geometry
HOW TO SOLVE WORD PROBLEMS IN
ARITHMETIC
By Phyllis Pullman
2001 / 160 pages
ISBN-13: 978-0-07-136271-9 / MHID: 0-07-136271-1
Contents
Chapter 1: Approaching Word Problems
Chapter 2: Reviewing the Basics
Chapter 3: Problems Involving Perimeter and Area
Chapter 4: Problems Involving the Circle
Chapter 5: Other Geometry Problems
Chapter 6: Problems Involving Percent
Chapter 7: Problems Involving Proportions
Chapter 8: Problems Involving Statistics
Chapter 9: Number Problems
Chapter 10: Problems Involving Problem Solving Skills Other Than
Arithmetic
Chapter 11: Some Mathematical Curiosities and Other Fun Stuff
Chapter 12: Miscellaneous Problem Drill.
Complimentary desk copies are available for
course adoption only. Kindly contact your
local McGraw-Hill Representative or fax the
Examination Copy Request Form available on
the back pages of this catalog.
Visit McGraw-Hill Education
Website: www.mheducation.com
COMPLIMENTARY COPIES
8
PreAlgebra
CHAPTER 4 Applications of Fractions and Equations
Pretest Chapter 4
4.1 Addition and Subtraction of Fractions
4.2 Operations on Mixed Numbers
4.3 Complex Fractions
4.4 Applications Involving Fractions
4.5 Equations Containing Fractions
4.6 Applications of Linear Equations in One Variable
Summary
Summary and Review Exercises
Chapter Test Cumulative Test for Chapters 1 to 4
CHAPTER 5 Decimals
Pretest Chapter 5
5.1 Introduction to Decimals, Place Value, and Rounding
5.2 Addition and Subtraction of Decimals
5.3 Multiplication of Decimals
5.4 Division of Decimals
5.5 Fractions and Decimals
5.6 Equations Containing Decimals
5.8 Applications
Summary
CHAPTER 6 Ratio, Rate, and Proportion
Pretest Chapter 6
6.1 Ratios
6.2 Rates
6.3 Proportions
6.4 Similar Triangles and Proportions
6.5 More Applications of Proportion
6.6 Linear Measurement and Conversion
Summary
CHAPTER 7 Percent
Pretest Chapter 7
7.1 Percents, Decimals, and Fractions
7.2 Solving Percent Problems Using Proportions
7.3 Solving Percent Applications Using Equations
7.4 Applications: Simple and Compound Interest
7.5 More Applications of Percent Summary
CHAPTER 8 Geometry
Pretest Chapter 8
8.1 Lines and Angles
8.2 Perimeter and Circumference
8.3 Area and Volume
Summary
Chapter Test. Cumulative Test for Chapters 1 to 8
CHAPTER 9 Graphing and Introduction to Statistics
Pretest Chapter 9
9.1 Circle Graphs
9.2 Pictographs, Bar Graphs, and Line Graphs
9.3 The Rectangular Coordinate System
9.4 Linear Equations in Two Variables
9.5 Mean, Median, and Mode
Summary
Chapter Test. Cumulative Test for Chapters 1 to 9
CHAPTER 10 Polynomials
Pretest Chapter 10
10.1 Introduction to Polynomials
10.2 Addition and Subtraction of Polynomials
10.3 Multiplying Polynomials
10.4 Introduction to Factoring Polynomials
Summary
Chapter Test. Practice Final Exam Chapters 1 to 10
PREALGEBRA
Second Edition
By Donald Hutchison, Barry Bergman, and Stefan Baratto, all of
Clackamas Community College
2007 (December 2005) / Softcover
ISBN-13: 978-0-07-325033-5 / MHID: 0-07-325033-3
(with MathZone)
Browse http://www.mhhe.com/streeter
Prealgebra: An Integrated Equations Approach, 2e, by Hutchison/
Bergman/Baratto extends the successful Streeter series in
developmental mathematics. This worktext utilizes an integrated
equations approach that pairs arithmetic concepts alongside
corresponding algebraic concepts. Beginning in chapter 1, students
are gradually exposed to key algebraic concepts such as variables
and equations. In this way, students gradually build their confidence
dealing with basic algebra concepts and are better prepared for an
introductory algebra course. Integers, fractions, and decimals are
used frequently after their initial introduction, developing students’
comfort with them. Students also develop valuable critical thinking
skills through numerous, varied examples and exercises that focus
on real-world applications and problem solving. The worktext is
Contents
CHAPTER 1 Whole Numbers
Pretest Chapter 1
1.1 Introduction to Whole Numbers, Place Value
1.2 Addition of Whole Numbers
1.3 Subtraction of Whole Numbers
1.4 Rounding, Estimation, and Ordering of Whole Numbers
1.5 Multiplication of Whole Numbers
1.6 Division of Whole Numbers
1.7 Exponents
1.9 An Introduction to Equations
Summary
Chapter Test
CHAPTER 2 Integers and Introduction to Algebra
Pretest Chapter 2
2.1 Introduction to Integers
2.2 Addition of Integers
2.3 Subtraction of Integers
2.4 Multiplication of Integers
2.5 Division of Integers
2.6 Introduction to Algebra: Variables and Expressions
2.8 Simplifying Algebraic Expressions
2.9 Introduction to Linear Equations
2.10 The Addition Property of Equality
Summary
Chapter Test
Cumulative Test for Chapters 1 and 2
CHAPTER 3 Fractions and Equations
Pretest Chapter 3
3.1 Introduction to Fractions
3.2 Prime Numbers and Factorization
3.3 Equivalent Fractions
3.4 Multiplication and Division of Fractions
3.5 The Multiplication Property of Equality
3.6 Linear Equations in One Variable
Summary
Chapter Test
Cumulative Test for Chapters 1 to 3
9
By Daniel Bach, Diablo Valley College and Patricia Leitner, Diablo
Valley College
2006 / Softcover
ISBN-13: 978-0-07-310157-6 / MHID: 0-07-310157-5
(with MathZone)
http://www.mhhe.com/bach
Bach/Leitner’s progressive text lays a solid foundation for elementary
algebra that carefully addresses student needs. The authors’ clear,
non-intimidating, and humorous style reassures math-anxious readers.
Unlike workbook-format Prealgebra texts that stress competence at
procedures, this text emphasizes understanding and mastery through
careful step-by-step explanations that strengthen students’ long-term
abilities to conceptualize and solve problems. The text’s innovative
sequencing builds students’ confidence with arithmetic operations
early on before extending the basic concepts to algebraic expressions
and equations. The authors’ unusually thorough introduction to
variables eases students through the crucial transition from working
with numbers. Throughout the text, interesting applied examples and
exercises and math-appreciation features highlight key concepts at
work in a wide variety of real-world contexts.
Contents
Part I Arithmetic Operations
1 Working with Whole Numbers
1.1 Whole Numbers and Place Value, Reading Tables
1.2 Addition and Subtraction of Whole Numbers, Estimation and
Calculators
1.3 Multiplication of Whole Numbers, the Laws of Arithmetic
1.4 Division, Quotients and Remainders; Divisibility
1.5 Prime Numbers, Factor Trees, Prime Factorizations
1.6 Greatest Common Divisors and Least Common Multiples
A World of Math
Chapter Summary, Chapter Review, Chapter Test
2 Whole Numbers and their Negatives
2.1 The Number Line, Integers, Absolute Value, Reading Bar
Charts
2.2 Inequality Symbols, Comparison of Integers
2.3 Addition of Positive and Negative Numbers
2.4 Subtraction of Positive and Negative Numbers; Applications
2.5 Multiplication and Division of Positive and Negative Numbers
2.6 Order of Operations and Using Parentheses
A World of Math. Chapter Summary, Chapter Review, Chapter Test
3 Fractions, Decimals, and Percentages
3.1 Signed Fractions, Lowest Terms, Improper Fractions and Mixed
Numbers
3.2 Ratios, Rates, Proportions, and Probability: An Introduction
3.3 Multiplying and Dividing Fractions; Reciprocals
3.4 Adding and Subtracting Fractions and Order of Operations
3.5 Working with Decimal Numbers
3.6 Introduction to Percentages and Pie Charts
A World of Math
4 Exponents and Square Roots
4.1 Exponents and Scientific Notation
4.2 Rules of Exponents (Part 1), Integer Exponents
4.3 Rules of Exponents (Part 2)
4.4 Exponents and the Order of Operations
A World of Math
Part II Expressions
5 Introduction to Variables
5.1 Introduction: What is a Variable?
5.2 Expressions Containing Variables, Geometry Formulas, Laws
of Arithmetic
5.3 Evaluating Algebraic Expressions; The Prime Code
5.4 Applications: Translating Word Phrases into Expressions
A World of Math
10
6 Working With Polynomials
6.1 Mono-mials and Like Terms
6.2 Adding and Subtracting Polynomials
6.3 Multiplying Monomials; Rules of Exponents Revisited
6.4 Multiplying Polynomials; The FOIL Method
6.5 Factoring Out a Common Factor
A World of Math
7 Algebraic Fractions
7.1 Reducing Algebraic Fractions to Lowest Terms
7.2 Multiplying and Dividing Algebraic Fractions
7.3 Building Fractions; Least Common Multiples
7.4 Adding and Subtracting Algebraic Fractions
A World of Math
Part III Equations
8 Solving Equations and Applications
8.1 Intro-duction: What is an Equation?
8.2 Solution Sets and Missing Number Statements
8.3 Solving Linear Equations Using Addition and Subtraction
8.4 Solving Linear Equations and Proportions Using Multiplication
and Division
8.5 Applications: Translating Word Statements Into Equations
8.6 Linear Equalities and Their Uses
A World of Math
9 Further Applications of Equations
9.1 Rates, Ratios and Proportions: A Variable Approach
9.2 Applications With More Than One Unknown Quantity
9.3 Percentage and Simple Interest Applications
9.4 Distance-Rate-Time and Mixture Problems
A World of Math Chapter Summary, Chapter Review, Chapter Test
10 Graphing and the Coordinate Plane
10.1 The Coordinate Plane; Plotting Points
10.2 Equations With Two Variables and Their Graphs
10.3 The Slope of a Line, Rates of Change
10.4 Finding the Equation of a Line (Optional)
10.5 Statistics, Charts, and Graphs
A World of Math
11 Geometry and Measurement
11.1 Geometry of Lines, Angles, and Polygons
11.2 Triangles; Congruence and Similarity; The Pythagorean
Theorem
11.3 Perimeters and Areas of Common Shapes
11.4 Composite Shapes, Volumes and Surface Areas
11.5 Measurement and Conversion Using U.S. Units
11.6 The Metric System and Conversion Between Systems
A World of Math
Pre-algebra
Third Edition
[email protected]
Beginning Algebra
1.2 The Real Numbers
1.3 Adding and Subtracting Real Numbers
1.4 Multiplying and Dividing Real Numbers
1.6 Properties of the Real Numbers
1.7 Simplifying Expressions
Chapter 2: Equations, Problem Solving, and Inequalities
2.1 The Addition and Subtraction Properties of Equality
2.2 The Multiplication and Division Properties of Equality
2.3 Linear Equations
2.4 Problem Solving: Integer, General, and Geometry Problems
2.5 Problem Solving: Motion, Mixture, and Investment Problems
2.6 Formulas and Geometry Applications
2.7 Properties of Inequalities
Chapter 3: Graphs of Linear Equations, Inequalities, and
Applications
3.1 Line, Bar Graphs and Applications
3.2 Graphing Linear Equations in Two Variables
3.3 Graphing Lines Using Intercepts: Horizontal and Vertical Lines
3.4 The Slope of a Line: Parallel and Perpendicular Lines
3.5 Graphing Lines Using Points and Slopes
3.6 Applications of Equations of Lines
3.7 Graphing Inequalities in Two Variables
Chapter 4: Exponents and Polynomials
4.1 The Product, Quotient, and Power Rules for Exponents
4.2 Integer Exponents
4.3 Application of Exponents: Scientific Notation
4.4 Polynomials: An Introduction
4.6 Multiplication of Polynomials
4.7 Special Products of Polynomials
4.8 Division of Polynomials
Chapter 5: Factoring
5.1 Common Factors and Grouping
5.2 Factoring x^2+bx+c
5.3 Factoring ax^2+bx+c, a¿0
5.4 Factoring Squares of Binomials
5.5 A General Factoring Strategy
5.6 Solving Quadratic Equations by Factoring
5.7 Applications of Quadratics
Chapter 6: Rational Expressions
6.1 Building and Reducing Rational Expressions
6.2 Multiplication and Division of Rational Expressions
6.3 Addition and Subtraction of Rational Expressions
6.5 Solving Equations Containing Rational Expressions
6.6 Ratio, Proportion, and Applications
6.7 Direct and Inverse Variation
Chapter 7: Solving Systems of Linear Equations and Inequalities
7.1 Solving Systems of Equations by Graphing
7.2 Solving Systems of Equations by Substitution
7.3 Solving Systems of Equations by Elimination
7.4 Coin, General Motion, and Investment Problems
7.5 Systems of Linear Inequalities
Chapter 8: Roots and Radicals
8.1 Finding Roots
8.2 Multiplication and Division of Radicals
8.3 Addition and Subtraction of Radicals
8.4 Simplifying Radicals
8.5 Applications
Chapter 9: Quadratic Equations
9.1 Solving Quadratic Equations by the Square Root Property
9.2 Solving Quadratic Equations by Completing the Square
9.3 Solving Quadratic Equations by the Quadratic Formula
9.4 Graphing Quadratic Equations
9.5 The Pythagorean Theorem and Other Applications
9.6 Functions
New
INTRODUCTORY ALGEBRA
Third Edition
By Ignacio Bello, University of South Florida-Tampa
2009 (January 2008) / 800 pages
ISBN-13: 978-0-07-353343-8 / MHID: 0-07-353343-2
Introductory Algebra prepares students for Intermediate Algebra by
covering fundamental algebra concepts and key concepts needed for
further study. Students of all backgrounds will be delighted to find a
refreshing book that appeals to every learning style and reaches out
to diverse demographics. Through down-to-earth explanations, patient
skill-building, and exceptionally interesting and realistic applications,
this worktext will empower students to learn and master algebra in
the real world.
New to this edition
Interesting writing style with student-centric context.
Paired Examples/Problems: examples are placed adjacent
to simmilar problems intended for students to obtain immediate
reinforcement of the skill they have just learned. There is an
abundance of quality, easily understood examples/problems
throughout the text.
Realistic applications based on real data which help the students
relate math to their own lives.
“Translate It” boxes to help students learn how to turn phrases
into equations. Part of the RSTUV method.
New “Calculator Corner” boxes explaining usage of calculators
found before the exercises sets.
End-of-section exercise sets to include exercises keyed to
objectives and to examples, applied exercises, and “skill checkers”
to confirm/reinforce skills needed for the next section.
McGraw-Hill’s MathZone is a complete, online tutorial and
course management system for mathematics and statistics,
designed for greater ease of use than any other system available.
Instructors can create and share courses and assignments with
colleagues and adjuncts in a matter of a few clicks of a mouse.
All instructor teaching resources are accessed online, as well as
student assignments, questions, e-Professors, online tutoring
and video lectures which are directly tied to text specific material.
MathZone courses are customized to your textbook, but you can
edit questions and algorithms, import your own content, create
announcements and due dates for assignments. MathZone has
automatic grading and reporting of easy-to-assign algorithmically
generated homework, quizzing and testing. Student activity within
MathZone is automatically recorded and available to you through
a fully integrated grade book than can be downloaded to Excel.
Go to www.mathzone.com to learn more
Contents
Introductory Algebra
Chapter R: Prealgebra Review
R.1 Fractions: Building and Reducing
R.2 Operations with Fractions and Mixed Numbers
R.3 Decimals and Percents
Chapter 1: Real Numbers and Their Properties
1.1 Introduction to Algebra
11
Contents
New
ELEMENTARY ALGEBRA
Sixth Edition
By Mark Dugopolski
2009 (January 2008)
ISBN-13: 978-0-07-722479-0 / MHID: 0-07-722479-5
Browse: http://www.mhhe.com/dugopolski
Elementary Algebra, 6e is part of the latest offerings in the successful
Dugopolski series in mathematics. The author’s goal is to explain
mathematical concepts to students in a language they can understand.
In this book, students and faculty will find short, precise explanations
of terms and concepts written in understandable language. The author
uses concrete analogies to relate math to everyday experiences. For
example, when the author introduces the Commutative Property of
Addition, he uses a concrete analogy that “the price of a hamburger
plus a Coke is the same as a Coke plus a hamburger”. Given the
importance of examples within a math book, the author has paid close
attention to the most important details for solving the given topic.
Dugopolski includes a double cross-referencing system between the
examples and exercise sets, so no matter which one the students
start with, they will see the connection to the other. Finally, the author
finds it important to not only provide quality, but also a good quantity
of exercises and applications. The Dugopolski series is known for
providing students and faculty with the most quantity and quality
of exercises as compared to any other developmental math series
on the market. In completing this revision, Dugopolski feels he has
developed the clearest and most concise developmental math series
on the market, and he has done so without comprising the essential
information every student needs to become successful in future
mathematics courses. The book is accompanied by numerous useful
supplements, including McGraw-Hill’s online homework management
system, MathZone.
New to this edition
Subsection heads are now in the end of section exercise sets,
and section heads are now in the Chapter Review Exercises.
References to page numbers on which Strategy Boxes are
located have been inserted into the direction lines for the exercises
when appropriate.
Study tips have been removed from the margins to give the pages
a better look. Two study tips now precede each exercise set.
McGraw-Hill’s MathZone is a complete, online tutorial and course
management system for mathematics and statistics, designed for
greater ease of use than any other system available. Instructors
can create and share courses and assignments with colleagues and
adjuncts in a matter of a few clicks of a mouse. All instructor teaching
resources are accessed online, as well as student assignments,
questions, e-Professors, online tutoring and video lectures which are
directly tied to text specific material. MathZone courses are customized
to your textbook, but you can edit questions and algorithms, import your
own content, create announcements and due dates for assignments.
MathZone has automatic grading and reporting of easy-to-assign
algorithmically generated homework, quizzing and testing. Student
activity within MathZone is automatically recorded and available to you
through a fully integrated grade book than can be downloaded to Excel.
Go to www.mathzone.com to learn more.
12
TO THE STUDENT
PREFACE
1 Real Numbers and Their Properties
1.2 Fractions
1.3 Addition and Subtraction of Real Numbers
1.4 Multiplication and Division of Real Numbers
1.5 Exponential Expressions and the Order of Operations
1.6 Algebraic Expressions
1.8 Using the Properties to Simplify Expressions
Chapter 1 Wrap-Up
• Summary
• Enriching Your Mathematical Word Power
• Review Exercises
• Chapter 1 Test
• Critical Thinking
2 Linear Equations and Inequalities in One Variable 2
.1 The Addition and Multiplication Properties of Equality
2.2 Solving General Linear Equations
2.3 More Equations
2.4 Formulas
2.5 Translating Verbal Expressions into Algebraic Expressions
2.6 Number, Geometric, and Uniform Motion Applications
2.7 Discount, Investment, and Mixture Applications
2.8 Inequalities
2.9 Solving Inequalities and Applications
Chapter 2 Wrap-Up
• Summary
• Chapter 2 Test
• Making Connections: A review of Chapters 1-2
3 Linear Equations in Two Variables and Their Graphs
3.1 Graphing Lines in the Coordinate Plane
3.2 Slope
3.3 Equations of Lines in Slope-Intercept Form
3.4 The Point-Slope Form
3.5 Variations
Chapter 3 Wrap-Up
• Summary
• Chapter 3 Test
• Making Connections: a review of Chapters 1-3
4 Systems of Linear Equations and Inequalities
4.1 The Graphing Method
4.2 The Substitution Method
4.3 The Addition Method
4.4 Graphing Linear Inequalities in Two Variables
4.5 Graphing Systems of Linear Inequalities
Chapter 4 Wrap-Up
• Summary
• Chapter 4 Test
5 Exponents and Polynomials
5.1 The Rules of Exponents
5.2 Negative Exponents and Scientific Notation
5.5 Multiplication of Binomials
5.6 Special Products
Chapter 5 Wrap-Up
• Summary
• Chapter 5 Test
6 Factoring
6.1 Factoring Out Common Factors
6.2 Special Products and Grouping
6.3 Factoring the Trinomial ax² + bx + c with a = 1
6.4 Factoring the Trinomial ax² + bx + c with a ¿ 1
6.5 The Factoring Strategy
Chapter 6 Wrap-Up
• Summary
• Chapter 6 Test
7 Rational Expressions
7.1 Reducing Rational Expressions
7.2 Multiplication and Division
7.3 Finding the Least Common Denominator
7.4 Addition and Subtraction
7.6 Solving Equations with Rational Expressions
7.7 Applications of Ratios and Proportions
7.8 Applications of Rational Expressions
Chapter 7 Wrap-Up
• Summary
• Chapter 7 Test
8 Powers and Roots
8.1 Roots, Radicals, and Rules
8.2 Simplifying Square Roots
8.3 Operations with Radicals
8.4 Solving Equations with Radicals and Exponents
8.5 Fractional Exponents
Chapter 8 Wrap-Up
• Summary
• Chapter 8 Test
9 Quadratic Equations, Parabolas, and Functions
9.1 The Square Root Property and Factoring
9.2 Completing the Square
9.3 The Quadratic Formula
9.4 Applications of Quadratic Equations
9.5 Complex Numbers
9.6 Graphing Parabolas
9.7 Introduction to Functions
9.8 Combining Functions
Chapter 9 Wrap-Up
• Summary
• Chapter 9 Test
Appendix A: Geometry Review Exercises
Appendix B: Sets
Appendix C: Final Exam Review Answers to Selected Exercises
Index
New
BEGINNING ALGEBRA
Seventh Edition
2008 (December 2006)
ISBN-13: 978-0-07-330960-6 / MHID: 0-07-330960-5
Beginning Algebra, 7/e by Baratto/Bergman is part of the latest
offerings in the successful Streeter-Hutchison Series in Mathematics.
The seventh edition continues the hallmark approach of encouraging
the learning of mathematics by focusing its coverage on mastering
math through practice. This worktext seeks to provide carefully
detailed explanations and accessible pedagogy to introduce basic
algebra skills and put the content in context. The authors use a
three-pronged approach (I. Communication, II. Pattern Recognition,
and III. Problem Solving) to present the material and stimulate critical
thinking skills. Items such as Math Anxiety boxes, Check Yourself
exercises, and Activities represent this approach and the underlying
philosophy of mastering math through practice. The exercise sets
have been expanded, organized, and clearly labeled. Vocational
and professional-technical exercises have been added throughout.
Repeated exposure to this consistent structure should help advance
the student’s skills in relating to mathematics. The book is designed
for a one-semester beginning algebra course and is appropriate
New to this edition
GRAPH PAPER INCLUDED--A graph paper card is bound into
the back of the book. This perforated card can be torn out and copied
as needed by the students, and can be used any time they need to
do graphing. An electronic version of the card is available through
the book’s website in the Information Center.
Contents
0 An Arithmetic Review
0.1 Prime Factorization and Least Common Multiples
0.2 Factoring and Mixed Numbers
0.3 Decimals and Percents
13
0.4 Exponents and the Order of Operations
0.5 Positive and Negative Numbers
1 The Language of Algebra
1.1 Properties of Real Numbers
1.4 From Arithmetic to Algebra
1.6 Adding and Subtracting Terms
1.7 Multiplying and Dividing Terms
2 Equations and Inequalities
2.1 Solving Equations by the Addition Property
2.2 Solving Equations by the Multiplication Property
2.3 Combining the Rules to Solve Equations
2.4 Formulas and Problem Solving
2.5 Applications of Linear Equations
2.6 Inequalities--An Introduction
3 Polynomials
3.1 Exponents and Polynomials
3.5 Dividing Polynomials
4 Factoring
4.1 An Introduction to Factoring
4.2 Factoring Trinomials of the Form x2 + bx + c
4.3 Factoring Trinomials of the Form ax2 + bx + c
4.4 Difference of Squares and Perfect Square Trinomials
4.5 Strategies in Factoring
5.1 Simplifying Rational Expressions
5.2 Multiplying and Dividing Rational Expressions
5.3 Adding and Subtracting Like Rational Expressions
5.4 Adding and Subtracting Unlike Rational Expressions
5.5 Complex Rational Expressions
5.6 Equations Involving Rational Expressions
6 An Introduction to Graphing
6.1 Solutions of Equations in Two Variables
6.2 The Rectangular Coordinate System
6.3 Graphing Linear Equations
6.4 The Slope of a Line
6.5 Reading Graphs
7 Graphing and Inequalities
7.1 The Slope-Intercept Form
7.2 Parallel and Perpendicular Lines
7.4 Graphing Linear Inequalities
7.5 An Introduction to Functions
8 Systems of Linear Equations
8.1 Systems of Linear Equations: Solving by Graphing
8.2 Systems of Linear Equations: Solving by the Addition Method
8.3 Systems of Linear Equations: Solving by Substitution
8.4 Systems of Linear Inequalities
9 Exponents and Radicals
9.1 Roots and Radicals
9.2 Simplifying Radical Expressions
9.3 Adding and Subtracting Radicals
9.4 Multiplying and Dividing Radicals
9.5 Solve Radical Equations
9.6 Applications of the Pythagorean Theorem
10 Quadratic Equations
10.1 More on Quadratic Equations
10.2 Completing the Square
10.4 Graphing Quadratic Equations
New
BEGINNING ALGEBRA
Second Edition
By Julie Miller and Molly O’Neill of Daytona
Beach Community College
2008 (January 2007)
ISBN-13: 978-0-07-331267-5 / MHID: 0-07-331267-3
Building on its first-edition success, Beginning Algebra 2/e by
Miller/O’Neill continues to offer an enlightened approach grounded
in the fundamentals of classroom experience. The practice of many
instructors in the classroom is to present examples and have their
students solve similar problems. This is realized through the Skill
Practice Exercises that directly follow the examples in the textbook.
Throughout the text, the authors have integrated many Study Tips
and Avoiding Mistakes hints, which are reflective of the comments
and instruction presented to students in the classroom. In this way,
the text communicates to students, the very points their instructors
are likely to make during lecture, helping to reinforce the concepts
and provide instruction that leads students to mastery and success.
The authors included in this edition, Problem-Recognition exercises,
that many instructors will likely identify to be similar to worksheets
they have personally developed for distribution to students. The intent
of the Problem-Recognition exercises, is to help students overcome
what is sometimes a natural inclination toward applying problemsolving algorithms that may not always be appropriate. In addition,
the exercise sets have been revised to include even more core
exercises than were present in the first edition. This permits instructors
to choose from a wealth of problems, allowing ample opportunity for
students to practice what they learn in lecture to hone their skills and
develop the knowledge they need to make a successful transition into
Intermediate Algebra. In this way, the book perfectly complements any
learning platform, whether traditional lecture or distance-learning; its
instruction is so reflective of what comes from lecture, that students
will feel as comfortable outside of class, as they do inside class with
their instructor. For even more support, students have access to a
wealth of supplements, including McGraw-Hill’s online homework
management system, MathZone.
New to this edition
NEW! Problem Recognition Exercises Developmental math
students are sometimes conditioned into algorithmic thinking to the
point where they want to automatically apply various algorithms to
solve problems, whether it is meaningful or not. These exercises
were built to decondition students from falling into that trap. Carefully
crafted by the authors, the exercises focus on the situations where
students most often get “mixed-up.” Working the Problem Recognition
Exercises, students become conditioned to Stop, Think, and Recall
what method is most appropriate to solve each problem in the set.
NEW! Skill Practice exercises follow immediately after the
examples in the text. Answers are provided so students can check
their work. By utilizing these exercises, students can test their
understanding of the various problem-solving techniques given in
the examples.
NEW! The section-ending Practice Exercises are newly revised,
with even more core exercises appearing per exercise set. Many of
the exercises are grouped by section objective, so students can refer
back to content within the section if they need some assistance in
completing homework. Review Problems appear at the beginning
14
of most Practice Exercise Sets to help students improve their study
habits and to improve their long-term retention of concepts previously
introduced.
6.6 General Factoring Summary
6.7 Solving Equations Using the Zero Product Rule
7.1 Introduction to Rational Expressions
7.3 Least Common Denominator
7.6 Rational Equations
7.7 Applications of Rational Equations and Proportions
7.8 Variations
Chapter 8: Radicals
8.1 Introducion to Roots and Radicals
8.2 Simplifying Radicals
8.4 Multiplication of Radicals
8.5 Rationalization
8.6 Radical Equations
8.7 Exponents
Chapter 9: Functions, Complex Numbers, and Quadratic
Equations
9.2 Complex Numbers
9.3 The Square Root Property and Completing the Square
9.4 Quadratic Formula
9.5 Graphing Quadratic Functions
NEW! Mixed Exercises are found in many of the Practice
Exercise sets. The Mixed Exercises contain no references to
objectives. In this way, students are expected to work independently
without prompting--which is representative of how they would work
through a test or exam.
NEW! Study Skills Exercises appear at the beginning of the
Practice Exercises, where appropriate. They are designed to help
students learn techniques to improve their study habits including
exam preparation, note taking, and time management.
NEW! The Chapter Openers now include a variety of puzzles
that may be used to motivate lecture. Each puzzle is based on key
vocabulary terms or concepts that are introduced in the chapter.
Contents
Chapter R : Reference
R.1 Study Tips
R.2 Fractions
R.3 Decimals and Percents
R.4 Introduction to Geometry
Chapter 1: Set of Real Numbers
1.1 Sets of Numbers and the Real Number Line
1.3 Addition of Real Numbers
1.4 Subtraction of Real Numbers
1.6 Properties of Real Numbers and Simplifying Expressions
Chapter 2: Linear Equations and Inequalities
2.1 Addition, Subtraction, Multiplication and Division Properties of
Equality
2.3 Linear Equations: Clearing Fractions and Decimals
2.4 Applications of Linear Equations: Introduction to Problem
Solving
2.5 Applications Involving Percents
2.6 Formulas and Applications of Geometry
2.7 Linear Inequalities
Chapter 3: Graphing Linear Equations in Two Variables
3.1 Rectangular Coordinate System
3.3 Slope of a Line
3.4 Slope-Intercept Form of a Line
3.5 Point-Slope Formula
3.6 Applications of Linear Equations
Chapter 4: Systems of Linear Equations and Inequalities in Two
Variables
4.1 Solving Systems of Equations by the Graphing Method
4.2 Solving Systems of Equations by the Substitution Method
4.3 Solving Systems of Equations by the Addition Method
4.4 Applications of Linear Equations in Two Variables
4.5 Linear Inequalities in Two Variables
4.6 Systems of Linear Inequalities in Two Variables
Chapter 5: Polynomials and Properties of Exponents
5.1 Exponents: Multiplying and Dividing Common Bases
5.2 More Properties of Exponents
5.3 Definitions of b^0 and b^-n
5.4 Scientific Notation
Chapter 6: Factoring Polynomials
6.1 Greatest Common Factor and Factoring by Grouping
6.2 Factoring Trinomials of the Form x^2+ bx+ c (optional)
6.3 Factoring Trinomials: Trial-and-Error Method
6.4 Factoring Trinomials: AC Method
6.5 Factoring Binomials
INTRODUCTORY ALGEBRA
By Julie Miller, Daytona Beach Community College-Daytona Beach,
Molly O’Neill, Daytona Beach Community College-Daytona Beach, and
Nancy Hyde, Broward Community College
2007 (January 2006)
ISBN-13: 978-0-07-322969-0 / MHID: 0-07-322969-5
(with MathZone, Softcover)
ISBN-13: 978-0-07-327629-8 / MHID: 0-07-327629-4
(with MathZone, Hardcover)
ISBN-13: 978-0-07-330945-3 / MHID: 0-07-330945-1
(MP, Softcover)
ISBN-13: 978-0-07-330946-0 / MHID: 0-07-330946-X
(MP, Hardcover)
http://www.mhhe.com/moh
Introductory Algebra offers a refreshing approach to the traditional
content of the course. Presented in worktext format, Introductory
Algebra focuses on solving equations and inequalities, graphing,
polynomials, factoring, rational expressions, and radicals. Other
topics include quadratic equations and an introduction to functions
and complex numbers. The text reflects the compassion and insight
of its experienced author team with features developed to address
the specific needs of developmental level students.
Contents
R Reference: Fractions, Decimals, Percents, Geometry, and Study
Skills
1 The Set of Real Numbers
2 Linear Equations and Inequalities
3 Graphing Linear Equations in Two Variables
4 Systems of Linear Equations in Two Variables
5 Polynomials and Properties of Exponents
6 Factoring Polynomials
8 Radicals
9 Complex Numbers and Quadratic Equations
15
BOB MILLER’S ALGEBRA FOR THE
CLUELESS
Second Edition
ALGEBRA DEMYSTIFIED
By Rhonda Huettenmueller
2003 / 349 pages
ISBN-13: 978-0-07-138993-8 / MHID: 0-07-138993-8
By Bob Miller, City College of the City University of New York
2007 (July 2006) / 240 pages
ISBN-13: 978-0-07-147366-8 / MHID: 0-07-147366-1
Contents
A is for Algebra-and that’s the grade you’ll pull when you use Bob
Miller’s simple guide to the math course every college-bound kid
must take.
With eight books and more than 30 years of hard-core classroom
experience, Bob Miller is the frustrated student’s best friend. He breaks
down the complexities of every problem into easy-to-understand
pieces that any math-phobe can understand-and this fully updated
second edition of Bob Miller’s Algebra for the Clueless covers
everything a you need to know to excel in Algebra I and II.
Contents
TO THE STUDENT
Chapter 1: Natural Numbers and Introductory Terms
Chapter 2: Integers Plus More
Chapter 3: First-Degree Equations
Chapter 4: Problems with Words: Why So Many Students Have
Problems on the SAT
Chapter 5: Factoring
Chapter 6: Algebraic Fractions
Chapter 7: Radicals and Exponents
Chapter 8: Quadratics
Chapter 9: Points, Lines, and Planes
Chapter 10: Odds and Ends
Chapter 11: Miscellaneous Miscellany
APPENDIX 1: FRACTIONS, DECIMALS, PERCENTS, AND
GRAPHS
APPENDIX 2: SETS
ACKNOWLEDGMENTS
ABOUT BOB MILLER: IN HIS OWN WORDS
INDEX
Preface
CHAPTER 1: Fractions
CHAPTER 2: Introduction to Variables
CHAPTER 3: Decimals
CHAPTER 4: Negative Numbers
CHAPTER 5: Exponents and Roots
CHAPTER 6: Factoring
CHAPTER 7: Linear Equations
CHAPTER 8: Linear Applications
CHAPTER 9: Linear Inequalities
CHAPTER 10: Quadratic Equations
CHAPTER 11: Quadratic Applications
Appendix. Final Review. Index
Beginning/Intermediate
Algebra Combined
New
ELEMENTARY AND
INTERMEDIATE ALGEBRA
Third Edition
SCHAUM’S OUTLINE OF ELEMENTARY
ALGEBRA
Third Edition
By Mark Dugopolski
By Barnett Rich (deceased); Philip Schmidt, State University College—
New Paltz
2004 / 400 pages
ISBN-13: 978-0-07-141083-0 / MHID: 0-07-141083-X
2009 (January 2008)
ISBN-13: 978-0-07-722482-0 / MHID: 0-07-722482-5
ISBN-13: 978-0-07-128402-8 / MHID: 0-07-128402-8 [IE]
This third edition of the perennial bestseller defines the recent changes
in how the discipline is taught and introduces a new perspective on
the discipline. New material in this third edition includes:
• A modernized section on trigonometry
• An introduction to mathematical modeling
• Instruction in use of the graphing calculator
• 2,000 solved problems
• 3,000 supplementary practice problems and more
16
Elementary & Intermediate Algebra, 3e is part of the latest offerings
in the successful Dugopolski series in mathematics. The author’s
goal is to explain mathematical concepts to students in a language
they can understand. In this book, students and faculty will find short,
precise explanations of terms and concepts written in understandable
language. The author uses concrete analogies to relate math to
everyday experiences. For example, when the author introduces the
Commutative Property of Addition, he uses a concrete analogy that
“the price of a hamburger plus a Coke is the same as a Coke plus a
hamburger”. Given the importance of examples within a math book,
the author has paid close attention to the most important details
for solving the given topic. Dugopolski includes a double crossreferencing system between the examples and exercise sets, so no
matter which one the students start with, they will see the connection
to the other. Finally, the author finds it important to not only provide
quality, but also a good quantity of exercises and applications. The
Dugopolski series is known for providing students and faculty with
the most quantity and quality of exercises as compared to any other
developmental math series on the market. In completing this revision,
Dugopolski feels he has developed the clearest and most concise
developmental math series on the market, and he has done so without
comprising the essential information every student needs to become
successful in future mathematics courses. The book is accompanied
by numerous useful supplements, including McGraw-Hill’s online
homework management system, MathZone.
3.2 Slope
3.3 Equations of Lines in Slope-Intercept Form
3.5 Variations
Chapter 3 Wrap-Up
• Summary
• Chapter 3 Test
4.1 The Rules of Exponents
4.5 Multiplication of Binomials
4.6 Special Products
Chapter 4 Wrap-Up
• Summary
• Chapter 4 Test
5 Factoring
5.1 Factoring Out Common Factors
5.2 Special Products and Grouping
5.3 Factoring the Trinomial ax² + bx + c with a = 1
5.4 Factoring the Trinomial ax² + bx + c with a ¿ 1
5.5 The Factoring Strategy
Chapter 5 Wrap-Up
• Summary
• Chapter 5 Test
6.1 Reducing Rational Expressions
6.3 Finding the Least Common Denominator
6.6 Solving Equations Involving Rational Expressions
6.7 Applications of Ratios and Proportions
Chapter 6 Wrap-Up
• Summary
• Chapter 6 Test
7.1 Solving Systems by Graphing and Substitution
7.3 Systems of Linear Equations in Three Variables
Chapter 7 Wrap-Up
• Summary
• Chapter 7 Test
8 More on Inequalities
8.1 Compound Inequalities in One Variable
8.2 Absolute Value Equations and Inequalities
New to this edition
when appropriate.
Contents
TO THE STUDENT
PREFACE
1 Real Numbers and Their Properties
1.2 Fractions
1.3 Addition and Subtraction of Real Numbers
1.5 Exponential Expressions and the Order of Operations
1.8 Using the Properties to Simplify Expressions
Chapter 1 Wrap-Up
• Summary
• Chapter 1 Test
2 Linear Equations and Inequalities in One Variable
2.1 The Addition and Multiplication Properties of Equality
2.2 Solving General Linear Equations
2.3 More Equations
2.4 Formulas
2.5 Translating Verbal Expressions into Algebraic Expressions
2.6 Number, Geometric, and Uniform Motion Applications
2.7 Discount, Investment, and Mixture Applications
2.8 Inequalities
2.9 Solving Inequalities and Applications
Chapter 2 Wrap-Up
• Summary
• Chapter 2 Test
3 Linear Equations and Inequalities in Two Variables
17
• Chapter 13 Test
14 Sequences and Series
14.1 Sequences
14.2 Series
14.3 Arithmetic Sequences and Series
14.4 Geometric Sequences and Series
14.5 Binomial Expansions
Chapter 14 Wrap-Up
• Summary
• Chapter 14 Test
• Making Connections: A Review of Chapter 1-14
Appendix A: Geometry Review Exercises
Appendix B: Sets
Appendix C: Chapters 1-6 Diagnostic Test
Appendix D: Chapters 1-6 Review Answers to Selected Exercises
Index
8.3 Compound Inequalities in Two Variables
8.4 Linear Programming
Chapter 8 Wrap-Up
• Summary
• Chapter 8 Test
9 Radicals and Rational Exponents
9.1 Radicals
9.2 Rational Exponents
9.3 Adding, Subtracting, and Multiplying Radicals
9.4 Quotients, Powers, and Rationalizing Denominators
9.6 Complex Numbers
Chapter 9 Wrap-Up
• Summary
• Chapter 9 Test
10 Quadratic Equations and Inequalities
10.1 Factoring and Completing the Square
10.4 Graphing Parabolas
10.5 Quadratic and Rational Inequalities
Chapter 10 Wrap-Up
• Summary
• Chapter 10 Test
11 Functions
11.1 Functions and Relations
11.2 Graphs of Functions and Relations
11.3 Transformations of Graphs
11.4 Graphs of Polynomial Functions
11.5 Graphs of Rational Functions
11.7 Inverse Functions
Chapter 11 Wrap-Up
• Summary
• Chapter 11 Test
12 Exponential and Logarithmic Functions
12.1 Exponential Functions and Their Applications
12.2 Logarithmic Functions and Their Applications
12.3 Properties of Logarithms
12.4 Solving Equations and Applications
Chapter 12 Wrap-Up
• Summary
• Chapter 12 Test
13 Nonlinear Systems and the Conic Sections
13.1 Nonlinear Systems of Equations
13.2 The Parabola
13.3 The Circle
13.4 The Ellipse and Hyperbola
13.5 Second-Degree Inequalities
Chapter 13 Wrap-Up
• Summary
New
BEGINNING AND INTERMEDIATE ALGEBRA
Second Edition
By Sherri Messersmith, College of Dupage
2009 (February 2008)
ISBN-13: 978-0-07-722483-7 / MHID: 0-07-722483-3
Browse: http://www.mhhe.com/messersmith
Beginning and Intermediate Algebra, 2e, by Messersmith is the
first text in a series of future offerings in developmental mathematics.
The author presents the content in bite-size pieces, focusing not only
on how to solve mathematical concepts, but also explaining the why
behind those concepts. For students, learning mathematics is not
just about the memorization of concepts and formulas, but it is also
about the journey of learning how to problem solve. By breaking the
sections down into manageable chunks, the author has identified the
core places where students traditionally struggle, and then assists
them in understanding that material to be successful moving forward.
Proven pedagogical features, such as You Try problems after each
example, reinforce a student’s mastery of a concept. While teaching
in the classroom, Messersmith has created worksheets for each
section that fall into three categories: review worksheets/basic skills,
worksheets to teach new content, and worksheets to reinforce/pull
together different concepts. These worksheets are a great way to
both enhance instruction and to give the students more tools to be
successful in studying a given topic. The author is also an extremely
popular lecturer, and finds it important to be in the video series that
accompany her texts. Finally, the author finds it important to not
only provide quality, but also an abundant quantity of exercises
and applications. The book is accompanied by numerous useful
supplements, including McGraw-Hill’s online homework management
system, MathZone.
Messersmith – mapping the journey to mathematical success!
New to this edition
Mid-Chapter Summary: Several chapters contain a Mid-Chapter
Summary section. In keeping with the author’s philosophy of breaking
sections into manageable chunks, Messersmith includes a midchapter summary where needed to help the student to synthesize
key topics before moving onto the rest of the chapter.
Worksheets: There are worksheets for each section that fall
into three categories: review worksheets/basic skills, worksheets
18
questions, e-Professors, online tutoring and video lectures which
are directly tied to text specific material. MathZone courses are
customized to your textbook, but you can edit questions and
algorithms, import your own content, create announcements and due
dates for assignments. MathZone has automatic grading and reporting
of easy-to-assign algorithmically generated homework, quizzing and
testing. Student activity within MathZone is automatically recorded
and available to you through a fully integrated grade book than can
be downloaded to Excel. Go to www.mathzone.com to learn more.
to teach new content, and worksheets to reinforce/pull together
different concepts. These worksheets are a great way to both enhance
instruction and to give the students more tools to be successful
in studying a given topic. These will be available online through
MathZone.
In-Class Examples: In order to give the instructors additional
material to use in the classroom, a matching In-Class Example is
provided in the margin of the AIE for every example in the book.
You Try Problems: After nearly every example, there is a “You
Try” problem that mirrors that example. This provides students with
the opportunity to practice a problem similar to what the instructor
has presented before moving on to the next concept. Answers are
provided at the end of the section for immediate feedback.
Chapter-Opening Vignettes: Each chapter opens with a realworld vignette to capture the student’s attention and engage them
in the upcoming material. The openers fall into five different themes
for consistency sake.
Contents
Chapter 1: The Real Number System and Geometry
Section 1.1 Review of Fractions
Section 1.2 Exponents and Order of Operations
Section 1.3 Geometry Review
Section 1.4 Sets of Numbers and Absolute Value
Section 1.5 Addition and Subtraction of Real Numbers
Section 1.6 Multiplication and Division of Real Numbers
Section 1.7 Algebraic Expressions and Properties of Real Numbers
Chapter 2: Variables and Exponents
Section 2.1 Simplifying Expressions
Section 2.2a The Product Rule and Power Rules for Exponents
Section 2.2b Combining the Rules
Section 2.3a Integer Exponents with Real-Number Bases
Section 2.3b Integer Exponents With Variable Bases
Section 2.4 The Quotient Rule
Mid-Chapter Summary
Section 2.5 Scientific Notation
Section 3.1 Solving Linear Equations Part I
Section 3.2 Solving Linear Equations Part II
Section 3.3 Applications of Linear Equations to General Problems,
Consecutive Integers, and Fixed and Variable Cost
Section 3.4 Applications of Linear Equations to Percent Increase/
Decrease and Investment Problems
Section 3.5 Geometry Applications and Solving Formulas for a
Specific Variable
Section 3.6 Applications of Linear Equations to Proportions, d = rt,
and Mixture Problems
Section 3.7 Solving Linear Inequalities in One Variable
Section 3.8 Solving Compound Inequalities
Chapter 4: Linear Equations in Two Variables
Section 4.1 Introduction to Linear Equations in Two Variables
Section 4.2 Graphing by Plotting Points and Finding Intercepts
Section 4.3 The Slope of a Line
Section 4.4 The Slope-Intercept Form of a Line
Section 4.5 Writing an Equation of a Line
Section 4.6 Parallel and Perpendicular Lines
Section 4.7 Introduction to Functions
Section 4.8 Function Notation and Linear Functions
Chapter 5: Solving Systems of Linear Equations
Section 5.1 Solving Systems by Graphing
Section 5.2 Solving Systems by Substitution
Section 5.3 Solving Systems by the Elimination Method
Mid-Chapter Summary
Section 5.4 Applications of Systems of Two Equations
Section 5.5 Systems of Linear Equations in Three Variables
Chapter 6: Polynomials
Section 6.1 Review of Rules of Exponents
Section 6.2 Addition and Subtraction of Polynomials
Section 6.3 Multiplication of Polynomials
Section 6.4 Division of Polynomials
Section 7.1 The Greatest Common Factor and Factoring by
Grouping
Learning Objectives are clearly identified at the beginning
of each section. The objectives then appear within the body of the
text, showing when a particular objective is about to be developed.
References are also included within the exercise sets to help students
quickly reference related material if they need more practice.
Be Careful Boxes: There are some mistakes that are very
common for students to make. The “Be Careful!” boxes make students
aware of these common errors so that, hopefully, they will not make
these mistakes themselves.
Using Technology Boxes: For those instructors who want to
make use of graphing calculator-related material, Using Technology
Boxes are included at the ends of sections where relevant. For
those instructors who don’t want to use this material, they are easily
skipped.
End-of-Section Exercise: The end-of-section exercise sets
have been organized similarly to the examples—they are presented
from the most basic to the most rigorous so that students may see
how the concepts work at the simplest level before progressing to
more difficult problems. Messersmith has incorporated interesting
real-world, up-to-date, relevant information that will appeal to students
of all backgrounds into the applications in the book. Students have
identified a number of the problems as interesting and fun in previous
use. Within these exercises, students and faculty will find video,
calculator, and writing exercise icons.
Chapter Summary: The comprehensive Summaries at the end
of each chapter enable students to review important concepts. A
definition or concept is presented, along with a related example and
a page reference from the relevant section.
End-of-Chapter Material: At the end of each chapter, you will
find a set of Review Exercises, a Chapter Test, and a comprehensive
Cumulative Review (starting with Chapter 2.)
Geometry Review: Chapter 1 includes a review of basic
concepts from geometry. Throughout beginning and intermediate
algebra courses, students need to know these basics, but many
do not. Section 1.3 provides the material necessary for faculty to
teach & students to practice the geometry concepts they will later in
the course. The book also includes geometry applications where
appropriate.
Functions Coverage: In response to reviewer feedback,
functions are now introduced beginning in chapter 4, and then
integrated in subsequent chapters as appropriate.
Beginning Algebra Review Appendix: Also as a result of
reviewer feedback, Messersmith has now included a Beginning
Algebra review in an appendix to bridge the gap to Intermediate
Algebra for those who need it. It is included as an Appendix so that
the instructor can use it where best fits their curriculum.
19
Section 7.2 Factoring Trinomials of the Form x^2 + bx + c
Section 7.3 Factoring Polynomials of the Form ax^2 + bx + c (a not
equal to 1)
Section 7.4 Factoring Binomials and Perfect Square Trinomials
Mid-Chapter Summary
Section 7.5 Solving Quadratic Equations by Factoring
Section 7.6 Applications of Quadratic Equations
Section 8.1 Simplifying Rational Expressions
Section 8.2 Multiplying and Dividing Rational Expressions
Section 8.3 Finding the Least Common Denominator
Section 8.4 Adding and Subtracting Rational Expressions
Mid-Chapter Summary
Section 8.5 Simplifying Complex Fractions
Section 8.6 Solving Rational Equations
Section 8.7 Applications
Chapter 9: Absolute Value Equations and Inequalities
Section 9.1 Solving Absolute Value Equations
Section 9.2 Solving Absolute Value Inequalities
Section 9.3 Linear Inequalities in Two Variables
Section 9.4 Solving Systems of Equations Using Matrices
Chapter 10: Radicals and Rational Exponents
Section 10.1 Finding Roots
Section 10.2 Rational Exponents
Section 10.3 Simplifying Expressions Containing Square Roots
Section 10.4 Simplifying Expressions Containing Higher Roots
Section 10.5 Adding and Subtracting Radicals
Section 10.6 Combining Multiplication, Addition, and Subtraction of
Radicals
Section 10.7 Dividing Radicals
Section 10.8 Solving Radical Equations
Chapter 11: Quadratic Equations
Section 11.1 Review of Solving Equations by Factoring
Section 11.2 Solving Quadratic Equations Using the Square Root
Property
Section 11.3 Complex Numbers
Section 11.4 Solving Quadratic Equations by Completing the
Square
Section 11.5 Solving Quadratic Equations Using the Quadratic
Formula
Mid-Chapter Summary
Section 11.6 Equations in Quadratic Form
Section 11.7 Formulas and Applications
Chapter 12: Functions and their Graphs
Section 12.1 Relations and Functions
Section 12.2 Graphs of Functions and Transformations
Section 12.3 Quadratic Functions and their Graphs
Section 12.4 Applications of Quadratic Functions and Graphing Other
Parabolas
Section 12.5 The Algebra of Functions
Section 12.6 Variation
Chapter 13: Inverse, Exponential, and Logarithmic Functions
Section 13.1 Inverse Functions
Section 13.2 Exponential Functions
Section 13.3 Logarithmic Functions
Section 13.4 Properties of Logarithms
Section 13.5 Common and Natural Logarithms and Change of Base
Section 13.6 Solving Exponential and Logarithmic Equations
Chapter 14: Conic Sections, Nonlinear Inequalities, and Nonlinear
Systems
Section 14.1 The Circle
Section 14.2 The Ellipse and the Hyperbola
Mid-Chapter Summary
Section 14.3 Nonlinear Systems of Equations
Section 14.4 Quadratic and Rational Inequalities
Chapter 15: Sequences and Series **Available online**
Section 15.1 Sequences and Series
Section 15.2 Arithmetic Sequences and Series
Section 15.3 Geometric Sequences and Series
Section 15.4 The Binomial Theorem
Appendix: Beginning Algebra Review
20
New
BEGINNING AND
2nd Edition
By James Hall and Brian Mercer of Parkland
College
2008 (January 2007)
ISBN-13: 978-0-07-322971-3 / MHID: 0-07-322971-7
Intended for schools that want a single text covering the standard
topics from Beginning and Intermediate Algebra. Topics are organized
by using the principles of the AMATYC standards as a guide, giving
strong support to teachers using the text. The book’s organization and
pedagogy are designed to work for students with a variety of learning
styles and for teachers with varied experiences and backgrounds.
The inclusion of multiple perspectives--verbal, numerical, algebraic,
and graphical--has proven popular with a broad cross section of
students. Use of a graphing calculator is assumed. BEGINNING AND
INTERMEDIATE ALGEBRA: THE LANGUAGE AND SYMBOLISM OF
MATHEMATICS is a reform-oriented book.
New to this edition
More Emphasis on Functions-- Chapters 7-11 will have more
of a functions emphasis than in the first edition of Beginning &
Intermediate Algebra.
More Exercises! New exercises have been added throughout
the text. Data has also been updated/revised to reflect more current
information in some problems.
Revised Page Layout--Some of the key pedigogical features
have been rearranged throughout the chapters. The Self-Check
answers now appear at the end of each section (not on the same
page as the questions), and several of the side notes have been
moved to the main text.
Contents
Chapter One: Review of Beginning Algebra
1.1 Preparing for an Algebra Class
1.2 The Real Number Line
1.4 Subtraction of Real Numbers
1.5 Multiplication of Real Numbers and Natural Number Exponents
1.6 Division of Real Numbers
Chapter Two: Linear Equations and Patterns
2.1 The Rectangular Coordinate System and Arithmetic Sequences
2.2 Function Notation and Linear Functions
2.3 Graphs of Linear Equations in Two Variables
2.4 Solving Linear Equations in One Variable Using the AdditionSubtraction Principle
2.5 Solving Linear Equations in One Variable Using the MultiplicationDivision Principle
2.6 Using and Rearranging Formulas
2.7 Proportions and Direct Variation
2.8 More Applications of Linear Equations
Chapter Three: Lines and Systems of Linear Equations in Two
Variables
3.1 Slope of a Line and Applications of Slope
3.2 Special Forms of Linear Equations in Two Variables
3.3 Solving Systems of Linear Equations in Two Variables Graphically
and Numerically
3.4 Solving Systems of Linear Equations in Two Variables by the
Substitution Method
3.5 Solving Systems of Linear Equations in Two Variables by the
Addition Method
3.6 More Applications of Linear Systems Cumulative Review of
Chapters 1-3
Chapter Four: Linear Inequalities and Systems of Linear
Inequalities
4.1 Solving Linear Inequalities Using the Addition-Subtraction
Principle
4.2 Solving Linear Inequalities Using the Multiplication-Divison
Principle
4.3 Solving Compound Inequalities
4.4 Solving Absolute Value Equations and Inequalities
4.5 Graphing Systems of Linear Inequalities in Two Variables
Chapter Five: Exponents and Operations with Polynomials
5.1 Product and Power Rules for Exponents
5.2 Quotient Rule and Zero Exponents
5.6 Dividing Polynomials
5.7 Special Products and Factors Cumulative Review of Chapters 1-5
Chapter Six: Factoring Polynomials
6.2 Factoring Trinomials of the Form x2 + bx + c
6.3 Factoring Trinomials of the Form ax2 + bx + c
6.4 Factoring Special Forms
6.5 A General Strategy for Factoring Polynomials
6.6 Solving Equations by Factoring
Chapter Seven: Quadratic Functions
7.1 Functions and Representations of Functions
7.2 Quadratic Functions,Parabolas and Modeling Using Quadratic
Equations
7.3 Solving Quadratic Equations and Inequalities by Factoring
7.4 Using the Quadratic Formula to find Real Solutions
7.5 More Applications of Quadratic Equations
7.6 Complex Numbers
7.7 Solving Quadratic Equations with Complex Solutions
Chapter Eight: Rational Functions
8.1 Properties of the Graphs of Rational Functions and Reducing
Rational Expressions
8.2 Multiplying and Dividing Rational Expressions
8.3 Adding and Subtracting Rational Expressions
8.4 Combining Operations and Simplifying Complex Rational
Expressions
8.5 Solving Equations Containing Rational Expressions
8.6 Inverse and Joint Variation and Other Applications Yielding
Equations with Fractions Cumulative Review of Chapters 1-8
Chapter Nine: Square Root and Cube Root Functions and
Rational Exponents
9.1 Evaluating Radical Expressions and Graphing Square Root and
Cube Root Functions
9.2 Adding and Subtracting Radical Expressions
9.3 Multiplying and Dividing Radical Expressions
9.4 Solving Equations Containing Radical Expressions
9.5 Rational Exponents and Radicals
Chapter Ten: Exponential and Logarithmic Functions
10.1 Geometric Sequences and Properties of the Graphs of
Exponential Functions
10.3 Logarithmic Functions
10.4 Evaluating Logarithms
10.6 Solving Exponential and Logarithmic Equations
10.7 Exponential Curve Fitting and Other Applications of Exponential
and Logarithmic Equations Cumulative Review of Chapters 1-10
Chapter Eleven: A Preview of College Algebra
11.1 Solving Systems of Linear Equations Using Augmented
Matrices
11.3 Horizontal and Vertical Translations of the Graphs of Functions
11.4 Stretching, Shrinking and Reflecting Graphs of Functions
11.5 Algebra of Functions
11.6 Sequences, Series and Summation Notation
11.7 Conic Sections
New
ELEMENTARY AND
3rd Edition
2008 (February 2007) / 1152 pages
ISBN-13: 978-0-07-304823-9 / MHID: 0-07-304823-2
ISBN-13: 978-0-07-110193-6 / MHID: 0-07-110193-4 [IE]
ISBN-13: 978-0-07-330961-3 / MHID: 0-07-330961-3
(with MathZone)
Elementary & Intermediate Algebra, 3/e by Baratto/Bergman is
part of the latest offerings in the successful Streeter-Hutchison
Series in Mathematics. The third edition continues the hallmark
approach of encouraging the learning of mathematics by focusing its
coverage on mastering math through practice. This worktext seeks
to provide carefully detailed explanations and accessible pedagogy
to introduce beginning and intermediate algebra concepts and put
the content in context. The authors use a three-pronged approach (I.
Communication, II. Pattern Recognition, and III. Problem Solving) to
present the material and stimulate critical thinking skills. Items such
as Math Anxiety boxes, Check Yourself exercises, and Activities
represent this approach and the underlying philosophy of mastering
math through practice. The exercise sets have been expanded,
organized, and clearly labeled. Vocational and professional-technical
exercises have been added throughout. Repeated exposure to this
consistent structure should help advance the student’s skills in relating
to mathematics. The book is designed for a combined beginning and
intermediate algebra course, or it can be used across two courses,
and is appropriate for lecture, learning center, laboratory, or selfpaced courses. It is accompanied by numerous useful supplements,
including McGraw-Hill’s online homework management system,
MathZone.
New to this edition
ACTIVITIES--An Activity is included in each chapter. These
Activities promote active learning by requiring students to find,
interpret, and manipulate real-world data. The Activity in each chapter
relates to the chapter-opening vignette, providing cohesiveness to
the chapter. Students can complete the Activities on their own, but
are best solved in small groups.
21
do graphing. An electronic version of the card is available through the
book’s website in the Information Center.
Contents
0 Prealgebra Review
0.1 A Review of Fractions
0.2 Real Numbers
0.5 Exponents and Order of Operation
1 From Arithmetic to Algebra
1.1 Transition to Algebra
1.4 Sets
2.1 Solving Equations by Adding and Subtracting
2.2 Solving Equations by Multiplying and Dividing
2.4 Literal Equations and Their Applications
2.5 Solving Linear Inequalities Using Addition
2.6 Solving Linear Inequalities Using Multiplication
2.7 Solving Absolute Value Equations (Optional)
2.8 Solving Absolute Value Inequalities (Optional)
3 Graphs and Linear Equations
3.2 The Cartesian Coordinate System
3.3 The Graph of a Linear Equation
3.5 Forms of Linear Equations
4.1 Positive Integer Exponents
4.2 Zero and Negative Exponents and Scientific Notation
4.5 Multiplication of Polynomials and Special Products
5.2 Factoring Special Polynomials
5.3* Factoring Trinomials: Trial and Error
5.4 Factoring Trinomials: The ac method
5.7 Problem Solving with Factoring
6 A Beginning Look at Functions
6.1 Relations and Functions
6.2 Tables and Graphs
6.4 Composition of Functions
6.5 Substitution and Synthetic Division
R A Review of Elementary Algebra
R.1 From Arithmetic to Algebra
R.2 Equations and Inequalities
R.3 Graphs and Linear Equations
R.4 Exponents and Polynomials
R.5 A Beginning Look at Functions
R.6 Factoring Polynomials
7.5 Solving Rational Expressions
7.6 Solving Rational Inequalities
8.1 Solving Systems of Linear Equations by Graphing
8.2 Systems of Equations in Two Variables with Applications
8.5 Matrices (Optional)
9 Graphical Solutions
9.1 Solving Equations in One Variable Graphically
9.2 Solving Linear Inequalities in One Variable Graphically
9.3 Solving Absolute Value Equations Graphically
9.4 Solving Absolute Value Inequalities Graphically
10 Radicals and Exponents
10.3 Operations on Radical Expressions
10.4 Solving Radical Equations
10.5 Rational Exponents 10.6 Complex Numbers
11 Quadratic Functions
11.3 An Introduction to the Parabola
11.4 Solving Quadratic Inequalities
12 Conic Sections
12.1 Conic Sections and the Circle
12.2 Ellipses
12.3 Hyperbolas
13.1 Inverse Relations and Functions
13.2 Exponential Functions
13.5 Logarithmic and Exponential Equations / Appendix A / Appendix
A.1 Determinants and Cramer’s Rule
22
2.2 Solving Equations by Multiplying and Dividing
2.4 Literal Equations and Their Applications
2.5 Solving Linear Inequalities Using Addition
2.6 Solving Linear Inequalities Using Multiplication
2.7 Solving Absolute Value Equations (Optional)
2.8 Solving Absolute Value Inequalities (Optional)
3 Graphs and Linear Equations
3.2 The Cartesian Coordinate System
3.3 The Graph of a Linear Equation
4.1 Positive Integer Exponents
4.2 Zero and Negative Exponents and Scientific Notation
4.5 Multiplication of Polynomials and Special Products
5.2 Factoring Special Polynomials
5.3* Factoring Trinomials: Trial and Error
5.4 Factoring Trinomials: The ac method
5.7 Problem Solving with Factoring
6 A Beginning Look at Functions
6.1 Relations and Functions
6.2 Tables and Graphs
6.5 Substitution and Synthetic Division
R A Review of Elementary Algebra
R.1 From Arithmetic to Algebra
R.2 Equations and Inequalities
R.3 Graphs and Linear Equations
R.4 Exponents and Polynomials
R.5 A Beginning Look at Functions
7.5 Solving Rational Expressions
7.6 Solving Rational Inequalities
8.2 Systems of Equations in Two Variables with Applications
8.5 Matrices (Optional)
9 Graphical Solutions
9.1 Solving Equations in One Variable Graphically
9.2 Solving Linear Inequalities in One Variable Graphically
9.3 Solving Absolute Value Equations Graphically
9.4 Solving Absolute Value Inequalities Graphically
10 Radicals and Exponents
10.6 Complex Numbers
11 Quadratic Functions
11.3 An Introduction to the Parabola
New
ELEMENTARY AND INTERMEDIATE
ALGEBRA
Alternate Hardcover Edition, Third Edition
By Donald Hutchinson, Stefan Baratto and Barry Bergman of Clackamas
Community College
ISBN-13: 978-0-07-330931-6 / MHID: 0-07-330931-1
http://www.mhhe.com/baratto
A Unified Text That Serves Your Needs. Most colleges offering
elementary and intermediate algebra use two different texts, one for
each course. As a result, students may be required to purchase two
texts; this can result in a considerable amount of topic overlap. Over
the last few years, several publishers have issued “combined” texts
that take chapters from two texts and merge them into a single book.
This has allowed students to purchase a single text, but it has done
little to reduce the overlap. The goal of this author team has been to
produce a text that was more than a combined text. They wanted to
unify the topics and themes of beginning and intermediate algebra
in a fluid, non-repetitive text. We also wanted to produce a text that
will prepare students from different mathematical backgrounds for
college algebra. We believe we have accomplished our goals. For
students entering directly from an arithmetic or pre-algebra course,
this is a text that contains all of the material needed to prepare for
college algebra. It can be offered in two quarters or in two semesters.
The new Review Chapter found between chapters 6 and 7 serves as
a mid-book review for students preparing to take a final exam that
covers the first seven chapters. Finally, we have produced a text
that will accommodate those students placing into the second term
of a two-term sequence. Here is where the Review Chapter is most
valuable. It gives the students an opportunity to check that they have
all of the background required to begin in Chapter 7. If the students
struggle with any of the material in the Review Chapter, they are
referred to the appropriate section for further review.
New to this edition
A new Review Chapter replaces “Moving to the Intermediate
Algebra Level.” The Review Chapter provides a concise, comprehensive
review of chapters 1 through 6. The chapter contains review exercises
and section references.
Overcoming Math Anxiety Boxes - Located within the first
few chapters are suggestions on overcoming math anxiety. These
suggestions are designed to be timely and useful, The are the same
suggestions most instructors make in class, but sometimes those
words are given extra weight when students see them in print.
The chapter on functions now follows the chapter on
polynomials.
Several new sections have been added to the text: Problem
Solving with Factoring A General Strategy for Factoring Rational
Functions Solving Radical Equations
Contents
0 Prealgebra Review
0.1 A Review of Fractions
0.2 Real Numbers
0.5 Exponents and Order of Operation
1 From Arithmetic to Algebra
1.1 Transition to Algebra
1.4 Sets
2.1 Solving Equations by Adding and Subtracting
23
11.4 Solving Quadratic Inequalities
12 Conic Sections
12.1 Conic Sections and the Circle
12.2 Ellipses
12.3 Hyperbolas
13.5 Logarithmic and Exponential Equations
Appendix A
Appendix A.1 Determinants and Cramer’s Rule
NEW! Skill Practice exercises follow immediately after the
examples in the text. Answers are provided so students can check
their work. By utilizing these exercises, students can test their
understanding of the various problem-solving techniques given in
the examples.
NEW! The section-ending Practice Exercises are newly revised,
with even more core exercises appearing per exercise set. Many of
the exercises are grouped by section objective, so students can refer
back to content within the section if they need some assistance in
completing homework. Review Problems appear at the beginning
of most Practice Exercise Sets to help students improve their study
habits and to improve their long-term retention of concepts previously
introduced.
New
NEW! Mixed Exercises are found in many of the Practice Exercise
sets. The Mixed Exercises contain no references to objectives.
In this way, students are expected to work independently without
prompting--which is representative of how they would work through
a test or exam.
BEGINNING AND
2nd Edition
NEW! Study Skills Exercises appear at the beginning of the
Practice Exercises, where appropriate. They are designed to help
students learn techniques to improve their study habits including exam
preparation, note taking, and time management.
Beach CC-Daytona Beach
NEW! The Chapter Openers now include a variety of puzzles
that may be used to motivate lecture. Each puzzle is based on key
vocabulary terms or concepts that are introduced in the chapter.
2008 (January 2007)
ISBN-13: 978-0-07-331269-9 / MHID: 0-07-331269-X
Browse: http://www.mhhe.com/miller_oneill
Building on its first-edition success, Beginning & Intermediate Algebra
2/e by Miller/O’Neill continues to offer an enlightened approach
grounded in the fundamentals of classroom experience. The practice
of many instructors in the classroom is to present examples and have
their students solve similar problems. This is realized through the Skill
what is sometimes a natural inclination toward applying problemsovling algorithms that may not always be appropriate. In addition,
develop the knowledge they need to make a successful transition
into College Algebra. In this way, the book perfectly complements any
New to this edition
NEW! Problem Recognition Exercises Developmental math
students are sometimes conditioned into algorithmic thinking to the
point where they want to automatically apply various algorithms to
solve problems, whether it is meaningful or not. These exercises
24
Classroom Activities are optional exercises that can be worked
out in class by individual students, or a group of students who work
collaboratively. The Annotated Instructor’s Edition refers to the
classroom activities, which are found in the Instructor’s Resource
Manual. Instructors have the option of making the classroom activities
available to students for use in class in conjunction with lecture, or for
use as extra practice in conjunction with homework.
MathZone, accessible via the Internet or through CD-ROM, will
allow the instructors and students to get all of the necessary help
they need to be successful in the course including state of the art
lecture videos, eProfessor practice, many problems from the text
algorithmically generated, a unified gradebook and a course built
online quickly and easily. MathZone icons will appear throughout the
text to tell the student when it’s appropriate to go to MathZone to either
do the problems, watch the videos, or get extra help.
Contents
Chapter R: Reference: Study Skills, Fractions, and Geometry
R.1 Study Tips
R.2 Fractions
R.3 Introduction to Geometry
Chapter 1: The Set of Real Numbers
1.1 Sets of Numbers and the Real Number Line
1.4 Subtraction of Real Numbers Mixed Review Exercises – Addition
and Subtraction of Real Numbers
1.6 Properties of Real Numbers and Simplifying Expressions Chapter 1
Summary Chapter 1
Review Exercises
Chapter 1 Test
2.1 Addition, Subtraction, Multiplication, and Division Properties of
Equality
2.3 Linear Equations: Clearing Fractions and Decimals
2.4 Applications of Linear Equations: Introduction to Problem
Solving
2.5 Applications Involving Percents
2.6 Formulas and Applications of Geometry
2.7 Linear Inequalities Chapter 2
Summary Chapter 2
Review Exercises
Chapter 2 Test
Cumulative Review Exercises Chapters 1 – 2
Chapter 3: Graphing Linear Equations in Two Variables
3.1 Rectangular Coordinate System (BA 2nd ed hardback—Section
3.1)
3.3 X- and Y-Intercepts, Horizontal and Vertical Lines
3.4 Slope of a Line (BA 2nd ed hardback – Section 3.3)
3.5 Slope-Intercept Form of a Line (BA 2nd ed hardback – Section 3.4)
3.6 Point-Slope Formula (BA 2nd ed hardback – Section 3.5 )
3.7 Applications of Linear Equations (BA 2nd ed hardback, Section
3.6)
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Test Cumulative
Review Exercises Chapters 1 – 3
Chapter 4: Systems of Linear Equations
4.1 Introduction to Systems of Linear Equations
4.2 Substitution Method
4.3 Addition Method
4.4 Applications of Linear Equations in Two Variables
Chapter 4 Summary
Chapter 5: Polynomials and Properties of Exponents
5.1 Exponents: Multiplying and Dividing Common Bases
5.2 More Properties of Exponents
5.3 Definitions of b0 and b-n
5.4 Scientific Notation Mixed Review Exercises – Properties of
Exponents
5.7 Division of Polynomials Mixed Review Exercises – Operations
on Polynomial
Chapter 5 Summary
Chapter 5 Test
6.2 Factoring Trinomials of the form ax2 + bx + c (Optional)
6.3 Factoring Trinomials: Trial-and-Error Method
6.4 Factoring Trinomials: The Grouping Method
6.6 General Factoring Summary
6.7 Solving Equations by Using the Zero Product Rule
Chapter 6 Summary
7.1 Introduction to Rational Expressions (this section introduces a
definition of domain)
7.3 Least Common Denominator
7.5 Complex Fractions Mixed Review Exercises – Operations on
7.6 Rational Equations Mixed Review Exercises – Comparing Rational
Equations and Rational Expressions
7.7 Applications of Rational Equations, Ratios and Proportions
Chapter 7 Summary
Chapter 8: Introduction to Relations and Functions
8.1 Review of Graphing
8.2 Introduction to Relations
8.4 Graphs of Basic Functions
8.5 Variation
Chapter 8 Summary
Review Exercises, Chapters 1 – 8
Chapter 9: Systems of Linear Equations in Three Variables
9.2 Applications of Systems of Equations in Three Variables
9.3 Solving systems of Linear Equations Using Matrices IA 2e
hardcover, 3.6
9.4 Determinants and Cramer’s Rule (combined 8.7 or 2nd ed hard
IA appendix A.2)
Chapter 9 Summary
Chapter 10: More Equations and Inequalities
10.1 Compound Inequalities
10.2 Polynomial and Rational Inequalities
10.3 Absolute Value Equations
10.4 Absolute Value Inequalities Mixed Review Exercises – Equations
and Inequalities
Chapter 10 Summary
Chapter 11: Radicals and Complex Numbers
11.1 Definition of an nth-Root
11.3 Properties of Radicals
11.6 Rationalization Mixed Review Exercises – Operations on
Radicals (from Chapter 8 BA 2nd ed.)
11.8 Complex Numbers
Chapter 11 Summary
Chapter 12: Quadratic Equations and Functions
12.1 Square Root Property and Completing the Square
12.3 Equations in Quadratic Form
12.4 Graphs of Quadratic Functions
12.5 Applications of Quadratic Functions
Chapter 12 Summary
Chapter 13: Exponential and Logarithmic Functions
13.1 Algebra of Functions and Composition of Functions
13.6 The Irrational Number, e
13.7 Exponential and Logarithmic Equations
Chapter 13 Summary
Chapter 14: Conic Sections and Nonlinear Systems
14.1 Distance Formulas and Circles
14.2 More on the Parabola
25
14.3 Ellipse and Hyperbola
14.4 Nonlinear Systems of Equations in Two Variables
14.5 Nonlinear Inequalities and Systems of Inequalities
Chapter 14 Summary
Chapter 15: Sequences, Series, and Binomial Theorem Counting,
and Probability
15.1 Sequences and Series
15.2 Arithmetic and Geometric Sequences and Series
15.4 Fundamentals of Counting
15.5 Introduction to Probability
Chapter 15 Summary
Beginning Algebra Review:
Review A Review of The Set of Real Numbers
Review B Review of Linear Equations and Inequalities
Review C Review of Graphing (authors need to revise)
Review D Review of Polynomials and Properties of Exponents
Review E Review of Factoring Polynomials
Review F Review of Rational Expressions
Appendix A.1 Synthetic Division
Appendix A.2 Mean, Median, and Mode
BEGINNING AND INTERMEDIATE ALGEBRA:
A Unified Worktext
By James Streeter (deceased); Donald Hutchison, Clackamas Community
College; Barry Bergman, Clackamas Community College and Stefan
Baratto, Clackamas Community College
2004 / 1,232 pages
ISBN-13: 978-0-07-301614- 6 / MHID: 0-07-301614-4
(with MathZone)
http://www.mhhe.com/hall
Contents
Prealgebra Review
Prime Factorization
Review of Fractions, Decimals, and Percents
1 Real Numbers and Algebraic Expressions:
Addition and Subtraction of Real Numbers
Multiplication and Division of Real Numbers.
Variables and Algebraic Expressions.
Properties of Exponents and Scientific Notation.
Order of Operations.
2 Equations and Inequalities:
The Addition Property of Equality.
The Multiplication Property of Equality.
Solve Linear Equations.
The Number Line.
Linear Inequalities.
Absolute Value Equations and Inequalities.
Applications and Problem Solving.
3 Graph Linear Equations and Inequalities in Two Variables:
The Cartesian Coordinate System.
The Graph of a Line.
The Slope of a Line.
Graph a Line Using the Slope-Intercept Method.
Find the Equation of a Line.
Graph Linear Inequalities.
4 Systems of Linear Equations and Inequalities:
Solve Systems of Linear Equations by Graphing.
26
Solve Systems of Linear Equations by Substitution.
Solve Systems of Linear Equations by Addition.
Solve Systems of Linear Inequalities.
5 Polynomials:
An Introduction to Polynomials.
Add and Subtract Polynomials.
Multiply Polynomials.
Divide Polynomials.
Synthetic Division.
6 Factoring:
The Greatest Common Factor and Factor by Grouping.
Use Special Patterns to Factor.
Factor Trinomials of the form x2 + bx + c.
Factor Trinomials for the form ax2 + bx + c.
Solve Equaitons by Factoring.
Review of Beginning Algebra.
Real Numbers and Algebraic Expressions.
Equations and Inequalities.
Graphs of Linear Equations and Inequalities.
Systems of Linear Equations and Inequalities.
R.5 Polynomials.
Factoring.
7 Rational Expressions:
Evaluate and Simplify Rational Expressions.
Multiply and Divide Rational Expressions.
Add and Subtract Rational Expressions.
Simplify Complex Fractions.
Solve Rational Equations.
Solve Literal Equations.
8 Functions:
Relations and Functions.
Tables and Graphs.
Algebra of Functions.
Composition of Functions.
One-to-One and Inverse Functions.
9 Radicals and Rational Exponents:
Evaluate Radicals.
Simplify Radicals.
Add and Subtract Radicals.
Multiply and Divide Radicals.
Radicals and Rational Exponents.
Solve Radical Equations. Complex Numbers.
10 Quadratic Equations and Inequalities:
Graphs of Quadratic Functions.
Solve Quadratic Equations Using Radicals.
Complete the Square.
The Quadratic Formula.
Solve Equatioins in Quadratic Form.
Solve Quadratic Inequalities.
11 Exponential and Logarithmic Functions:
Exponential Functions.
Logarithmic Functions.
Properties of Logarithms.
Solve Logarithmic and Exponential Equations.
12 Conic Sections:
Parabolas.
Circles.
Ellipses.
Hyperbolas.
Systems of Nonlinear Equations and Inequalities.
Appendices
A.1 Matrices
A.2 Determinants
MATH WORD PROBLEMS DEMYSTIFIED
By Allan G Bluman, Community College of Allegheny County-South
ISBN-13: 978-0-07-144316-6 / MHID: 0-07-144316-9
Contents
New
Preface.
Lesson 1: Introduction to Solving Word Problems.
Lesson 2: Solving Word Problems Using Whole Numbers.
REFRESHER I: DECIMALS:
Lesson 3: Solving Word Problems Using Decimals.
REFRESHER II: FRACTIONS:
Lesson 4: Solving Word Problems Using Fractions.
QUIZ 1.
REFRESHER III: PERCENTS:
Lesson 5: Solving Word Problems Using Percents.
Lesson 6: Solving Word Problems Using Proportions.
Lesson 7: Solving Word Problems Using Formulas.
QUIZ 2.
REFRESHER IV: EQUATIONS:
Lesson 8: Algebraic Representation.
Lesson 9: Solving Number Problems.
Lesson 10: Solving Digit Problems.
Lesson 11: Solving Coin Problems.
QUIZ 3:
Lesson 12: Solving Age Problems.
Lesson 13: Solving Distance Problems.
Lesson 14: Solving Mixture Problems.
Lesson 15: Solving Finance Problems.
Lesson 16: Solving Lever Problems.
Lesson 17: Solving Work Problems.
QUIZ 4.
REFRESHER V: SYSTEMS OF EQUATIONS:
Lesson 18: Solving Word Problems Using Two Equations.
REFRESHER VI: QUADRATIC EQUATIONS:
Lesson 19: Solving Word Problems Using Quadratic Equations.
Lesson 20: Solving Word Problems in Geometry.
QUIZ 5.
Lesson 21: Solving Word Problems Using Other Strategies.
Lesson 22: Solving Word Problems in Probability.
Lesson 23: Solving Word Problems in Statistics.
Quiz 6.
Final Exam. Answer To Quizzes And Final Exam.
Supplement: Suggestions For Success In Mathematics.
Index
Sixth Edition
By Mark Dugopolski
2009 (January 2008)
ISBN-13: 978-0-07-722481-3 / MHID: 0-07-722481-7
Intermediate Algebra, 6e is part of the latest offerings in the
successful Dugopolski series in mathematics. The author’s goal is
to explain mathematical concepts to students in a language they
can understand. In this book, students and faculty will find short,
New to this edition
when appropriate.
[email protected]
27
Contents
TO THE STUDENT
PREFACE
1 The Real Numbers
1.1 Sets
1.3 Operations on the Set of Real Numbers
1.4 Evaluating Expressions
1.6 Using the Properties
Chapter 1 Wrap-Up
• Summary
• Chapter 1 Test
2.2 Formulas and Functions
2.3 Applications
2.4 Inequalities
Chapter 2 Wrap-Up
• Summary
• Chapter 2 Test
3.2 Slope of a Line
3.3 Three Forms for the Equation of a Line
3.4 Linear Inequalities and Their Graphs
Chapter 3 Wrap-Up
• Summary
• Chapter 3 Test
4.4 Solving Linear Systems Using Matrices
4.5 Determinants and Cramer’s Rule
Chapter 4 Wrap-Up
• Summary
• Chapter 4 Test
5.1 Integral Exponents and Scientific Notation
5.2 The Power Rules
5.3 Polynomials and Polynomial Functions
5.4 Multiplying Binomials
5.5 Factoring Polynomials
5.6 Factoring ax² + bx + c
5.7 Factoring Strategy
28
Chapter 5 Wrap-Up
• Summary
• Chapter 5 Test
6 Rational Expressions and Functions
6.1 Properties of Rational Expressions and Functions
6.7 Applications
Chapter 6 Wrap-Up
• Summary
• Chapter 6 Test
7.1 Radicals
7.6 Complex Numbers
Chapter 7 Wrap-Up
• Summary
• Chapter 7 Test
8 Quadratic Equations, Functions, and Inequalities
8.4 Quadratic Functions and Their Graphs
Chapter 8 Wrap-Up
• Summary
• Chapter 8 Test
9 Additional Function Topics
9.5 Variation
Chapter 9 Wrap-Up
• Summary
• Chapter 9 Test
Chapter 10 Wrap-Up
• Summary
• Chapter 10 Test
11.2 The Parabola
11.3 The Circle
Chapter 11 Wrap-Up
• Summary
• Chapter 11 Test
12.1 Sequences
12.2 Series
Chapter 12 Wrap-Up
• Summary
• Chapter 12 Test
Appendix A
Answers to Selected Exercises
Index
New
By Donald Hutchison, Stefan Baratto of
Clackamas Community College and Barry
Bergman, Clackamas Community College
2008 (January 2007)
ISBN-13: 978-0-07-330930-9 / MHID: 0-07-330930-3
Browse http://www.mathzone.com/hutchinson
Intermediate Algebra by Baratto/Kohlmetz/Bergman is part of the latest
offerings in the successful Streeter-Hutchison Series in Mathematics.
By popular demand, we are now offering an Intermediate Algebra
book in the series again. This book combines the best of earlier
versions of Intermediate Algebra, along with new material requested
by a cross-section of Intermediate Algebra instructors across
the country. This first edition maintains the hallmark approach of
encouraging the learning of mathematics by focusing its coverage
on mastering math through practice. This worktext seeks to provide
carefully detailed explanations and accessible pedagogy to introduce
intermediate algebra concepts and put the content in context. The
authors use a three-pronged approach (I. Communication, II. Pattern
Recognition, and III. Problem Solving) to present the material and
stimulate critical thinking skills. Items such as Math Anxiety boxes,
Check Yourself exercises, and Activities represent this approach and
the underlying philosophy of mastering math through practice. The
exercise sets are well-organized, and clearly labeled. Vocational and
professional-technical exercises have been included throughout.
Repeated exposure to this consistent structure should help advance
the student’s skills in relating to mathematics. The book is designed
for a one-semester intermediate algebra course and is appropriate
Features
provide students with interesting, relevant scenarios that will
capture their attention and engage them in the upcoming material.
Furthermore, exercises and Activities related to the Opening Vignettes
are included in each chapter. These exercises are marked with a
special icon next to them.
ACTIVITIES--An Activity is included in each chapter. These
Activities promote active learning by requiring students to find,
interpret, and manipulate real-world data. The Activity in each chapter
relates to the chapter-opening vignette, providing cohesiveness to
the chapter. Students can complete the Activities on their own, but
are best solved in small groups.
CHECK YOURSELF EXERCISES--Check Yourself exercises
have been the hallmark of the Streeter-Hutchison Series; they are
designed to actively involve students throughout the learning process.
Each example is followed by an exercise that encourages students to
solve a problem similar to the one just presented and check/practice
what they have just learned. Answers to these exercises are provided
at the end of the section for immediate feedback.
“READING YOUR TEXT”--This feature is a set of quick exercises
presented at the end of each section meant to quiz students
29
CLEAR STRUCTURE FOR END-OF-SECTION EXERCISES-The comprehensive End-of-Section exercises are organized to
clearly identify the different types of exercises being presented. This
structure highlights the progression in level and type of exercise for
each section. The application exercises, which are integrated into
every section, are a crucial component of this organization.
SUMMARY AND SUMMARY EXERCISES--The comprehensive
chapter summaries and exercises are found at the end of every
chapter and review the important concepts from that chapter. The
comprehensive Summaries at the end of each chapter enable
students to review important concepts. The Summary Exercises
provide an opportunity for the student to practice these important
concepts. Answers to odd-numbered exercises are provided in the
Answers Appendix.
CUMULATIVE REVIEWS--Cumulative Reviews are included
starting with Chapter 2, following the Self-Tests. These reviews help
students build on previously covered material and give them an
opportunity to reinforce the skills necessary in preparing for midterm
and final exams. The answers to these exercises are also given at
the end of the book, along with section references.
do graphing. An electronic version of the card is available through the
book’s website in the Information Center.
MathZone--MathZone, accessible via the Internet or through CDROM, will allow the instructors and students to get all of the necessary
help they need to be successful in the course--including state of the
art lecture videos, eProfessor practice, many problems from the text
online quickly and easily. MathZone icons will appear throughout the
text to tell the student when it’s appropriate to go to MathZone to either
do the problems, watch the videos, or get extra help.
NEW TO THE HUTCHISON SERIES: Kelly Kaiser Kohlmetz, of
University of Wisconsin-Milwaukee, brings a great deal to the author
team due to her experience in academics.
5.7 Factoring Trinomials: The ac Method
6.1 Simplification of Rational Expressions and Functions
6.5 Solving Rational Equations 6.6 Variation
7 Radical and Radical Exponents
7.2 Simplification of Radical Expressions
7.5 Geometric and Other Applications
7.7 Complex Numbers
8.1 Graphing Factorable Quadratic Functions
8.3 Solving Quadratic Equations by Using the Quadratic Formula
8.4 Solving Equations that are Quadratic in Form
8.5 Quadratic Inequalities and Rational Inequalities
9 Conic Sections
9.1 Parabolas
9.2 Circles
9.3 Ellipses and Hyperbolas
9.4 Nonlinear Systems
10 Additional Properties of Functions
11.4 Solving Logarithmic and Exponential Equations / Appendix:
Determinants and Cramer’s Rule
Contents
1 The Real Numbers
1.1 The Set of Real Numbers
1.2 Operations and Properties
1.3 Inequalities and Absolute Values
1.5 Properties of Exponents and Scientific Notation
2 Linear Equations and Inequalities
2.1 Solutions of Linear Equations in One Variable
2.2 Literal Equations and Formulas
2.3 Applications and Problem Solving
2.4 Linear Inequalities
3 Graphs of Linear Relations and Functions
3.1 Graphing Linear Equations
3.2 An Introduction to Functions
3.5 Graphing Absolute Value Functions and Linear Inequalities
4 Systems of Linear Relations
4.1 Systems of Linear Equations in Two Variables
4.3 Solving Systems of Equations Using Matrices
4.4 Graphing Systems of Linear Inequalities
5 Polynomials and Polynomial Functions
5.4 Common Factors and Factoring by Grouping
5.5 Factoring Special Binomials
5.6 Factoring Trinomials: Trial and Error
30
[email protected]
their study habits and to improve their long-term retention of concepts
previously introduced.
New
Feature : NEW! Mixed Exercises are found in many of the
Practice Exercise sets. The Mixed Exercises contain no references to
objectives. In this way, students are expected to work independently
without prompting--which is representative of how they would work
through a test or exam.
Second Edition
Feature : NEW! Study Skills Exercises appear at the beginning
of the Practice Exercises, where appropriate. They are designed to
help students learn techniques to improve their study habits including
exam preparation, note taking, and time management.
Beach Community College
Feature : NEW! The Chapter Openers now include a variety
of puzzles that may be used to motivate lecture. Each puzzle is
based on key vocabulary terms or concepts that are introduced in
the chapter.
2008 (January 2007)
ISBN-13: 978-0-07-331268-2 / MHID: 0-07-331268-1 (Hardcover)
Feature : Classroom Activities are optional exercises that can
be worked out in class by individual students, or a group of students
who work collaboratively. The Annotated Instructor’s Edition refers to
the classroom activities, which are found in the Instructor’s Resource
Manual. Instructors have the option of making the classroom activities
available to students for use in class in conjunction with lecture, or
for use as extra practice in conjunction with homework.
Building on its first-edition success, Intermediate Algebra 2/e by
Miller/O’Neill continues to offer an enlightened approach grounded
in the fundamentals of classroom experience. The practice of many
instructors in the classroom is to present examples and have their
students solve similar problems. This is realized through the Skill
what is sometimes a natural inclination toward applying problemsovling algorithms that may not always be appropriate. In addition,
develop the knowledge they need to make a successful transition into
College Algebra. In this way, the book perfectly complements any
Feature : MathZone, accessible via the Internet or through CDROM, will allow the instructors and students to get all of the necessary
help they need to be successful in the course including state of the
art lecture videos, eProfessor practice, many problems from the text
online quickly and easily. MathZone icons will appear throughout
the text to tell the student when it’s appropriate to go to MathZone to
either do the problems, watch the videos, or get extra help.
Contents
Chapter 1: Review of Basic Algebraic Concepts
1.1 Sets of Numbers and Interval Notation
1.2 Operations on Real Numbers
1.3 Simplifying Expressions
1.5 Applications of Linear Equations in One Variable
1.6 Literal Equations and Applications to Geometry
1.7 Linear Inequalities in One Variable
1.8 Properties of Integer Exponents and Scientific Notation
Chapter 1 Summary
Chapter 1 Test
Chapter 2: Linear Equations in Two Variables
2.1 Rectangular Coordinate System and Midpoint Formula
2.3 Slope of a Line
2.4 Equations of a Line
2.5 Applications of Linear Equations and Graphing
Chapter 2 Summary
Chapter 2 Test
3.2 Solving Systems of Equations by Using the Substitution
Method
3.3 Solving Systems of Equations by Using the Addition Method
3.4 Applications of Systems of Linear Equations in Two Variables
3.5 Systems of Linear Equations in Three Variables and
Applications
3.6 Solving Systems of Linear Equations by Using Matrices
Chapter 3 Summary
Chapter 3 Test
Cumulative Review Exercises, Chapters 1 – 3
New to this edition
Feature : NEW! Problem Recognition Exercises Developmental
math students are sometimes conditioned into algorithmic thinking to
the point where they want to automatically apply various algorithms
to solve problems, whether it is meaningful or not. These exercises
Feature : NEW! Skill Practice exercises follow immediately
after the examples in the text. Answers are provided so students
can check their work. By utilizing these exercises, students can test
their understanding of the various problem-solving techniques given
in the examples.
Feature : NEW! The section-ending Practice Exercises are newly
revised, with even more core exercises appearing per exercise set.
Many of the exercises are grouped by section objective, so students
can refer back to content within the section if they need some
assistance in completing homework. Review Problems appear at the
beginning of most Practice Exercise Sets to help students improve
31
Chapter 4: Introduction to Relations and Functions
4.1 Introduction to Relations
4.3 Graphs of Functions
4.4 Variation
Chapter 4 Summary
Chapter 4 Test
Chapter 5: Polynomials
5.1 Addition and Subtraction of Polynomials and Polynomial
Functions
5.3 Division of Polynomials / Mixed Review Exercises – Operations
on Polynomials
5.5 Factoring Trinomials
5.7 Additional Factoring Strategies
5.8 Solving Equations by Using the Zero Product Rule
Chapter 5 Summary
Chapter 5 Test
Chapter 6: Rational Expressions and Rational Equations
6.1 Rational Expressions and Rational Functions
6.4 Complex Fractions / Mixed Review Exercises – Operations on
6.5 Rational Equations
6.6 Applications of Rational Equations and Proportions
Chapter 6 Summary
Chapter 6 Test
Chapter 7: Radicals and Complex Numbers
7.1 Definition of an nth Root
7.6 Rationalization
7.8 Complex Numbers
Chapter 7 Summary
Chapter 7 Test
Chapter 8: Quadratic Equations and Functions
8.1 Square Root Property and Completing the Square
8.3 Equations in Quadratic Form
8.4 Graphs of Quadratic Functions
8.5 Vertex of a Parabola and Applications
Chapter 8 Summary
Chapter 8 Test
Chapter 9: More Equations and Inequalities
9.2 Polynomial and Rational Inequalities
9.3 Absolute Value Equations
9.4 Absolute Value Inequalities Mixed Review Exercises – Equations
and Inequalities
Chapter 9 Summary
Chapter 9 Test
Cumulative Review Exercises, Chapters 1–9
10.1 Algebra and Composition of Functions
32
10.6 The Irrational Number e / Mixed Review Exercises – Logarithmic
and Exponential Forms
10.7 Logarithmic and Exponential EquationsChapter 10 Summary /
Chapter 10 Review ExercisesChapter 10 Test
Chapter 11: Conic Sections
11.1 Distance Formula and Circles
11.2 More on the Parabola
11.4 Nonlinear Systems of Equations in Two Variables
11.5 Nonlinear Inequalities and Systems of Inequalities
Chapter 11 Summary
Chapter 11 Test
Appendix
A.1 Binomial Expansions
A.2 Sequences and Series
A.3 Arithmetic and Geometric Sequences and Series
INTERMEDIATE ALGEBRA: THE LANGUAGE
AND SYMBOLISM OF MATHEMATICS
By James W. Hall, Parkland College, and Brian A. Mercer, Parkland
College
ISBN-13: 978-0-07-330544-8 / MHID: 0-07-330544-8
ISBN-13: 978-0-07-322968-3 / MHID: 0-07-322968-7
(with MathZone)
Browse http://www.mhhe.com/hallmercer
Intended for schools that want a single text covering the standard
topics from Intermediate Algebra. Topics are organized not following
the historical pattern, but by using as the guiding prinicples, the
AMATYC standards as outlined in Crossroads in Mathematics. Use of
a graphing calculator is assumed. BEGINNING AND INTERMEDIATE
ALGEBRA: THE LANGUAGE AND SYMBOLISM OF MATHEMATICS
is a reform-oriented book.
Contents
1 Review of Beginning Algebra. Preparing for an Algebra
Class.
The Real Number Line and Algebraic Expressions. Operations with
Real Numbers. Exponents and Order of Operations. Properties
of Exponents and Scientific Notation. Solving Linear Equations in
One Variable. Ratios, Proportions, and Direct Variation. Using and
Rearranging Formulas.
2 An Introduction To Functions And Linear Modeling.
The Rectangular Coordinate System, Tables, and Graphs. Functions
and Representations of Functions. Linear Functions. Slope of a Line
and Applications of Slope. Special Forms of Linear Equations In Two
Variables. Properties of the Graphs of Linear and Absolute Value
Functions. Curve Fitting--Selecting the Line of Best Fit.
3 Linear Equations and Systems of Linear Equations.
Problem Solving and Applications of Linear Equations. Solving
Systems of Linear Equations In Two Variables Graphically and
Numerically. Solving Systems of Linear Systems In Two Variables
by the Substitution Method. Solving Systems of Linear Systems In
Two Variables by the Addition Method. More Applications of Linear
Systems. Solving Systems of Linear Equations Using Augmented
Matrices. Systems of Linear equations in Three Variables.
4 Linear Inequalities and Systems of Linear Inequalities.
Solving Linear Inequalities in One Variable. Solving Compound
Inequalities. Solving Absolute Value Equations and Inequalities.
Graphing Systems of Linear Inequalities in Two Variables.
Problems.
2.5 Linear and Compound Inequalities.
2.6 Absolute-Value Equations and Inequalities.
3. Graphs and Functions
3.1 Graphs.
3.2 Introduction to Functions: Linear Functions.
3.3 Using Slopes to Graph Lines.
3.4 Equations of Lines.
3.5 Linear Inequalities in Two Variables.
4. Solving Systems of Linear Equations and Inequalities
4.1 Systems with Two Variables.
4.2 Systems with Three Variables.
4.3 Coin, Distance-Rate-Time, Investment, and Geometry
Problems.
4.4 Matrices.
4.5 Determinants and Cramer’s Rule.
4.6 Systems of Linear Inequalities.
5. Polynomials
5.1 Polynomials: Addition and Subtraction.
5.2 Multiplication of Polynomials.
5.3 The Greatest Common Factor and Factoring by Grouping.
5.4 Factoring Trinomials.
5.5 Special Factoring.
5.6 General Methods of Factoring.
5.7 Solving Equations by Factoring: Applications.
6. Rational Expressions
6.1 Rational Expressions.
6.2 Multiplication and Division of Rational Expressions.
6.3 Addition and Subtraction of Rational Expressions.
6.4 Complex Fractions.
6.5 Division of Polynomials and Synthetic Division.
6.6 Equations Involving Rational Expressions.
6.7 Applications: Problem Solving.
6.8 Variation.
7. Rational Exponents and Radicals
7.1 Rational Exponents and Radicals.
7.2 Simplifying Radicals.
7.3 Operations with Radicals.
7.4 Solving Equations Containing Radicals.
7.5 Complex Numbers.
8. Quadratic Equations and Inequalities
8.1 Solving Quadratics by Completing the Square.
8.2 The Quadratic Formula: Applications.
8.3 The Discriminant and Its Applications.
8.4 Solving Equations in Quadratic Form.
8.5 Nonlinear Inequalities.
9. Quadratic Functions and the Conic Sections
9.1 Quadratic Functions and their Graphs.
9.2 Circles and Ellipses.
9.3 Hyperbolas and Identification of Conics.
9.4 Nonlinear Systems of Equations.
9.5 Nonlinear Systems of Inequalities.
10. Inverse, Exponential, and Logarithmic Functions.
10.1 The Algebra of Functions.
10.2 Inverse Functions.
10.3 Exponential Functions.
10.4 Logarithmic Functions and Their Properties.
10.5 Common and Natural Logarithms.
10.6 Exponential and Logarithmic Equations and Applications.
11. Sequences and Series.
11.1 Sequences and Series.
11.2 Arithmetic Sequences and Series.
11.3 Geometric Sequences and Series.
11.4 The Binomial Expansion
5 Polynomials and Polynomial Functions.
Polynomials and Properties of the graphs of Polynomial Functions.
Adding and Subtracting Polynomials. Multiplying Polynomials and
Special Products. An Introduction to Factoring Factoring Trinomials
of the Form. A General Strategy for Factoring Polynomials. Using
Factoring solve equations and Inequalities.
6 Quadratic Functions.
Quadratic Functions, Parabolas, and Modeling Using Quadratic
Equations. Solving Equations by Factoring. Using the Quadratic
Formula to Find Real Solutions. More Applications of Quadratic
Equations. Complex Numbers. Solving Quadratic Equations with
Imaginary Solutions.
7 Rational Functions.
Properties of the Graphs of Rational Functions and Reducing
Rational Expressions. Multiplying, Dividing, and Reducing Rational
Expressions. Adding and Subtracting Rational Expressions. Combining
Operations and Simplifying Complex Rational Expressions Dividing
Polynomials. Solving Equations Containing Rational Expressions.
Inverse and Joint Variation and Other Applications Yielding equations
with Fractions.
8 Square Root and Cube Root Functions and Rational
Exponents.
Properties of the Graphs of Radical Functions. Evaluating Radical
Expressions. Adding and Subtracting Radical Expressions. Multiplying
and Dividing Radical Expressions. Solving Equations Containing
Radical Expressions. Rational Exponents and Radicals.
9 Exponential and Logarithmic Functions.
Geometric Sequences and Properties of the Graphs of Exponential
Functions. Inverse Functions. Logarithmic Functions. Evaluating
Logarithms. Properties of Logarithms. Exponential and Logarithmic
Equations. Exponential Curve Fitting and Other Applications of
Exponential and Logarithmic Equations.
10 A Preview of College Algebra.
Horizontal and Vertical Translations of Functions. Stretching,
Shrinking, and Reflecting Graphs of Functions. Algebra of Functions.
Sequences, Series, and Summation Notation. Conic Sections.
Second Edition
By Ignacio Bello, University of South Florida -Tampa and Fran Hopf,
University of South Florida -Tampa
2006 / Softcover
ISBN-13: 978-0-07-330918-7 / MHID: 0-07-330918-4 (MP)
ISBN-13: 978-0-07-299100-0 / MHID: 0-07-299100-3
(with MathZone)
Intermediate Algebra prepares students for further courses in the
college math curriculum. Students of all backgrounds will be delighted
to find a refreshing book that appeals to every learning style and
reaches out to diverse demographics. Through down-to-earth
explanations, patient skill-building, and exceptionally interesting and
realistic applications, this worktext will empower students to learn and
master algebra in the real world.
Contents
1. The Real Numbers
1.1 Numbers and Their Properties.
1.2 Operations and Properties of Real Numbers.
1.3 Properties of Exponents.
1.4 Algebraic Expressions and the Order Of Operations.
2. Linear Equations and Inequalities
2.1 Linear Equations in One Variable.
2.2 Formulas, Geometry, and Problem Solving.
2.3 Problem Solving: Integers and Geometry.
2.4 Problem Solving: Percent, Investment, Motion, and Mixture
33
Algrebra for College
Students
SCHAUM’S EASY OUTLINE INTERMEDIATE
ALGEBRA
By Ray Steege and Kerry Bailey, Laramie County Community
College, Wyoming
ISBN-13: 978-0-07-142243-7 / MHID: 0-07-142243-9
What could be better than the bestselling Schaum’s Outline series?
For students looking for a quick nuts-and-bolts overview, it would have
to be Schaum’s Easy Outline series. Every book in this series is a
pared-down, simplified, and tightly focused version of its predecessor.
With an emphasis on clarity and brevity, each new title features a
streamlined and updated format and the absolute essence of the
subject, presented in a concise and readily understandable form.
Graphic elements such as sidebars, reader-alert icons, and boxed
highlights stress selected points from the text, illuminate keys to
learning, and give students quick pointers to the essentials.
• Designed to appeal to underprepared students and readers turned
off by dense text
• Cartoons, sidebars, icons, and other graphic pointers get the material
across fast
• Concise text focuses on the essence of the subject
• Deliver expert help from teachers who are authorities in their
fields
• Perfect for last-minute test preparation
New
ALGEBRA FOR COLLEGE
STUDENTS
Fifth Edition
By Mark Dugopolski
2009 (January 2008) / 250 pages
ISBN-13: 978-0-07-353352-0 / MHID: 0-07-353352-1
ISBN-13: 978-0-07-722484-4 / MHID: 0-07-722484-1
(Mandatory Package)
http://www.mhhe.com/dugopolski
Algebra for College Students, 5e is part of the latest offerings in the
successful Dugopolski series in mathematics. The author’s goal is
to explain mathematical concepts to students in a language they
can understand. In this book, students and faculty will find short,
• So small and light that they fit in a backpack!
SCHAUM’S OUTLINE OF INTERMEDIATE
ALGEBRA
By Ray Steege and Kerry Bailey, Laramie County Community College,
Wyoming
1997 / 381 pages
ISBN-13: 978-0-07-060839-9 / MHID: 0-07-060839-3
http://books.mcgraw-hill.com/cgi-bin/getbook.pl?isbn=0070608393&ad
key=W02003
Contents
Properties of Real Numbers.
Polynomials.
Rational Expressions.
First-Degree Equations and Inequalities.
Exponents, Roots, and Radicals.
Second-Degree Equations and Inequalities.
Systems of Equations and Inequalities.
Relations and Functions Exponential and Logarithmic Functions.
Sequences, Series, and the Binomial Theorem.
New to this edition
when appropriate.
questions, e-Professors, online tutoring and video lectures which are
directly tied to text specific material. MathZone courses are customized
34
to your textbook, but you can edit questions and algorithms, import your
own content, create announcements and due dates for assignments.
MathZone has automatic grading and reporting of easy-to-assign
algorithmically generated homework, quizzing and testing. Student
activity within MathZone is automatically recorded and available to
you through a fully integrated grade book than can be downloaded
to Excel. Go to www.mathzone.com to learn more.
5.6 Factoring ax² + bx + c
5.7 Factoring Strategy
Chapter 5 Wrap-Up
• Summary
• Chapter 5 Test
6.1 Properties of Rational Expressions and Functions
6.7 Applications
Chapter 6 Wrap-Up
• Summary
• Chapter 6 Test
7.1 Radicals
7.6 Complex Numbers
Chapter 7 Wrap-Up
• Summary
• Chapter 7 Test
8.4 Quadratic Functions and Their Graphs
Chapter 8 Wrap-Up
• Summary
• Chapter 8 Test
9 Additional Function Topics
9.5 Variation
Chapter 9 Wrap-Up
• Summary
• Chapter 9 Test
10 Polynomial and Rational Functions
10.1 The Factor Theorem
10.2 Zeros of a Polynomial Function
10.3 The Theory of Equations
10.4 Graphs of Polynomial Functions
10.5 Graphs of Rational Functions
Contents
TO THE STUDENT
PREFACE
1 The Real Numbers
1.1 Sets
1.3 Operations on the Set of Real Numbers
1.4 Evaluating Expressions
1.6 Using the Properties
Chapter 1 Wrap-Up
• Summary
• Chapter 1 Test
2.2 Formulas and Functions
2.3 Applications
2.4 Inequalities
Chapter 2 Wrap-Up
• Summary
• Chapter 2 Test
3.2 Slope of a Line
3.3 Three Forms for the Equation of a Line
3.4 Linear Inequalities and Their Graphs
Chapter 3 Wrap-Up
• Summary
• Chapter 3 Test
4.4 Solving Linear Systems Using Matrices
Chapter 4 Wrap-Up
• Summary
• Chapter 4 Test
5.1 Integral Exponents and Scientific Notation
5.2 The Power Rules
5.3 Polynomials and Polynomial Functions
5.4 Multiplying Binomials
5.5 Factoring Polynomials
35
ALGEBRA FOR COLLEGE STUDENTS
Chapter 10 Wrap-Up
• Summary
• Chapter 10 Test
Chapter 11 Wrap-Up
• Summary
• Chapter 11 Test
12.2 The Parabola
12.3 The Circle
Chapter 12 Wrap-Up
• Summary
• Chapter 12 Test
13.1 Sequences
13.2 Series
Chapter 13 Wrap-Up
• Summary
• Chapter 13 Test
14 Counting and Probability
14.1 Counting and Permutations
14.2 Combinations
14.3 Probability
Chapter 14 Wrap-Up
• Summary
• Chapter 14 Test
Appendix A
Answers to Selected Exercises
Index
By Julie Miller, Daytona Beach Community College—Daytona Beach and
Molly O’Neill, Daytona Beach Community College—Daytona Beach
2004 / Hardcover
ISBN-13: 978-0-07-301612-2 / MHID: 0-07-301612-8
(with MathZone)
http://www.mhhe.com/miller_oneill
Contents
1 Review of Basic Algebraic Concepts.
2 Linear Equations in Two Variables.
3 Systems of Linear Equations and Matrices.
4 Introduction to Relations and Functions.
5 Polynomials.
6 Radicals and Complex Numbers.
7 Factoring and Quadratic Functions.
8 Rational Expressions.
9 More Equations and Inequalities.
11 Conic Sections and Nonlinear Systems.
12 Polynomial and Rational Functions.
13 Sequences, Series, Counting, and Proba
36
37
MATHEMATICS
SERVICE COURSES
Business Mathematics........................................................................................41
Discrete Mathematics..........................................................................................45
Finite Mathematics..............................................................................................44
Geometry.............................................................................................................39
Liberal Arts Mathematics.....................................................................................41
Mathematics For Elementary Teachers...............................................................43
Technical Mathematics........................................................................................46
NEW TITLES
Mathematics Service Courses
2007
Author
ISBN-13
MHID
Mathematics For Technicians, 6e
Alldis
9780070131651
0070131651
38
Page
46
MATHEMATICS SERVICE COURSES
Internaltional Edition
GEOMETRY WITH GEOMETRY EXPLORER
By Michael Hvidsten, Gustavus Adolphus College
2005 / 352 pages
ISBN-13: 978-0-07-312990 7 / MHID: 0-07-312990-9
(with CD)
ISBN-13: 978-0-07-124865-5 / MHID: 0-07-124865-X
[IE wth CD]
Contents
1. Geometry and the Axiomatic Method:
Early Origins of Geometry. Thales and Pythagoras. Thales.
Pythagoras. Project 1 - The Ratio Made of Gold. Golden Section.
Golden Rectangles. Project Report. The Rise of the Axiomatic Method.
Properties of Axiomatic Systems. Consistency. Independence.
Completeness. Gödel’s Incompleteness Theorem. Euclid’s Axiomatic
Geometry. Euclid’s Postulates. Project 2 - A Concrete Axiomatic
System. Project Report
2. Euclidean Geometry:
Angles, Lines, and Parallels. Congruent Triangles and Pasch’s Axiom.
Project 3 -Special Points of a Triangle. Circumcenter. Orthocenter.
Incenter. Project Report. Measurement in Euclidean Geometry. MiniProject: Area in Euclidean Geometry. Cevians and Areas. Similar
Triangles. Mini-Project: Finding Heights. Circle Geometry. Project
4 -Circle Inversion and Orthogonality. Project Report. Orthogonal
Circles, Redux.
3. Analytic Geometry:
The Cartesian Coordinate System. Vector Geometry. Angles in
Coordinate Geometry. The Complex Plane. Polar Form. Complex
Functions. Analytic Functions and Conformal Maps. Birkhoff’s
Axiomatic System for Analytic Geometry.
4. Transformational Geometry:
Euclidean Isometrics. Reflections. Mini-Project: Isometries Through
Reflection. Reflection and Symmetry. Translations. Translational
Symmetry. Rotations. Rotational Symmetry. Project 5 - Quilts and
Transformations. Glide Reflections. Glide Reflection Symmetry.
Structure and Representation of Isometries. Matrix Form of Isometries.
Compositions of Rotations and Translations. Compositions of
Reflections and Glide Reflections. Isometries in Computer Graphics.
Summary of Isometry Compositions. Project 6 -Constructing
Compositions.
5. Symmetry:
Finite Plane Symmetry Groups. Frieze Groups. Wallpaper Groups.
Tiling the Plane. Escher. Regular Tessellations of the Plane. Project
7 - Constructing Tessellations.
6. Non-Euclidean Geometry:
Background and History. Models of Hyperbolic Geometry. Poincaré
Model. Mini-Project: The Klein Model. Basic Results in Hyperbolic
Geometry. Parallels in Hyperbolic Geometry. Omega Points
and Triangles. Project 8 - The Saccheri Quadrilateral. Lambert
Quadrilaterals and Triangles. Lambert Quadrilaterals. Triangles in
Hyperbolic Geometry. Area in Hyperbolic Geometry. Project 9 -Tiling
the Hyperbolic Plane. Models and Isomorphism.
7. Non-Euclidean Transformations:
Möbius Transformations. Fixed Points and the Cross Ratio. Geometric
Properties of Möbius Transformations. Isometries in the Poincaré
Model. Isometries in the Klein Model. Mini-Project: The Upper HalfPlane Model. Weierstrass Model.
8. Non-Euclidean Calculation:
Projection and the Angle of Parallelism. Horocycles. Project 10
-Parameterizing Horocycle Arcs. Concentric Horocycles. Hyperbolic
Trigonometry. Hyperbolic Right Triangle Trigonometry. General
Hyperbolic Trigonometry. Simplified Hyperbolic Trig Formulas.
Mini-Project: Calculations in Lambert Quadrilaterals. Arclength in
Cartesian Coordinates. Arclength in Polar Coordinates. Beltrami
39
Coordinates and Categoricalness. Area. Calculation in the Poincaré
Model. Arclength of Parameterized Curves. Geodesics. The Angle of
Parallelism. Right Triangles. Area. Project 11 - Infinite Real Estate?
9. Fractal Geometry:
The Search for a “Natural” Geometry. Self-Similarity. Sierpinski’s
Triangle. Cantor Set. Similarity Dimension. Project 12 - An Endlessly
Beautiful Snowflake. Contraction Mappings and The Space of
Fractals. Fractal Dimension. Project 13 - IFS Ferns. Algorithmic
Geometry. Turtle Geometry. Grammars and Productions. Spacefilling Curves. Project 14 - Words Into Plants: The Geometry of Life.
Constructions. Euclidean Constructions. Project 15 - Euclidean Eggs.
Hilbert’s Geometry. Incidence Geometry. Betweenness Geometry.
Project 16 - Angles and Ray Betweenness. Betweenness and
Triangles. Congruence Geometry. Triangle and Angle Congruence
Results. Segment Ordering. Project 17 - Angle Order. Continuity
Geometry. Segment Measure. Angle Measure. Basic Results of
Absolute Geometry. Continuity and Intersections. Parallelism.
A. Book I of Euclid’s Elements.
A.1 Definitions.
A.2 The Postulates (Axioms).
A.3 Common Notions.
A.4 Propositions (Theorems).
B. Brief Guide to Geometry Explorer.
B.1 The Main Geometry Explorer Window.
B.2 Selecting Objects.
B.3 Active vs. Inactive Tools.
B.4 Labels.
B.5 Object Coloring.
B.6 On-Line Help.
B.7 Undo/Redo of Actions.
B.8 Clearing, Resizing the Canvas.
B.9 Saving Files as Images.
B.10 Main Window Button Panels.
B.10.1 Create Panel.
B.10.2 Construct Panel.
B.10.3 Transform Panel.
B.11 Measurement in Geometry Explorer.
B.11.1 Neutral Measurements.
B.11.2 Euclidean-only Measurements.
B.11.3 Hyperbolic-only Measurements.
B.11.4 User Input Measurements.
B.12 Using Tables.
B.13 Using the Calculator.
B.14 Hyperbolic Geometry.
B.15 Analytic Geometry.
B.16 Turtle Geometry.
C. Birkhoff’s Axioms for Euclidean Geometry.
D. The 17 Wallpaper Groups
Geometry
[email protected]
SCHAUM’S OUTLINE OF GEOMETRY
Fourth Edition
Chapter 9: Regular Polygons and the Circle.
Chapter 10: Constructions.
By Barnett Rich (deceased) and Christopher Thomas
2009 (July 2008) / 369 pages
ISBN-13: 978-0-07-154412-2 / MHID: 0-07-154412-7
A classic Schaum’s bestseller, thoroughly updated to match the latest
course scope and sequence. The ideal review for the hundreds of
thousands of college and high school students who enroll in geometry
courses
CONTENTS
Schaum’s Outline of Geometry
Third Edition
By Barnett Rich (deceased) and Philip A Schmidt, Associate Dean at
Berea College
2000 / 322 pages
ISBN-13: 978-0-07-052766-9 / MHID: 0-07-052766-0
ISBN-13: 978-0-07-118345-1 / MHID: 0-07-118345-0 [IE]
1. Fundamentals of Algebra: Laws and Operations
2. Fundamentals of Algebra: Equations and Formulas
3. Lines, Angles, and Triangles
4. Methods of Proof
5. Congruent Triangles
6. Parallel Lines, Distances, and Angle Sums
7. Parallelograms, Trapezoids, Medians, and Midpoints
8. Circles
9. Similarity
10. Areas
11. Regular Polygons and the Circle
12. Locus
13. Inequalities and Indirect Reasoning
14. Improvement of Reasoning
15. Constructions
16. Proofs of Important Theorems
17. Transformational Geometry
(International Edition is not for sale in Japan.)
Contents
Fundamentals of Algebra: Laws and Operations.
Fundamentals of Algebra: Equations and Formulas.
Lines, Angles, and Triangles.
Methods of Proof.
Congruent Triangles.
Methods of Proof.
Congruent Triangles.
Parallel Lines, Distances, and Angle Sums.
Parallelograms, Trapezoids, Medians, and Midpoints.
Circles.
Similarity.
Areas.
Regular Polygons and the Circle.
Locus.
Inequalities and Indirect Reasoning.
Improvement of Reasoning.
Constructions.
Proofs of Important Theorems.
Transforma-tional Geometry.
BOB MILLER’S GEOMETRY FOR THE
CLUELESS
Second Edition
By Bob Miller, City College of the City University of New York
2006 (September 2005) / 160 pages
ISBN-13: 978-0-07-145902-0 / MHID: 0-07-145902-2
Bob Miller’s Geometry for the Clueless tackles a subject more than
three million students face every year. Miller acts as a private tutor,
painstakingly covering the high school curriculum as well as post
secondary courses in geometry.
Schaum’s Easy OutlineS: Geometry
By Barnett Rich (deceased) and Philip A Schmidt, Associate Dean at
Berea College
2001 / 144 pages
ISBN-13: 978-0-07-136973-2 / MHID: 0-07-136973-2
Contents
Chapter 1: Lines, Angles, and Triangles.
Chapter 2: Deductive Reasoning.
Chapter 3: Congruent Triangles.
Chapter 4: Parallel Lines, Distances, and Angle Sums.
Chapter 5: Trapezoids and Parallelograms.
Chapter 6: Circles.
Chapter 7: Similarity.
Chapter 8: Areas.
40
Liberal Arts Mathematics
Business Mathematics
MATHEMATICS IN OUR WORLD
SOLVING BUSINESS PROBLEMS USING A
CALCULATOR
Sixth Edition
By Allan G Bluman, Community College of Allegheny County-South
2005 / 840 pages /Hardcover
ISBN-13: 978-0-07-331182-1 / MHID: 0-07-331182-0
(with MathZone)
By Mildred Polisky
2003 / 288 pages
ISBN-13: 978-0-07-830020-2 / MHID: 0-07-830020-7
Contents
One Problem Solving:
The Nature of Mathematical Reasoning. Problem Solving.
Estimation.
Two Sets:
The Nature of Sets. Subsets and Set Operations. Venn Diagrams.
Using Sets to Solve Problems. Infinite Sets.
Three Logic:
Statements. Truth Tables. Types of Statements. Arguments. Euler
Circles.
Four Numeration Systems:
Early and Modern Numeration Systems. Base Number Systems.
Operations in Base Numbers.
Five The Real Number System:
The Natural Numbers. The Integers. The Rational Numbers. The
Irrational Numbers. The Real Numbers. Exponents and Scientific
Notation. Arithmetic and Geometric Sequences.
Six Other Mathematical Systems:
Clock Arithmetic. Modular Systems. Mathematical Systems without
Numbers.
Seven Topics in Algebra:
Fundamental Concepts of Algebra. Solving Linear Equations.
Applications of Linear Equations. Solving Linear Inequalities. Ratio,
Proportion, and Variation. Solving Quadratic Equations.
Eight Additional Topics in Algebra:
The Rectangular Coordinate System and the Line. Systems of Linear
Equations. Systems of Linear Inequalities. Linear Programming.
Functions.
Nine Consumer Mathematics:
Percent. Interest. Installment Buying. Home Ownership. Markup and
Markdown.
Ten Geometry:
Points, Lines, Planes, and Angles. Triangles, Polygons and Perimeter.
Areas of Polygons and the Circle. Surface Area and Volume. Right
Triangle Trigonometry. Networks.
Eleven Probability and Counting Techniques:
Basic Concepts of Probability. Tree Diagrams, Tables, and Sample
Spaces. Odds and Expectation. The Addition Rules for Probability.
The Multiplication Rules and Conditional Probability. The Fundamental
Counting Rule and Permutations. Combinations. Probability Using
Permutations and Combinations.
Twelve Statistics:
The Nature of Statistics and Organizing Data. Picturing Data.
Measures of Average. Measures of Variation. Measures of Position.
The Normal Distribution. Applications of the Normal Distribution.
Correlation and Regression Analysis.
Thirteen Voting Methods:
Preference Tables and the Plurality Method. The Borda Count Method
and the Plurality-with-Elimination Method. The Pairwise Comparison
Method and Approval Voting. Appendix A Measurement. Appendix B
Trigonometric Ratios. Appendix C Area Under the Standard Normal
Distribution. Appendix D Significan Values for the Correlation
Coefficient. Appendix E Using the Ti83+ Graphing Calculator
41
Contents
Section 1 10-Key Touch Method:
Lesson 1 Touch Addition of Whole Numbers.
Lesson 2 Touch Addition and Subtraction of Whole Numbers.
Lesson 3 Crossfooting.
Lesson 4 Touch Addition and Subtraction of Dollars and Cents.
Lesson 5 Rounding and Estimating Without a Calculator.
Lesson 6 Multiplication.
Lesson 7 Division.
Business Calculator Applications 1: Keypad Introduction.
Practice Test 1.
Section 2 Multiplication and Division:
Lesson 8 Constant Multiplication and Division.
Lesson 9 Multiplying Three or More Factors.
Lesson 10 Mixed Operations.
Lesson 11 Accumulative Multiplication.
Lesson 12 Negative Multiplication.
Business Calculator Applications 2: Using Memory Keys for Repeated
Operations.
Practice Test 2.
Section 3 Percents and Discounts:
Lesson 13 Fractions and Decimals.
Lesson 14 Percents.
Lesson 15 Finding Percentage, Rate, and Base.
Lesson 16 Amounts and Percents of Increase or Decrease.
Lesson 17 Single Discounts.
Lesson 18 Series Discounts.
Lesson 19 Extending Invoices and Quantity Pricing.
Lesson 20 Auditing Invoices.
Business Calculator Applications 3: Percent of Change, The
Percentage Formula, and Discounts .
Practice Test 3.
Section 4 Retail Calculations and Payroll:
Lesson 22 Markdown.
Lesson 23 Monthly and Semimonthly Payrolls.
Lesson 24 Payrolls for Hourly Workers.
Lesson 25 Commission Payroll Plans.
Business Calculator Applications 4: Retail Calculations.
Practice Test 4.
Section 5 Stocks and Bonds:
Lesson 27 Investments in Bonds.
Lesson 28 Yields on Investments.
Lesson 29 Selling Price of Stocks.
Business Calculator Applications 5: Prices of Treasury Bonds and
Notes.
Practice Test 5.
Section 6 Interest and the Metric System:
Lesson 30 Interest and Mortgage Interest.
Lesson 31 True Annual Interest Rate.
Lesson 32 Installment Buying.
Lesson 33 Prorating.
Lesson 34 Measurement.
Business Calculator Applications 6: Interest and Proration.
Practice Test 6. Progress Tests.
Answer Tabs
Chapter 11: GRE and GMAT Data Interpretation Questions
Section IV: Math Practice Tests
GRE Math Practice Test 1
GRE Math Practice Test 2
GMAT Math Practice Test 1
GMAT Math Practice Test 2
Applied Mathematics for Business,
Economics and the Social Science
Fourth Edition
By Frank S. Budnick, University of Rhode Island
1993 / 1,056 pages
ISBN-13: 978-0-07-008902-0 / MHID: 0-07-008902-7 (Out-of-Print)
ISBN-13: 978-0-07-112580-2 / MHID: 0-07-112580-9 [IE]
BUSINESS MATH DEMYSTIFIED
Contents
1 Some Preliminaries
2 Linear Equations
4 Functions and Graphs
5 Linear Functionsand Applications
6 Quadratic and Polynomial Functions
8 Mathematics of Finance
9 Matrix Algebra
10 Linear ProgrammingAn Introduction
11 The Simplex Method
12 Trans-portation and Assignment Models
13 Introduction to Probability Theory
14 Probability Distributions
15 Differentiation
16 Optimization Methodology and Applications
17 Integral Calculus An Introduction
18 Integral CalculusApplications
19 Optimization Functions of Several Variables
Appendix A Review of Algebra
By Allan Bluman, Community College of Allegheny County-South
2006 (March 2006) / 390 pages)
ISBN-13: 978-0-07-146470-3 / MHID: 0-07-146470-0
This work teaches business-management students all the basic
mathematics used in a retail business and follows the standard
curriculum of Business Math courses.
Contents
McGRAW-HILL’S CONQUERING GRE/GMAT
MATH
By Robert Moyer
2007 (December 2006) 352 pages
ISBN-13: 978-0-07-147243-2 / MHID: 0-07-147243-6
Practice problems, study guidance, and expert advice to boost
your math confidence and scores on the GRE and GMAT.
PREFACE
Chapter 1: Fractions--Review
Chapter 2: Decimals--Review
Chapter 3: Percent--Review
Chapter 4: Formulas--Review
Chapter 5: Checking Accounts
Chapter 6: Payroll and Commission
Chapter 7: Markup
Chapter 8: Discounts
Chapter 9: Simple Interest and Promissory Notes
Chapter 10: Compound Interest
Chapter 11: Annuities and Sinking Funds
Chapter 12: Consumer Credit
Chapter 13: Mortgages
Chapter 14: Insurance
Chapter 15: Taxes
Chapter 16: Stocks and Bonds
Chapter 17: Depreciation
Chapter 18: Inventory
Chapter 19: Financial Statements
Chapter 20: Statistics
Chapter 21: Charts and Graphs
FINAL EXAM / ANSWERS TO QUIZZES AND FINAL EXAM /
INDEX
A complete math-building program for both the GMAT and the GRE,
this is an ideal refresher course to sharpen your math skills and
improve your scores. It includes intensive reviews of every type
of math problem, in-depth practice questions, and step-by-step
strategies.
Contents
PREFACE
ACKNOWLEDGMENT
Section I: Introduction
Chapter 1: The GRE and GMAT Mathematics Sections
Chapter 2: The Mathematics You Need to Review
Chapter 3: How the Questions Are Asked
Section II: Basic Mathematics Review
Chapter 4: Number Properties
Chapter 5: Arithmetic Computation
Chapter 6: Algebra
Chapter 7: Geometry
Section III: Item Formats
Chapter 8: GRE and GMAT Quantitative Ability Questions
Chapter 9: GRE Quantitative Comparisons
Chapter 10: GMAT Data Sufficiency Questions
42
Mathematics for
Elementary Teachers
SCHAUM’S OUTLINE OF INTRODUCTION
TO MATHEMATICAL ECONOMICS
Third Edition
MATHEMATICS FOR ELEMENTARY
TEACHERS
A Conceptual Approach, Seventh Edition
By Edward T Dowling, Fordham University
2001 / 523 pages
ISBN-13: 978-0-07-135896-5 / MHID: 0-07-135896-X
ISBN-13: 978-0-07-135896-5 / MHID: 0-07-135896-1 [IE]
By Albert B. Bennett, University Of New Hampshire, and Ted Nelson,
Portland State University
2007 (June 2006) / 896 pages / Hardcover
ISBN-13: 978-0-07-302284-0 / MHID: 0-07-302284-5
ISBN-13: 978-0-07-322462-6 / MHID: 0-07-322462-6
(Mandatory Package)
Contents
Review.
Economic Applications of Graphs and Equations.
The Derivative and the Rules of Differentiation.
Uses of the Derivative in Mathematics and Economics.
Calculus of Multivariable Functions.
Caculus of Multivariable Functions in Economics.
Exponential and Logarithmic Functions in Economics.
Differentiation of Exponential and Logarithmic Functions.
The Fundamentals of Linear (or Matrix) Algebra.
Matrix Inversion.
Special Determinants and Matrices and Their Use in Economics.
Comparative Statics and Concave Programming.
IUntegral Calculus: The Indefinite Integral.
Integral Calculus: The Definite Integral.
First-Order Differential Equations.
First Order Difference Equations.
Second-Order Differential Equations and Difference Equations.
Simultaneous Differential and Difference Equations.
The Calculus of Variations.
Optimal Control Theory.
Albert B. Bennett, Jr. and L. Ted Nelson have presented hundreds
of workshops on how to give future teachers the conceptual
understanding and procedural fluency they will need in order to
successfully teach elementary-school mathematics. The Seventh
Edition of Mathematics for Elementary Teachers: A Conceptual
Approach continues their innovative, time-tested approach: an
emphasis on learning via specific, realistic examples and the
extensive use of visual aids, hands-on activities, problem-solving
strategies and active classroom participation. Special features in
the text ensure that prospective teachers will gain not only a deeper
understanding of the mathematical concepts, but also a better sense
of the connections between their college math courses and their future
teaching experiences, along with helpful ideas for presenting math
to their students in a way that will generate interest and enthusiasm.
The text draws heavily on NCTM Standards and contains many
pedagogical elements designed to foster reasoning, problem-solving
and communication skills. The Seventh Edition will also incorporate
in-text references to the virtual manipulative kit and other online
resources that enhance the authors’ explanations and examples.
Contents
Schaum’s Outline of Mathematical
Methods for Business and
Economics
By Edward T. Dowling, Fordham University
1993 / 320 pages
ISBN-13: 978-0-07-017697-3 / MHID: 0-07-017697-3
Contents
Review.
Equations and Graphs.
Functions.
Systems of Equations.
Linear (or Matrix) Algebra.
Solving Linear Equations with Matrix Algebra.
Linear Programming: Using Graphs.
Linear Programming: The Simplex Algorithm and the Dual.
Differential Calculus: The Derivative and the Rules of
Differentiation.
Differential Calculus: Uses of the Derivative.
Exponential and Logarithmic Functions.
Integral Calculus.
Calculus of Multivariable Functions.
Index.
43
1 Problem Solving and Algebraic Thinking
1.1 Introduction to Problem Solving
1.2 Patterns and Problem Solving
1.3 Problem Solving with Algebra
2 Sets, Functions, and Reasoning
2.1 Sets and Venn Diagrams
2.2 Functions, Coordinates and Graphs
2.3 Introduction to Deductive Reasoning
3 Whole Numbers
3.1 Numeration Systems
3.3 Multiplication
3.4 Division and Exponents
4 Number Theory
4.1 Factors and Multiples
4.2 Greatest Common Divisor and Least Common Multiple
5 Integers and Fractions
5.1 Integers
5.2 Introduction to Fractions
5.3 Operations with Fractions
6 Decimals: Rational and Irrational Numbers
6.1 Decimals and Rational Numbers
6.2 Operations with Decimals
6.3 Ratio, Percent, and Scientific Notation
6.4 Irrational and Real Numbers
7 Statistics
7.1 Collecting and Graphing Data
7.2 Describing and Analyzing Data
7.3 Sampling, Predictions, and Simulations
8 Probability
8.1 Single-Stage Experiments
8.2 Multistage Experiments
9 Geometric Figures
9.1 Plane Figures
9.2 Polygons and Tessellations
9.3 Space Figures
9.4 Symmetric Figures
10 Measurement
10.1 Systems of Measurement
10.2 Area and Perimeter
10.3 Volume and Surface Area
11 Motions in Geometry
11.1 Congruence and Constructions
11.2 Congruence Mappings
11.3 Similarity Mappings.
References for Resarch Statements by Chapter
Answers to Selected One-Page Math Activities
Answers to Puzzlers
Answers to Odd-Numbered Exercises
Credits
Index
6: Decimals: Rational and Irrational
6.1 Decimal Squares Model
6.2 Operations With Decimal Squares
6.3 A Model For Introducing Percent
6.4 Irrational Numbers On the Geoboard
7: Statistics
7.1 Scatter Plots: Looking for Relationships
7.2 Analyzing Data, Sampling and Simulation
7.3 Statistical Distributions: Observations and Applications
8: Probability
8.1 Probability Experiments
8.2 Multistage Probability Experiments
9: Geometric Figures
9.1 Figures On Rectangular and Circular Geoboards
9.2 Regular and Semiregular Tessellations
9.3 Models for Regular and Semiregular Polyhedra
9.4 Creating Symmetric Figures: Pattern Blocks and Paper Folding
10: Measurement
10.1 Measuring With Metric Units
10.2 Areas On Geoboards
10.3 Models For Volume and Surface Area
11: Motions In Geometry
11.1 Locating Sets of Points in the Plane
11.2 Drawing Escher-Type Tessellations
11.3 Devices For Indirect Measurement.
MATHEMATICS FOR ELEMENTARY
TEACHERS
An Activity Approach, Seventh Edition
By Albert B. Bennett, University Of New Hampshire, and Ted Nelson,
Portland State University
2007 (June 2006) / 416 pages / Spiral Bound/Comb
ISBN-13: 978-0-07-305370- 7 / MHID: 0-07-305370-8
ISBN-13: 978-0-07-329856-6 / MHID: 0-07-329856-5
(with Man Kit)
ISBN-13: 978-0-07-128651-0 / MHID: 0-07-128651-9
[IE, Man Kit]
Finite Mathematics
Contents
Activity Sets.
1: Problem Solving
1.1 Seeing and Extending Patterns With Pattern Blocks
1.2 Geometric Number Patterns With Color Tiles
1.3 Solving Story Problems With Algebra Pieces
2: Sets, Functions and Reasoning
2.1 Sorting and Classifying With Attribute Pieces
2.2 Graphing Spirolaterals
2.3 Logic Problems For Cooperative Learning Groups
3: Whole Numbers
3.1 Models For Numeration With Multibase Pieces
3.2 Adding and Subtracting With Multibase Pieces
3.3 Multiplying With Base-Ten Pieces
3.4 Dividing With Base-Ten Pieces
4: Number Theory
4.1 Models For Even Numbers, Odd Numbers, Factors and Primes
4.2 Models For Greatest Common Factor and Least Common
Multiple
5: Integers and Fractions
5.1 Black and Red Tile Model For Integers
5.2 Fraction-Bar Model For Equality and Inequality
5.3 Computing With Fraction Bars
44
SCHAUM’S OUTLINE OF BEGINNING FINITE
MATHEMATICS
By Seymour Lipschutz , Temple University -Philadelphia; John J Schiller
and R. Alu Srinivasan, Temple University
ISBN-13: 978-0-07-138897-9 / MHID: 0-07-138897-4
Most colleges and universities now require their non-science majors to
take a one- or two-semester course in mathematics. Taken by 300,000
students annually, finite mathematics is the most popular. Updated and
revised to match the structures and syllabuses of contemporary course
offerings, Schaum’s Outline of Beginning Finite Mathematics provides
a thorough review-- with worked examples--of the fundamentals of
linear equations and linear growth. Topics covered include games
theory, descriptive statistics, normal distribution, probability, binomial
distribution, and voting systems and apportionment.
This book is designed for a mathematics for elementary school
teachers course where instructors choose to focus on and/or take
an activities approach to learning. It provides inductive activities for
prospective elementary school teachers and incorporates the use
of physical models, manipulatives, and visual images to develop
concepts and encourage higher-level thinking. This text contains an
activity set that corresponds to each section of the companion text,
Mathematics for Elementary Teachers: A Conceptual Approach which
is also by Bennett/Nelson. The Activities Approach text can be used
independently or along with its companion volume. The authors are
pleased to welcome Laurie Burton, PhD, Western Oregon University
to this edition of Mathematics for Elementary Teachers: An Activity
Approach.
[email protected]
Discrete Mathematics
DISCRETE MATHEMATICS AND ITS
APPLICATIONS
Sixth Edition
By Kenneth H. Rosen, AT&T Laboratories
2007 (January 2006) / Hardcover with Access card
ISBN-13: 978-0-07-322972-0 / MHID: 0-07-322972-5
(with MathZone)
ISBN-13: 978-0-07-331271-2 / MHID: 0-07-331271-1
(with Math Zone Kit)
ISBN-13: 978-0-07-124474-9 / MHID: 0-07-124474-3 [IE]
Browse http://www.mhhe.com/rosen
Discrete Mathematics and its Applications, Sixth Edition, is intended
for one- or two-term introductory discrete mathematics courses taken
by students from a wide variety of majors, including computer science,
mathematics, and engineering. This renowned best-selling text, which
has been used at over 500 institutions around the world, gives a
focused introduction to the primary themes in a discrete mathematics
course and demonstrates the relevance and practicality of discrete
mathematics to a wide a wide variety of real-world applications…from
computer science to data networking, to psychology, to chemistry,
to engineering, to linguistics, to biology, to business, and to many
other important fields.
Contents
Preface. The Companion Website. To the Student.
1 The Foundations: Logic and Proof, Sets, and Functions
1.1 Logic
1.2 Propositional Equivalences
1.3 Predicates and Quantifiers
1.4 Nested Quantifiers
1.5 Methods of Proof
1.6 Sets
1.7 Set Operations
1.8 Functions
End-of-Chapter Material.
2 The Fundamentals: Algorithms, the Integers, and Matrices
2.1 Algorithms
2.2 The Growth of Functions
2.3 Complexity of Algorithms
2.4 The Integers and Division
2.5 Integers and Algorithms
2.6 Applications of Number Theory
2.7 Matrices
3 Mathematical Reasoning, Induction, and Recursion
3.1 Proof Strategy
3.2 Sequences and Summations
3.3 Mathematical Induction
3.4 Recursive Definitions and Structural Induction
3.5 Recursive Algorithms
3.6 Program Correctness
4 Counting
4.1 The Basics of Counting
4.2 The Pigeonhole Principle
4.3 Permutations and Combinations
4.4 Binomial Coefficients
4.5 Generalized Permutations and Combinations
4.6 Generating Permutations and Combinations.
5 Discrete Probability
5.1 An Introduction to Discrete Probability
5.2 Probability Theory
45
5.3 Expected Value and Variance.
6 Advanced Counting Techniques
6.1 Recurrence Relations
6.2 Solving Recurrence Relations
6.3 Divide-and-Conquer Algorithms and Recurrence Relations
6.4 Generating Functions
6.5 Inclusion-Exclusion
6.6 Applications of Inclusion-Exclusion
7 Relations
7.1 Relations and Their Properties
7.2 n-ary Relations and Their Applications
7.3 Representing Relations
7.4 Closures of Relations
7.5 Equivalence Relations
7.6 Partial Orderings
8 Graphs
8.1 Introduction to Graphs
8.2 Graph Terminology
8.3 Representing Graphs and Graph Isomorphism
8.4 Connectivity
8.5 Euler and Hamilton Paths
8.6 Shortest-Path Problems
8.7 Planar Graphs
8.8 Graph Coloring
9 Trees
9.1 Introduction to Trees
9.2 Applications of Trees
9.3 Tree Traversal
9.4 Spanning Trees
9.5 Minimum Spanning Trees
End-of-Chapter Material
10 Boolean Algebra
10.1 Boolean Functions
10.2 Representing Boolean Functions
10.3 Logic Gates
10.4 Minimization of Circuits
11 Modeling Computation
11.1 Languages and Grammars
11.2 Finite-State Machines with Output
11.3 Finite-State Machines with No Output
11.4 Language Recognition
11.5 Turing Machines End-of-Chapter Material
Appendixes
A.1 Exponential and Logarithmic Functions
A.2 Pseudocode Suggested Readings
Answers to Odd-Numbered Exercises
Photo Credits
Index of Biographies
Index
Discrete Mathematics by Example
Schaum’s 2,000 Solved Problems in
Discrete Mathematics
By Andrew Simpson, Oxford Brookes
2002 / 450 pages
ISBN-13: 978-0-07-709840-7 / MHID: 0-07-709840-4
ISBN-13: 978-0-07-122914-2 / MHID: 0-07-122914-0 [IE]
McGraw-Hill UK Title
By Seymour Lipschutz, Temple University
1992 / 412 pages
ISBN-13: 978-0-07-038031-8 / MHID: 0-07-038031-7
ISBN-13: 978-0-07-112690-8 / MHID: 0-07-112690-2 [IE]
(Out of Print)
Contents
1 Introduction.
2 Numbers.
3 Propositional logic.
4 Set theory.
5 Boolean algebra.
6 Typed set theory.
7 Predicate logic.
8 Relations.
9 Functions.
10 Sequences.
11 Induction.
12 Graph theory.
13 Combinatorics.
14 Modelling.
15 Analysis.
Contents
Set Theory.
Relations.
Functions.
Vectors and Matrices.
Graph Theory.
Planar Graphs and Trees.
Directed Graphs and Binary Trees.
Combinatorial Analysis.
Algebraic Systems.
Languages, Grammars, Automata.
Ordered Sets and Lattices.
Propositional Calculus.
Boolean Algebra.
Logic Gates.
SCHAUM’S OUTLINE OF DISCRETE
MATHEMATICS
3rd Edition
Technical Mathematics
By Seymour Lipschutz, Temple University-Philadelphia and Marc Lipson,
University of Georgia
2008 (July 2007) / 496 pages
ISBN-13: 978-0-07-147038-4 / MHID: 0-07-147038-7
Discrete mathematics becomes more and more important as the
digital age goes forward. This newly revised third edition updates all
areas of the subject.
CONTENTS
New
MATHEMATICS FOR TECHNICIANS
Sixth Edition
Set Theory
Relations
Functions and Algorithms
Logic and Propositional Calculus
Counting
Advanced Counting Techniques
Computer Arithmetic
Probability Theory
Graph Theory
Directed Graphs
Binary Trees
Properties of the Integers
Cryptology
Languages, Grammar, Machines
Ordered Sets and Lattices
Boolean Algebra
Appendix A: Vectors and Matrices
Appendix B: Algebraic Systems
By Alldis
2007 (October 2007)
ISBN-13: 978-0-07-013165-1 / MHID: 0-07-013165-1
(Details unavailable at press time)
46
TECHNICAL MATH DEMYSTIFIED
By Stan Gibilisco
2006 (April 2006) / 412 pages
ISBN-13: 978-0-07-145949-5 / MHID: 0-07-145949-9
Here is a complete self-teaching guide for anyone needing knowledge
of math as it applies to engineering and technical fields.
Contents
PREFACE / ACKNOWLEDGMENTS
Chapter 1: Numbering Systems
Chapter 2: Principles of Calculation
Chapter 3: Specific Notation
Chapter 4: Coordinates in Two Dimensions
Chapter 5: Coordinates in Three Dimensions
Chapter 6: Equations in One Variable
Chapter 7: Multivariable Equations
Chapter 8: Perimeter and Area in Two Dimensions
Chapter 9: Surface Area and Volume in Three Dimensions
Chapter 10: Boolean Algebra
Chapter 11: Trigonometric Functions
Chapter 12: Vectors in Two and Three Dimensions
Chapter 13: Logarithmic and Exponential Functions
Chapter 14: Differentiation in One Variable
Chapter 15: Integration in One Variable
Final Exam / Answers to Quiz and Exam Questions / Suggested
Additional References / Index
47
48
49
PRECALCULUS
College Algebra...................................................................................................51
College Algebra With Trigonometry.....................................................................56
Precalculus..........................................................................................................58
Trigonometry.......................................................................................................54
NEW TITLES
Precalculus
2009
Author
ISBN-13
MHID
College Algebra: Graphs And Models, 3e
Barnett
9780073051956
0073051950
51
Precalculus: Graphs And Models, 3e
Barnett
9780077221294
007722129X
58
College Algebra, 8e
Barnett
9780073312620
0073312622
52
College Algebra With Trigonometry, 8e
Barnett
9780073312644
0073312649
56
Precalculus With Limits, 6e
Barnett
9780073365800
0073365807
60
Precalculus With Mathzone, 6e
Barnett
9780073312637
0073312630
61
Trigonometry With Mathzone
Coburn
9780073312668
0073312665
54
Page
2008
50
PRECALCULUS
College Algebra
Contents
New
COLLEGE ALGEBRA: GRAPHS AND
MODELS
3rd Edition
By Raymond A Barnett, Merritt College, Michael R Ziegler and Karl
E Byleen of Marquette University, David Sobecki, Miami UniversityHamilton
ISBN-13: 978-0-07-305195-6 / MHID: 0-07-305195-0
ISBN-13: 978-0-07-722128-7 / MHID: 0-07-722128-1
(Mandatory Package)
http://www.mhhe.com/barnett
The Barnett Graphs & Models series in college algebra and
precalculus maximizes student comprehension by emphasizing
computational skills, real-world data analysis and modeling, and
problem solving rather than mathematical theory. Many examples
feature side-by-side algebraic and graphical solutions, and each is
followed by a matched problem for the student to work. This active
involvement in the learning process helps students develop a more
thorough understanding of concepts and processes. A hallmark of
the Barnett series, the function concept serves as a unifying theme.
A major objective of this book is to develop a library of elementary
functions, including their important properties and uses. Employing
this library as a basic working tool, students will be able to proceed
through this course with greater confidence and understanding as
they first learn to recognize the graph of a function and then learn
to analyze the graph and use it to solve the problem. Applications
included throughout the text give the student substantial experience
in solving and modeling real world problems in an effort to convince
even the most skeptical student that mathematics is really useful.
New to this edition
The narrative has been extensively reworked in order to make
the language less formal and more engaging for students.
A new interior design offers a cleaner presentation of concepts
and pedagogy.
More examples featuring side-by-side algebraic and graphical
solutions have been added to better integrate solution methods.
Annotated steps, in small colored type, are used more frequently
to walk students through each critical step in the problem-solving
process.
Expanded exercise sets provide additional practice, especially
at the easy to moderate levels.
An Annotated Instructor’s Edition is now available for instructors
and provides answers to each problem in the exercise set on the
same page as the problem appears.
MATHZONE McGraw-Hill’s MathZone is a complete, online
tutorial and course management system for mathematics and
statistics, designed for greater ease of use than any other system
available. Instructors can create and share courses and assignments
with colleagues and adjuncts in a matter of a few clicks of a mouse.
51
CHAPTER 1 FUNCTIONS, GRAPHS, AND MODELS
1-1 Using Graphing Utilities
1-2 Functions
1-3 Functions: Graphs and Properties
1-4 Functions: Graphs and Transformations
1-5 Operations on Functions; Composition
1-6 Inverse Functions
Chapter 1 Review
Chapter 1 Group Activity: Mathematical Modeling–Choosing a Long
Distance Calling Plan
CHAPTER 2 MODELING WITH LINEAR AND QUADRATIC
FUNCTIONS
2-1 Linear Functions
2-2 Linear Equations and Models
2-3 Quadratic Functions
2-4 Complex Numbers
2-5 Quadratic Equations and Models
2-6 Additional Equation Solving Techniques
2-7 Solving Inequalities
Chapter 2 Review
Chapter 2 Group Activity: Mathematical Modeling in Population
Studies
Cumulative Review Exercise for Chapters 1 and 2
CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS
3-1 Polynomial Functions And Models
3-2 Polynomial Division
3-3 Real Zeros and Polynomial Inequalities
3-4 Complex Zeros and Rational Zeros of Polynomials
3-5 Rational Functions and Inequalities
3-6 Variation and Modeling
Chapter 3 Review
Chapter 3 Group Activity: Interpolating Polynomials
CHAPTER 4 MODELING WITH EXPONENTIAL AND LOGARITHMIC
FUNCTIONS
4-1 Exponential Functions
4-2 Exponential Models
4-3 Logarithmic Functions
4-4 Logarithmic Models
4-5 Exponential and Logarithmic Equations
Chapter 4 Review
Cumulative Review Chapters 3 and 4
Chapter 4 Group Activity: Comparing Regression Models
CHAPTER 5 MODELING WITH SYSTEMS OF EQUATIONS AND
INEQUALITIES
5-1 Systems of Linear Equations in Two Variables
5-2 Systems of Linear Equations in Three Variables
5-3 Systems of Linear Inequalities
5-4 Linear Programming
Chapter 5 Review
Chapter 5 Group Activity: Modeling with Systems of Equations
CHAPTER 6 MATRICES AND DETERMINANTS
6-1 Matrix Solutions to Linear Systems
6-2 Matrix Operations
6-3 Inverse of a Square Matrix
6-4 Matrix Equations and Systems of Linear Equations
6-5 Determinants
6-6 Properties of Determinants
6-7 Determinants and Cramer’s Rule
Chapter 6 Review
Chapter 6 Group Activity: Using Matrices to Find Cost, Revenue,
and Profit
CHAPTER 7 SEQUENCES, INDUCTION, PROBABILITY
7-1 Sequences and Series
PRECALCULUS
7-2 Mathematical Induction
7-3 Arithmetic and Geometric Sequences
7-4 Multiplication Principle, Permutations, and Combinations
7-5 Sample Spaces and Probability
7-6 Binomial Formula
Chapter 7 Review
Chapter 7 Group Activity: Sequences Specified by Recursion
Formulas
CHAPTER 8 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY
8-1 Conic Sections; Parabola
8-2 Ellipse
8-3 Hyperbola
8-4 Systems of Nonlinear Equations
8-5 Rotation of Axes
Chapter 8 Review
Chapter 8 Group Activity: Focal Chords
Appendix A BASIC ALGEBRA REVIEW
A-1 Algebra and Real Numbers
A-2 Exponents
A-3 Radicals
A-4 Polynomials: Basic Operations
A-5 Polynomials: Factoring
A-6 Rational Expressions: Basic Operations
A-7 Linear Equations and Inequalities
A-8 Cartesian Coordinate System
A-9 Basic Formulas in Analytic Geometry
Appendix A Review
Appendix A Group Activity: Rational Number Representations
Appendix B SPECIAL TOPICS
B-1 Significant Digits
B-2 Partial Fractions
B-3 Parametric Equations
Appendix C GEOMETRIC FORMULAS
New
COLLEGE ALGEBRA
Eighth Edition
By Raymond Barnett, Merritt College, Michael
Ziegler and Karl Byleen of Marquette University
2008 (January 2007)
ISBN-13: 978-0-07-331262-0 / MHID: 0-07-331262-2
The Barnett, Ziegler, Byleen College Algebra series is designed to be
user friendly and to maximize student comprehension. The goal of this
series is to emphasize computational skills, ideas, and problem solving
rather than mathematical theory. The large number of pedagogical
devices employed in this text will guide a student through the course.
Integrated throughout the text, the students and instructors will find
Explore-Discuss boxes which encourage students to think critically
about mathematically concepts. In each section, the worked examples
are followed by matched problems that reinforce the concept being
taught. In addition, the text contains an abundance of exercises and
applications that will convince students that math is useful.
New to this edition
Objective Based Learning: Introductory section objectives have
been expanded to include the “what and why” of the objectives,
followed by icons within the text identifying the specific areas of focus.
A summary of chapter objectives will now be featured in the chapter
52
summary material.
Mathematical Modeling and Data Analysis: A focus on
mathematical modeling and data analysis, specifically establishing a
step by step process for understanding word problems and gathering
the data from said problems.
Graphical Interpretation: Throughout both examples and
exercises, this feature focuses on the importance of learning to
read and extract data from a given graph. This is developed by first
presenting a graph and using a problem solving approach to read
said graph. This focus aids in conceptualizing functions and building
mathematical models.
Throughout both examples and exercises, this feature focuses on
the importance of learning to read and extract data from a given graph.
This is developed by first presenting a graph and using a problem
solving approach to read said graph. This focus aids in conceptualizing
functions and building mathematical models.
Contents
Chapter R: Basic Algebraic Operations
R-1 Algebra and Real Numbers
R-2 Exponents
R-3 Radicals
R-4 Polynomials: Basic Operations
R-5 Polynomials: Factoring
R-6 Rational Expressions: Basic Operations
Chapter R Review
Chapter R Group Activity: Rational Number Representations
Chapter 1: Equations and Inequalities
1-1 Linear Equations and Applications
1-2 Linear Inequalities
1-3 Absolute Value
1-4 Complex Numbers
1-5 Quadratic Equations and Applications
1-6 Equations Involving Radicals
Chapter 1 Review
Chapter 1 Group Activity: Solving a Cubic Equation
Chapter 2: Graphs
2-1 Cartesian Coordinate system
2-2 Distance in the Plane
2-3 Equations of a line
Chapter 2 Review
Chapter 2 Group Activity: Rates of Change
Chapter 3: Functions
3-1 Functions
3-2 Graphing Functions
3-3 Transformations of Functions
3-5 Combining Functions; Composition
Chapter 3 Review
Chapter 3 Group Activity: Mathematical Modeling: Choosing a LongDistance Calling Plan
Chapters 1-3 Cumulative Review Exercises
Chapter 4: Polynomials and Rational Functions
4-1 Polynomial Functions and Models
Chapter 4 Review
Chapter 5 Review
PRECALCULUS
Chapter 5 Group Activity: Growth of Increasing Functions
Chapter 6: Additional Topics in Analytic Geometry
6-1 Conic Sections; Parabolas
6-2 Ellipses
6-3 Hyperbolas
Chapter 6 Review
Chapter 7: Systems of Equations and Inequalities; Matrices
7-1 Systems of Linear Equations: Graphing and Substitution
7-2 Systems of Linear Equations: Elimination
7-3 Systems of Linear Equations: Gauss-Jordan Elimination
7-4 Matrices: Basic Operations
7-5 Systems of Linear Equations: Matrix Inverse Methods
7-7 Systems of Linear Inequalities in Two Variables
Chapter 7 Review
Chapter 7 Group Activity: Modeling With Systems of Linear
Equations
Chapter 8: Sequences and Series
8-4 Counting Techniques: Multiplication Principle, Permutations, and
Combinations
Chapter 8 Review
Formulas
Appendix A: Special Topics
A-1 Scientific Notation and Significant Digits
A-2 Partial Fractions
A-3 Parametric Equations
Appendix B: Geometric Formulas
COLLEGE ALGEBRA
By John W. Coburn, St Louis Community College-Flors Valley
ISBN-13: 978-0-07-330542-4 / MHID: 0-07-330542-1
ISBN-13: 978-0-07-322982-9 / MHID: 0-07-322982-2
(with MathZone)
Browse http://www.mhhe.com/coburn
This college algebra text is written in a friendly and an easy to
understand manner in order to help students understand the concept
presented. This feature combined with ample examples, various types
of exercises, and well thought out, real-world applications give the
student the right tools to succeed. There are specific features and
exercise problems to incorporate graphing calculator technology for
those interested, however the material is presented in a way so that
it may be skipped for those not utilizing technology.
Contents
Chapter R: Review of Basic Concepts and Skills
R.1 The Language, Notation and Numbers of Mathematics
R.2 Algebraic Expressions and the Properties of Real Numbers
R.3 Exponents, Polynomials and Operations on Polynomials
R.4 Rational Expressions
R.5 Radicals and Rational Exponents
1.1 Linear Equations, Formulas and Problem Solving
1.2 Linear Inequalities in One Variable with Applications
1.3 Solving Polynomial and Other Equations
53
1.4 Complex Numbers
1.5 Solving Non-Factorable Quadratic Equations
Chapter 2: Functions and Graphs
2.1 Rectangular Coordinates and the Graph of a Line
2.2 Relations, Functions and Graphs
2.3 Linear Functions and Rates of Change
2.4 Quadratic and Other Toolbox Functions
2.5 Functions and Inequalities--A Graphical View
2.6 Regression, Technology and Data Analysis
Chapter 3: Operations on Functions and Analyzing Graphs
3.1 The Algebra and Composition of Functions
3.2 One-to-One and Inverse Functions
3.3 Toolbox Functions and Transformations
3.4 Graphing General Quadratic Functions
3.5 Asymptotes and Simple Rational Functions
3.6 Toolbox Applicaitons: Direct and Inverse Variation
3.7 Piecewise-Defined Functions
3.8 Analyzing the Graph of a Function
Chapter 4: Polynomial and Rational Functions
4.1 Polynomial Long Division and Synthetic Division
4.2 The Remainder and Factor Theorems
4.3 Zeroes of Polynomial Functions
4.4 Graphing Polynomial Functions
4.5 Graphing Rational Functions
4.6 Additional Insights into Rational Functions
4.7 Polynomial and Rational Inequalities–Analytical View
5.2 Logarithms and Logarithmic Functions
5.3 The Natural Logarithmic Function and Properties of Logarithms
5.4 Exponential/Logarithmic Equations and Applications
5.5 Applications from Investment, Finance and Physical Science
5.6 Exponential, Logarithmic and Logistic Regression Models
Chapter 6: Systems of Equations and Inequalities
6.1 Linear Systems in Two Variables with Applications
6.2 Linear Systems in Three Variables with Applications
6.3 Systems of Linear Inequalities and Linear Programming
6.4 Systems and Absolute Value Equations and Inequalities
6.5 Solving Linear Systems using Matrices and Row Operations
6.6 The Algebra of Matrices
6.7 Solving Linear Systems using Matrix Equations
6.8 Matrix Applications: Cramer’s Rule, Partial Fractions and More
Chapter 7: Conic Sections and Non-Linear Systems
7.1 The Circle and the Ellipse
7.2 The Hyperbola
7.3 Non-Linear Systems of Equations and Inequalities
7.4 Foci and the Analytic Ellipse and Hyperbola
7.5 The Analytic Parabola
Chapter 8: Additional Topics in Algebra
8.2 Arithmetic Sequences
8.3 Geometric Sequences
8.5 Fundamentals of Quick-Counting
8.6 Counting Techniques: Permutations and Combinations
8.8 The Binomial Theorem and Binomial Probabilities
Additional Topics Available on the Web.
Strengthening Core Skills: Probability and The Birthday Paradox.
Technology Extension: Nth Terms and the Nth Partial Sum.
Calculator Exploration and Discover: The Normal Distribution
Formula.
Math in Action: Empirical versus Theoretical Probability.
Appendix I: U.S. Customary and Metric Conversion Factors.
Appedix II: Rounding, Estimation and Significant Digits.
Appendix III: Rational Expressions and the Least Common
Denominator.
Appendix IV: Augmented Matrices and Matrix Inverses.
Appendix V: Deriving the Equation of a Conic.
Appendix VI: Basic Principles for Good Programming.
PRECALCULUS
Trigonometry
SCHAUM’S OUTLINE OF COLLEGE
ALGEBRA
Third Edition
By Robert Moyer, Ph.D., Fort Valley State College, and Murray R.
Spiegel, Deceased
2007 (December 2005) / 376 pages / Softcover
ISBN-13: 978-0-07-145227-4 / MHID: 0-07-145227-3
New
Algebra, the foundation for all higher mathematics, is explained
to both beginners and those reviewing algebra for further work in
math, science, and engineering. This superior study guide--with a
first edition that sold more than 600,000 copies--examines the most
current terminology, emphasis, and technology. The new edition also
includes:
TRIGONOMETRY WITH
MATHZONE
Greater emphasis on graphing calculators
Clarified material on logarithms and determinants
By John Coburn, St Louis Community CollegeFlors Valley
A simplified review of fractions
2008 (January 2007)
ISBN-13: 978-0-07-331266-8 / MHID: 0-07-331266-5
SCHAUM’S EASY OUTLINE: College
Algebra
This trigonometry text is written in a friendly and an easy to understand
manner in order to help students understand the concepts presented.
This feature combined with ample examples, a broad range of
exercises, and engaging real-world applications, give the student
the right tools to succeed. There are specific features and exercise
problems to incorporate graphing calculator technology for those
interested, however the material is presented in a way so that it may
be skipped for those not utilizing technology.
By Murray R. Spiegel (Deceased) and Robert Moyer, Fort Valley State
College
2000 / 160 pages
ISBN-13: 978-0-07-052709-6 / MHID: 0-07-052709-1
A Scahum’s Publication
Contents
Features
Functions, Limits, Continuity.
Fundamental Differentiation.
Implicit Differentiation.
Tangents and Normals.
Maxima and Minima.
Differentiating for Special Functions.
Implicit Differentiating.
The Law of the Mean.
Indeterminate Forms.
Differentials.
Curve Tracing.
Fundamental Integration.
Applications of Indefinite Integrals.
The Definite Integral.
Plane Areas of Integration.
Exponential Growth and Decay.
Improper Integrals.
Exercises--a wealth of exercises support the text’s main ideas,
and due to their range of difficulty, there is strong support for weaker
students, while advanced students are challenged to reach even
further.
Examples--abundant examples carefully prepare the students
for homework and exams. Easily located on the page, Coburn’s
numerous examples expose the learner to more exercise types than
most other texts.
Applications--large quantity of applications that explore a wide
variety of interests and illustrate how mathematics is connected to
other disciplines and the world around us.
Student-friendly exposition--Coburn provides a smooth and
conversational writing style that includes helpful hints, mathematical
connections, cautions and opportunities for further exploration.
MATHZONE--MathZone sets the bar for classroom technology.
Algorithmically generated problems, video lectures, interactive
exercise walk-throughs, as well as, online testing and assessment
using ALEKS technology, which all feed to a unified gradebook. www.
mathzone.com
ALEKS (Assessment and Learning in Knowledge Spaces)--an
artificial intelligence-based system for mathematics and statistics
learning, available online 24/7. Using unique adaptive questioning,
ALEKS accurately assesses what topics each students knows and
then determines exactly what each student is ready to learn next.
ALEKS interacts with a student much as a skilled human tutor would,
moving between explanation and practice as needed, correcting and
analyzing errors, defining terms and changing topics on request, and
helping them master the course content more quickly and easily. www.
highed.aleks.com.
54
PRECALCULUS
Contents
Chapter 1: An Introduction to Trigonometry
Preview
1.1 Angle Measure, Special Triangles, and Special Angles
1.2 The Trigonometry of Right Triangles
1.3 Trigonometry and the Coordinate Plane
1.4 Unit Circles and Trigonometric Functions
Chapter 2: Trigonometric Graphs and Models
2.1 Graphs of Sine and Cosine Functions
2.2 Graphs of Tangent and Cotangent Functions
2.3 Transformations and Applications of Trigonometric Graphs
2.4 Trigonometric Models
Chapter 3: Trig Identities: Their Purpose, Place, and Application
Preview
3.1 Fundamental Identities and Families of Identities
3.2 Constructing and Verifying Identities
3.3 The Sum and Difference Identities
3.4 Double Angle, Half Angle, and Product-to-Sum Identities
Chapter 4: Trigonometric Equations
Preview
4.2 The Inverse Trig Functions and their Application
4.3 Solving Basic Trig Equations
4.4 General Trig Equations and Applications
4.5 Parametric Equations and Graphs
Chapter 5: Applications of Trigonometry
Preview
5.1 Oblique Triangles and the Law of Sines
5.2 Law of Sines and the Ambiguous Case
5.3 The Law of Cosines
5.4 Vectors and Vector Diagrams
5.5 Vectors Applications and the Dot Product
5.6 Complex Numbers
5.7 Complex Numbers in Trigonometric Form
5.8 Demoivre’s Theorem and the Nth Roots Theorem
Chapter 6: Conic Sections and Polar Coordinates
Preview
6.2 The Hyperbola
6.5 Polar Coordinates, Equations, and Graphs
6.6 More on the Conic Sections: Rotations of Axes and Polar Form
[email protected]
55
TRIGONOMETRY
Revised Third Edition
By John D Baley, Cerritos College and Gary Sarell, Cerritos College
2003
ISBN-13: 978-0-07-283337-9 / MHID: 0-07-283337-8
Contents
PREFACE
CHAPTER 1: Measurement of Angles, Arcs and Sectors.
Using Radians, Degrees, or Grads to Measure Angles.
Length of an Arc and Area of a Sector of a Circle.
Circular Motion.
Key Ideas.
Review Test.
Chapter 2: The Trigonometric Functions
Definition of the Six Trigonometric Functions.
Values of the Trigonometric Functions for 0, 30, 45, 60, 90, 180
degree Angles.
Trigonometric Functions for Right Triangles.
Solving Right Triangles.
Applications of Right Triangle Trigonometry.
Circular Functions.
Key Ideas.
Review Test.
Chapter 3: Graphs of the Trigonometric Functions
Graphing Generic Sine and Cosine Functions.
Shifting Generic Curves Right/Left or Up/Down.
Using the Graphing Calculator to Graph Functions by Addition of
Ordinates.
Graphing the Tangent and Cotangent Functions.
Graphing the Secant and Cosecant Functions.
Qualitative Analysis of Trigonometric Functions.
Key Ideas.
Review Test.
Chapter 4: Inverse Trigonometric Functions
Relations, Functions, and Their Inverses.
Inverse of the Trigonometric Functions.
Finding Inverses of Trigonometric Functions Using a Calculator.
Key Ideas.
Review Test.
Chapter 5: Basic Trigonometric Identities
Fundamental Identities.
Opposite Angle Identities.
Additional Techniques to Prove Identities.
Key Ideas.
Review Test.
Chapter 6: Sum and Difference Identities
Sum and Difference Formulas for Cosine.
Some Identities Useful in Calculus.
Tan ( ).
Identities Involving Sums and Differences of n or +n.
Key Ideas.
Review Test.
Chapters 1-6 Cumulative Review.
Chapter 7: Additional Identities
Double-Angle Identities.
Half-Angle Identities.
Identities to Rewrite Sums and Products.
Key Ideas.
Review Test.
Chapter 8: Trigonometric Equations
Solving Basic Trigonometric Equations.
Solving Trigonometric Equations Involving Factoring.
Solving Trigonometric Equations Where the Argument is a
Function.
Using Identities to Solve Trigonometric Equations.
Applications.
Key Ideas.
Review Test.
Chapter 9: Laws of Sines and Law of Cosines
Derivation of the Law of Sines.
PRECALCULUS
The Ambiguous Case.
Applications of the Law of Sines.
Derivations of the Law of Cosines.
Applications of the Law of Cosines.
Area of a Triangle.
Key Ideas.
Review Test.
Chapter 10: Vectors
Addition of Vectors.
Geometric Resolution of Vectors.
Algebraic Resolution of Vectors.
Work, Inclined Planes, and the Dot Product.
Key Ideas.
Review Test.
Chapter 11: Complex Numbers
Algebraic Operations with Complex Numbers.
Trigonometric and Polar Representation of Complex Numbers.
DeMoivre’s Theorem.
Key Ideas.
Review Test.
Chapter 12: Polar Coordinates
The Polar Coordinate System.
Parametric Equations.
Other Curves in Polar Coordinates.
Key Ideas.
Review Test.
Chapters 1-12 Cumulative Review.
Appendix Rounding Off And Significant Figures.
Selected Answers.
Index
College Algebra with
Trigonometry
New
COLLEGE ALGEBRA WITH
TRIGONOMETRY
Eighth Edition
By Raymond A Barnett, Merritt College, Michael
ISBN-13: 978-0-07-331264-4 / MHID: 0-07-331264-9
ISBN-13: 978-0-07-111127-0 / MHID: 0-07-111127-1 [IE]
Browse http://www.mhhe.com/barnett
SCHAUM’S OUTLINE OF TRIGONOMETRY
Fourth Edition
By Robert Moyer, Fort Valley State University and Frank Ayres (deceased)
2008 (July 2008) / 211 pages
ISBN-13: 978-0-07-154350-7 / MHID: 0-07-154350-3
A classic Schaum’s bestseller, thoroughly updated to match the
latest course scope and sequence. The ideal review for the hundreds
of thousands of college and high school students who enroll in
trigonometry courses.
CONTENTS
1. Angles and Applications
2. Trigonometric Functions of a General Angle
3. Trigonometric Functions of an Acute Angle
4. Solutions of Right Triangles
5. Practical Applications
6. Reduction to Functions of Positive Acute Angles
7. Variation and Graphs of the Trigonometric Functions
8. Basic Relationships and Identities
9. Trigonometric Functions of Two Angles
10. Sum, Difference, and Product Formulas
11. Oblique Triangles
12. Area of a Triangle
13. Inverses of Trigonometric Functions
14. Trigonomeric Equations
15. Complex Numbers
user friendly and to maximize student comprehension. The goal of this
series is to emphasize computational skills, ideas, and problem solving
rather than mathematical theory. College Algebra with Trigonometry,
7/E, introduces a right angle approach to trigonometry and can be
used in one or two semester college algebra with trig or precalculus
courses. The large number of pedagogical devices employed in this
text will guide a student through the course. Integrated throughout the
text, the students and instructors will find Explore-Discuss boxes which
encourage students to think critically about mathematical concepts.
In each section, the worked examples are followed by matched
problems that reinforce the concept that is being taught. In addition,
the text contains an abundance of exercises and applications that will
convince students that math is useful. A Smart CD is packaged with
the seventh edition of the book. This CD reinforces important concepts,
and provides students with extra practice problems.
New to this edition
summary material.
Graphical Interpretation: Throughout both examples and
exercises, this feature focuses on the importance of learning to
read and extract data from a given graph. This is developed by first
presenting a graph and using a problem solving approach to read
said graph. This focus aids in conceptualizing functions and building
mathematical models.
Throughout both examples and exercises, this feature focuses on
the importance of learning to read and extract data from a given graph.
This is developed by first presenting a graph and using a problem
solving approach to read said graph. This focus aids in conceptualizing
functions and building mathematical models.
56
PRECALCULUS
Contents
R-2 Exponents
R-3 Radicals
Chapter R Review
1-3 Absolute Value
1-4 Complex Numbers
Chapter 1 Review
Chapter 2: Graphs
Chapter 2 Review
3-1 Functions
Chapter 3 Review
Chapter 4 Review
Chapter 5 Review
6-1 Angles and Their Measure
6-2 Right-Triangle Trigonometry
6-3 Trigonometric Functions: A Unit Circle Approach
6-4 Trigonometric Functions: Properties and Graphs
6-5 More General Trigonometric Functions
6-6 Inverse Trigonometric Functions
Chapter 6 Review
Chapter 6 Group Activity: A Predator-Prey Analysis Involving Mountain
Lions and Deer
Chapter 7: Trigonometric Identities and Conditional Equations
7-1 Basic Identities and Their Use
7-2 Sum, Difference, and Cofunction Identities
7-3 Double-Angle and Half-Angle Identities
7-4 Product-Sum and Sum-Product Identities
7-5 Trigonometric Equations
Chapter 7 Review
57
Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin(Bt + C):
A Harmonic Analysis Tool
Chapter 8: Additional Topics in Trigonometry
8-1 Law of Sines
8-2 Law of Cosines
8-3 Vectors in the Plane
8-4 Polar Coordinates and Graphs
8-5 Complex Numbers and De Moivre’s Theorem
Chapter 8 Review
Chapter 8 Group Activity: Conic Sections and Planetary Orbits
9-2 Ellipses
9-3 Hyperbolas
Chapter 9 Review
Chapter 10 Review
Equations
11-4 Counting Techniques: Multiplication Principle, Permutations,
and Combinations
Chapter 11 Review
Formulas
A-1 Scientific Notation
And Significant Digits
COLLEGE ALGEBRA WITH TRIGONOMETRY:
Graphs and Models
By Raymond A Barnett, Merritt College—Oakland; Michael R. Ziegler,
Marquette University and Karl E Byleen, Marquette University
2005 / 1,120 pages
ISBN-13: 978-0-07-292231-8 / MHID: 0-07-292231-1
(with MathZone)
http://www.mhhe.com/barnett/
Contents
1 Functions, Graphs, and Models:
1-1 Using Graphing Utilities.
1-2 Functions.
1-3 Functions: Graphs and Properties.
1-4 Functions: Graphs and Transformations.
1-5 Operations on Functions; Composition.
PRECALCULUS
Precalculus
1-6 Inverse Functions.
2 Modeling with Linear and Quadratic Functions
2-1 Linear Functions.
2-2 Linear Equations and Models.
2-3 Quadratic Functions.
2-4 Complex Numbers.
2-5 Quadratic Equations and Models.
2-6 Additional Equation-Solving Techniques.
2-7 Solving Inequalities.
3 Polynomial and Rational Functions
3-1 Polynomial Functions and Models.
3-2 Real Zero and Polynomial Inequalities.
3-3 Complex Zeros and Rational Zeros of Polynomials.
3-4 Rational Functions and Inequalities.
4-1 Exponential Functions.
4-2 Exponential Models.
4-3 Logarithmic Functions.
4-4 Logarithmic Models.
4-5 Exponential and Logarithmic Equations.
5 Trigonometric Functions
5-1 Angles and Their Measure.
5-2 Right Triangle Trigonometry.
5-3 Trigonometric Functions: A Unit Circle Approach.
5-4 Properties of Trigonometric Functions.
5-5 More General Trigonometric Functions.
5-6 Inverse Trigonometric Functions.
6 Trigonometric Identities and Conditional Equations
6-1 Basic Identities and Their Use.
6-2 Sum, Difference, and Cofunction Identities.
6-3 Double-Angle and Half-Angle Identities.
6-4 Product-Sum and Sum-Product Identities.
6-5 Trigonometric Equations.
7 Additional Topics in Trigonometry
7-1 Law of Sines.
7-2 Law of Cosines.
7-3 Geometric Vectors.
7-4 Algebraic Vectors.
7-5 Polar Coordinates and Graphs.
7-6 Complex Numbers in Rectangular and Polar Forms.
7-7 De Moivre’s Theorem.
8 Modeling with Linear Systems
8-1 Systems of Linear Equations in Two Variables.
8-2 Systems of Linear Equations and Augmented Matrices.
8-3 Gauss-Jordan Elimination.
8-4 Systems of Linear Inequalities.
8-5 Linear Programming.
9 Matrices and Determinants
9-1 Matrix Operations.
9-2 Inverse of a Square Matrix.
9-3 Matrix Equations and Systems of Linear Equations.
9-4 Determinants.
9-5 Properties of Determinants.
9-6 Determinants and Cramer’s Rule.
10 Sequences, Induction, and Probability
10-1 Sequences and Series.
10-2 Mathematical Induction.
10-3 Arithmetic and Geometric Sequences.
10-4 Multiplication Principle, Permutations, and Combinations.
10-5 Sample Spaces and Probability.
10-6 Binomial Formula.
11 Additional Topics in Analytic Geometry
11-1 Conic Sections; Parabola.
11-2 Ellipse.
11-3 Hyperbola.
11-4 Translation of Axes.
11-5 Rotation of Axes.
11-6 Nonlinear Systems.
Appendix A Basic Algebra Review.
Appendix B Special Topics.
Appendix C Geometric Formulas
New
PRECALCULUS: GRAPHS AND MODELS
Third Edition
By Raymond A Barnett, Merritt College, Michael R Ziegler and Karl
E Byleen of Marquette University, David Sobecki, Miami UniversityHamilton
ISBN-13: 978-0-07-722129-4 / MHID: 0-07-722129-X
http://www.mhhe.com/barnett
The Barnett Graphs & Models series in college algebra and
precalculus maximizes student comprehension by emphasizing
computational skills, real-world data analysis and modeling, and
problem solving rather than mathematical theory. Many examples
feature side-by-side algebraic and graphical solutions, and each is
followed by a matched problem for the student to work. This active
involvement in the learning process helps students develop a more
thorough understanding of concepts and processes.
A hallmark of the Barnett series, the function concept serves as a
unifying theme. A major objective of this book is to develop a library
of elementary functions, including their important properties and
uses. Employing this library as a basic working tool, students will
be able to proceed through this course with greater confidence and
understanding as they first learn to recognize the graph of a function
and then learn to analyze the graph and use it to solve the problem.
Applications included throughout the text give the student substantial
experience in solving and modeling real world problems in an effort
to convince even the most skeptical student that mathematics is
really useful.
New to this edition
The narrative has been extensively reworked in order to make
the language less formal and more engaging for students.
A new interior design offers a cleaner presentation of concepts
and pedagogy.
More examples featuring side-by-side algebraic and graphical
solutions have been added to better integrate solution methods.
Annotated steps, in small colored type, are used more frequently
to walk students through each critical step in the problem-solving
process.
Expanded exercise sets provide additional practice, especially
at the easy to moderate levels.
An Annotated Instructor’s Edition is now available for instructors
and provides answers to each problem in the exercise set on the same
page as the problem appears.
MATHZONE McGraw-Hill’s MathZone is a complete, online
tutorial and course management system for mathematics and
statistics, designed for greater ease of use than any other system
available. Instructors can create and share courses and assignments
with colleagues and adjuncts in a matter of a few clicks of a mouse.
58
PRECALCULUS
Contents
CHAPTER 1 FUNCTIONS, GRAPHS, AND MODELS
1-1 Using Graphing Utilities
1-2 Functions
1-3 Functions: Graphs and Properties
1-4 Functions: Graphs and Transformations
Chapter 1 Review
Chapter 1 Group Activity: Mathematical Modeling–Choosing a Long
Distance Calling Plan
CHAPTER 2 MODELING WITH LINEAR AND QUADRATIC
FUNCTIONS
2-1 Linear Functions
2-4 Complex Numbers
2-5 Quadratic Equations and Models
2-6 Additional Equation Solving Techniques
2-7 Solving Inequalities
Chapter 2 Review
Chapter 2 Group Activity: Mathematical Modeling in Population
Studies
CHAPTER 3 POLYNOMIAL AND RATIONAL FUNCTIONS
3-1 Polynomial Functions And Models
3-2 Polynomial Division
Chapter 3 Review
CHAPTER 4 MODELING WITH EXPONENTIAL AND LOGARITHMIC
FUNCTIONS
Chapter 4 Review
Cumulative Review Chapters 3 and 4
CHAPTER 5 TRIGONOMETRIC FUNCTIONS
5-3 Solving Right Triangles
5-4 Properties of Trigonometric Functions
5-5 More General Trigonometric Functions and and Models
Chapter 5 Review
Lions and Deer
CHAPTER 6 TRIGONOMETRIC IDENTITIES AND CONDITIONAL
EQUATIONS
Chapter 6 Review
Chapter 6 Group Activity: From M sin Bt + N cos Bt to A sin
(Bt + C)--A Harmonic Analysis Tool
CHAPTER 7 ADDITIONAL TOPICS IN TRIGONOMETRY
7-1 Law of Sines
7-2 Law of Cosines
59
Chapter 7 Review
Cumulative Review Exercise for Chapters 5, 6, and 7
CHAPTER 8 MODELING WITH SYSTEMS OF EQUATIONS AND
INEQUALITIES
8-3 Systems of Linear Inequalities
Chapter 8 Review
Chapter 8 Group Activity: Modeling with Systems of Equations
CHAPTER 9 MATRICES AND DETERMINANTS
9-1 Matrix Solutions to Linear Systems
9-3 Inverse of a Square Matrix
9-4 Matrix Equations and Systems of Linear Equations
9-5 Determinants
9-6 Properties of Determinants
9-7 Determinants and Cramer’s Rule
Chapter 9 Review
Chapter 9 Group Activity: Using Matrices to Find Cost, Revenue,
and Profit
CHAPTER 10 SEQUENCES, INDUCTION, PROBABILITY
Chapter 10 Review
Formulas
CHAPTER 11 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY
11-1 Conic Sections; Parabola
11-2 Ellipse
11-3 Hyperbola
Chapter 11 Review
Appendix A BASIC ALGEBRA REVIEW
A-1 Algebra and Real Numbers
A-2 Exponents
A-3 Radicals
A-4 Polynomials: Basic Operations
A-5 Polynomials: Factoring
A-6 Rational Expressions: Basic Operations
A-7 Linear Equations and Inequalities
A-8 Cartesian Coordinate System
A-9 Basic Formulas in Analytic Geometry
Appendix A Review
Appendix A Group Activity: Rational Number Representations
Appendix B Special Topics
B-1 Significant Digits
B-2 Partial Fractions
B-3 Parametric Equations
Appendix C Geometric Formulas
PRECALCULUS
New
PRECALCULUS WITH LIMITS
Sixth Edition
By Raymond A Barnett, Merritt College, Michael
R Ziegler and Karl E Byleen of Marquette
University
2008 (March 2007)
ISBN-13: 978-0-07-336580-0 / MHID: 0-07-336580-7
user friendly and to maximize student comprehension, emphasizing
computational skills, ideas, and problem solving as opposed to
mathematical theory. Suitable for a one or two semester college
algebra with trigonometry or precalculus course, Precalculus with
Limits introduces a unit circle approach to trigonometry and includes a
chapter on limits to provide students with a solid foundation for calculus
concepts. The large number of pedagogical devices employed in this
text will guide a student through the course. Integrated throughout the
text, students and instructors will find Explore-Discuss boxes which
encourage students to think critically about mathematical concepts. In
each section, the worked examples are followed by matched problems
that reinforce the concept being taught. In addition, the text contains
an abundance of exercises and applications that will convince students
that math is useful. A MathZone site featuring algorithmic exercises,
videos, and other resources accompanies the text.
New to this edition
Preview of Calculus: Unique to this edition, a chapter on limits
offers coverage of computing limits algebraically, limits at infinity, and
the derivative, in addition to other topics, to better prepare students
for calculus.
summary material.
Contents
R-2 Exponents
R-3 Radicals
Chapter R Review
Chapter R Review Exercises
Chapter R Group Activity: Rational and Irrational Numbers
1-3 Absolute Value in Equations and Inequalities
1-4 Complex Numbers
1-6 Additional Equation-Solving Techniques
Chapter 1 Review
60
Chapter 2: Graphs
2-1 Cartesian Coordinate System
2-3 Equations of a Line
Chapter 2 Review
3-1 Functions
Chapter 3 Review
Cumulative Review Exercises Chapters 1-3
Chapter 4 Review
Chapter 5 Review
6-4 Properties of Trigonometric Functions
6-5 More General Trigonometric Functions and Models
Chapter 6 Review
Lions and Deer
Chapter 7 Review
Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin (Bt + C):
8-1 Law of Sines
8-2 Law of Cosines
Chapter 8 Review
PRECALCULUS
9-2 Ellipse
9-3 Hyperbola
9-4 Translation and Rotation of Axes
Chapter 9 Review
Chapter 10 Review
Equations
Chapter 11: Sequences, Induction, and Probability
Chapter 11 Review
Formulas
Chapter 12 Limits: An Introduction to Calculus
12-1 Introduction to Limits
12-2 Computing Limits Algebraically
12-3 Limits at Infinity
12-4 The Derivative
12-5 Area and Calculus
Chapter 12 Review
Chapter 12 Group Activity: Derivatives of Exponential and Log
Functions
Appendix A: Special Topics A-1 Scientific Notation and Significant
Digits A-2 Partial Fractions A-3 Parametric Equations Appendix B:
Geometric Formulas Student Answers Subject Index
New
PRECALCULUS WITH
MATHZONE
Sixth Edition
By Raymond Barnett, Merritt College, Michael
ISBN-13: 978-0-07-331263-7 / MHID: 0-07-331263-0
ISBN-13: 978-0-07-111319-9 / MHID: 0-07-111319-3 [IE]
user friendly and to maximize student comprehension. The goal of
this series is to emphasize computational skills, ideas, and problem
solving rather than mathematical theory. Precalculus introduces a
unit circle approach to trigonometry and can be used in one or two
semester college algebra with trig or precalculus courses. The large
number of pedagogical devices employed in this text will guide a
student through the course. Integrated throughout the text, students
and instructors will find Explore-Discuss boxes which encourage
students to think critically about mathematical concepts. In each
section, the worked examples are followed by matched problems that
reinforce the concept being taught. In addition, the text contains an
abundance of exercises and applications that will convince students
that math is useful. A Smart CD is packaged with the seventh edition
of the book. This CD reinforces important concepts, and provides
students with extra practice problems.
New to this edition
Preview of Calculus: This precalculus text includes a further focus
on those skills considered prerequisite for calculus. Foundations of
Calculus icons are included throughout identifying key examples and
exercises needed to build this skill set. A review chapter summarizing
these skills will round out the text.
summary material.
Contents
R-2 Exponents
R-3 Radicals
Chapter R Review
1-3 Absolute Value
1-4 Complex Numbers
Chapter 1 Review
61
PRECALCULUS
Chapter 2: Graphs
Chapter 2 Review
3-1 Functions
Chapter 3 Review
Chapter 4 Review
Chapter 5 Review
6-4 Trigonometric Functions: Properties and Graphs
6-5 More General Trigonometric Functions
Chapter 6 Review
Lions and Deer
Chapter 7 Review
Chapter 7 Group Activity: From M sin Bt + N cos Bt to A sin(Bt + C):
8-1 Law of Sines
8-2 Law of Cosines
Chapter 8 Review
9-2 Ellipses
9-3 Hyperbolas
Chapter 9 Review
62
Chapter 10 Review
Equations
11-4 Counting Techniques: Multiplication Principle, Permutations,
and Combinations
Chapter 11 Review
Formulas
A-1 Scientific Notation and Significant Digits
PRECALCULUS
Concepts, Connections and Applications
By John W Coburn, St Louis Community College-Flors Valley
2007 (April 2006)
ISBN-13: 978-0-07-322981-2 / MHID: 0-07-322981-4
(with MathZone)
This Precalculus text is written in a friendly and an easy to understand
manner in order to help students understand the concept presented.
This feature combined with ample examples, various types of
exercises, and well thought out, real-world applications give the
student the right tools to succeed. There are specific features and
exercise problems to incorporate graphing calculator technology for
those interested, however the material is presented in a way so that
it may be skipped for those not utilizing technology.
Contents
1.1 Linear Equations, Formulas and Problem Solving
1.2 Linear Inequalities in One Variable with Applications
1.3 Solving Polynomial and Other Equations
1.4 Complex Numbers
1.5 Solving Non-Factorable Quadratic Equations
Chapter 2: Functions and Graphs
2.1 Rectangular Coordinates and the Graph of a Line
2.2 Relations, Functions and Graphs
2.3 Linear Functions and Rates of Change
2.4 Quadratic and Other Toolbox Functions
2.5 Functions and Inequalities--A Graphical View
2.6 Regression, Technology and Data Analysis
Chapter 3: Operations on Functions and Analyzing Graphs
3.1 The Algebra and Composition of Functions
3.3 Toolbox Functions and Transformations
3.4 Graphing General Quadratic Functions
PRECALCULUS
3.5 Asymptotes and Simple Rational Functions
3.6 Toolbox Applications: Direct and Inverse Variation
3.7 Piecewise-Defined Functions
3.8 Analyzing the Graph of a Function
Chapter 4: Polynomial and Rational Functions
4.1 Polynomial Long Division and Synthetic Division
4.2 The Remainder and Factor Theorems
4.3 Zeroes of Polynomial Functions
4.4 Graphing Polynomial Functions
4.5 Graphing Rational Functions
4.6 Additional Insights into Rational Functions
4.7 Polynomial and Rational Inequalities--Analytical View
5.2 Logarithms and Logarithmic Functions
5.3 The Natural Logarithmic Function and Properties of Logarithms
5.4 Exponential/Logarithmic Equations and Applications
5.5 Applications from Investment, Finance and Physical Science
5.6 Exponential, Logarithmic and Logistic Regression Models
Chapter 6: An Introduction to Trigonometric Functions
6.0 An Introduction to Cycles and Periodic Functions (on the Web)
6.1 Radian Measure and the Trigonometric Functions
6.3 Graphs of the Sine and Cosine Functions
6.4 Graphs of the Tangent and Cotangent Functions
6.5 Transformations and Applications of Trigonometric Graphs
6.6 Angle Measure, Special Triangles and Special Angles
6.7 The Trigonometry of Right Triangles
6.8 Trigonometry and the Coordinate Plane
Chapter 7: Trigonometric Identities, Inverses and Equations
7.1 Fundamental Identities and Families of Identities
7.2 Constructing and Verifying Identities
7.3 The Sum and Difference Identities
7.4 Double Angle, Half Angle and Product-to-Sum Identities
7.5 The Inverse Trig Functions and their Application
7.6 Solving Basic Trig Equations
7.7 General Trig Equations and Applications
7.8 Trigonometric Models and Sinusoidal Regression
Chapter 8: Applications of Trigonometry
8.1 Oblique Triangles and the Law of Sines
8.2 Law of Sines and the Ambiguous Case
8.3 the Law of Cosines
8.4 Vectors and Vector Diagrams
8.5 Vectors Applications and the Dot Product
8.6 Complex Numbers in Trigonometric Form; Products and
Quotients
8.7 Demoivre’s Theorem and the Nth Roots Theorem
9.1 Linear Systems in Two Variables with Applications
9.2 Linear Systems in Three Variables with Applications
9.3 Systems of Linear Inequalities and Linear Programming
9.4 Systems and Absolute Value Equations and Inequalities
9.5 Solving Linear Systems using Matrices and Row Operations
9.6 The Algebra of Matrices
9.7 Solving Linear Systems using Matrix Equations
9.8 Matrix Applications: Cramer’s Rule, Partial Fractions and More
Chapter 10: Topics From Analytical Geometry
10.0 An Introdcution to Analytical Geometry (on the Web)
10.2 The Hyperbola
10.3 Non-Linear Systems of Equations and Inequalities
10.6 Polar Coordinates, Equations and Graphs
10.7 More on the Conic Sections: Rotation of Axes and Polar Form
10.8 Parametric Equations of Graphs
Chapter 11: Additional Topics In Algebra
11.2 Arithmetic Sequences
11.3 Geometric Sequences
11.5 Fundamentals of Quick-Counting
63
11.6 Counting Techniques: Permutations and Combinations
11.8 The Binomial Theorem and Binomial Probabilities
11.9 Conditional Probability and Expected Value
11.10 Probability and the Normal Curve--Applications for Today
Chapter R: Review of Basic Concepts and Skills
R.1 The Language, Notation and Numbers of Mathematics
R.2 Algebraic Expressions and the Properties of Real Numbers.
R.3 Exponents, Polynomials and Operations on Polynomials
R.5 Rational Expressions
R.6 Radicals and Rational Exponents
R.7 Geometry Review with Unit Conversions
R.8 Expressions, Tables and Graphing Calculators.
SCHAUM’S OUTLINE OF PRECALCULUS
Second Edition
By Fred Safier, City College of San Francisco
2009 (July 2008) / 426 pages
ISBN-13: 978-0-07-150864-3 / MHID: 0-07-150864-3
latest course scope and sequence. The ideal review for the hundreds
of thousands of college and high school students who enroll in
precalculus courses.
CONTENTS
1. Polynomials
2. Exponents
3. Rational and Radical Expressions
4. Linear and Non-Linear Equations
5. Linear and Non-Linear Inequalities
6. Absolute Value in Equations and Inequalities
7. Analytic Geometry
8. Functions
9. Linear Functions
10. Transformations and Graphs
11. Quadratic Functions
12. Algebra of Functions
13. Polynomial Functions
14. Rational Functions
15. Algebraic Functions; Variations
16. Exponential Functions
17. Logarithmic Functions
18. Exponential and Logarithmic Equations
19. Trigonometric Functions
20. Graphs of Trignometric Functions
21. Angles
22. Trigonometric Identities and Equations
23. Sum, Difference, Multiple, and Half-Angle Formulas
24. Inverse Trigonometric Functions
25. Triangles
26. Vectors
27. Polar Coordinates; Parametric Equations
28. Trigonometric Form of Complex Numbers
29. Systems of Linear Equations
30. Gaussian and Gauss-Jordan Elimination
31. Partial Fraction
32. Decomposition
33. Non-Linear Systems of Equations
34. Introduction to Matrix Algebra
35. Matrix Multiplication and Inverses
36. Determinants and Cramer’s Rule
37. Loci; Parabolas
38. Ellipses and Hyperbolas
PRECALCULUS
39. Rotation of Axes
40. Conic Sections
41. Sequences and Series
42. The Principle of Mathematical Induction
43. Special Sequences and Series
44. The Binomial Theorem
64
65
CALCULUS
Applied/Business Calculus..................................................................................67
Calculus and Analytic Geometry.........................................................................69
Multi-Variable Calculus........................................................................................80
Single Variable Calculus......................................................................................74
NEW TITLES
calculus
2008
Author
ISBN-13
MHID
Smith
9780073312705
0073312703
69
Smith
9780073314204
007331420X
80
Smith
9780073314198
0073314196
74
66
Page
CALCULUS
Applied /
Business Calculus
International Business
APPLIED CALCULUS FOR BUSINESS,
ECONOMICS, AND THE SOCIAL AND LIFE
SCIENCES, expanded edition
Ninth Edition
By Laurence D. Hoffmann, Salomon Smith Barney and Gerald L. Bradley,
all of Claremont Mckenna College
2007 (January 2006) / 576 pgs / Hardcover
ISBN-13: 978-0-07-305192-5 / MHID: 0-07-305192-6
ISBN-13: 978-0-07-322979-9 / MHID: 0-07-322979-2
(with MathZone)
ISBN-13: 978-0-07-330926-2 / MHID: 0-07-330926-5 (MP)
ISBN-13: 978-0-07-110818-8 / MHID: 0-07-110818-1
[IE with MathZone]
ISBN-13: 978-0-07-110672-6 / MHID: 0-07-110672-3 [IE]
Browse http://www.mhhe.com/hoffmann
Applied Calculus for Business, Economics, and the Social and Life
Sciences introduces calculus in real-world contexts and provides a
sound, intuitive understanding of the basic concepts students need
as they pursue careers in business, the life sciences, and the social
sciences. This EXPANDED EDITION includes four additional chapters
on Differential Equations, Infinite Series and Taylor Approximations,
Probability, and Trigonometric Functions. The new Ninth Edition
builds on the straightforward writing style, practical applications from
a variety of disciplines, clear step-by-step problem solving techniques,
and comprehensive exercise sets that have been hallmarks of
Hoffmann/Bradley’s success through the years.
Contents
Preface.
1 Functions, Graphs, and Limits
1.1 Functions
1.2 The Graph of a Function
1.3 Linear Functions
1.4 Functional Models
1.5 Limits
1.6 One-Sided Limits and Continuity Chapter Summary. Important
Terms, Symbols, and Formulas. Checkup for Chapter
1. Review Problems. Explore! Update. Think About It.
2 Differentiation: Basic Concepts.
2.1 The Derivative
2.2 Techniques of Differentiation
2.3 Product and Quotient Rules; Higher Order Derivatives
2.4 The Chain Rule.
2.5 Marginal Analysis and Approximations Using Increments
2.6 Implicit Differentiation and Related Rates. Chapter Summary.
Important Terms, Symbols, and Formulas. Checkup for Chapter
3 Additional Applications of the Derivative
3.1 Increasing and Decreasing Functions; Relative Extrema
3.2 Concavity and Points of Inflection
3.3 Curve Sketching
3.4 Optimization
3.5 Additional Applied Optimization. Chapter Summary. Important
Terms, Symbols, and Formulas. Checkup for Chapter
4.3 Differentiation of Logarithmic and Exponential Functions
4.4 Additional Exponential Models. Chapter Summary. Important
Terms, Symbols, and Formulas. Checkup for Chapter 4. Review
67
Problems. Explore! Update. Think About It.
5 Integration
5.1 Antidifferentiation: The Indefinite Integral
5.2 Integration by Substitution
5.3 The Definite Integral and the Fundamental Theorem of
Calculus.
5.4 Applying Definite Integration: Area Between Curves and Average
Value
5.5 Additional Applications to Business and Economics
5.6 Additional Applications to the Life and Social Sciences. Chapter
Summary. Important Terms, Symbols, and Formulas. Checkup for
Chapter 5 Review Problems. Explore! Update. Think About It.
6 Additional Topics in Integration
6.1 Integration by Parts; Integral Tables
6.2 Improper Integrals
6.3 Numerical Integration. Chapter Summary. Important Terms,
Symbols, and Formulas. Checkup for Chapter 6. Review Problems.
Explore! Update. Think About It.
7 Calculus of Several Variables
7.1 Functions of Several Variables
7.2 Partial Derivatives
7.3 Optimizing Functions of Two Variables
7.4 The Method of Least-Squares
7.5 Constrained Optimization: The Method of Lagrange Multipliers
7.6 Double Integrals. Chapter Summary. Important Terms, Symbols,
and Formulas. Checkup for Chapter 7. Review Problems. Explore!
Update. Think About It.
8 Differential Equations
8.1 Introduction to Differential Equations
8.2 First-Order Linear Differential Equations
8.3 Additional Applications of Differential Equations
8.4 Approximate Solutions of Differential Equations
8.5 Difference Equations. Chapter Summary. Important Terms,
Symbols, and Formulas. Checkup for Chapter 8. Review Problems.
Explore! Update. Think About It.
9 Infinite Series and Taylor Series Approximations
9.1 Infinite Series
9.2 Tests for Convergence
9.3 Functions as Power Series; Taylor Series. Chapter Summary.
Important Terms, Symbols, and Formulas. Checkup for Chapter 9.
Review Problems. Explore! Update. Think About It.
10 Probability and Calculus.
10.1 Discrete Random Variables
10.2 Continuous Random Variables
10.3 Expected Value and Variance of Continuous Random
Variables
10.4 Normal and Poisson Probability Distributions. Chapter Summary.
Important Terms, Symbols, and Formulas. Checkup for Chapter 10.
Review Problems. Explore! Update. Think About It.
11 Trigonometric Functions
11.1 The Trigonometric Functions
11.2 Differentiation and Integration of Trigonometric Functions
11.3 Additional Applications Involving Trigonometric Functions.
Chapter Summary. Important Terms, Symbols, and Formulas.
Checkup for Chapter 11. Review Problems. Explore! Update. Think
About It.
Appendix A: Algebra Review
A.1 A Brief Review of Algebra
A.2 Factoring Polynomials and Solving Systems of Equations
A.3 Evaluating Limits with L’Hôpital’s Rule. Appendix Summary.
Important Terms, Symbols, and Formulas. Review Problems. Think
About It.
Tables
I Powers of e
II The Natural Logarithm (Base e)
III Trigonometric Functions.
Text Solutions
Answers to Odd-Numbered Problems, Chapter Checkup Problems,
and Chapter Review Problems.
Index
CALCULUS
CALCULUS FOR BUSINESS, ECONOMICS,
AND THE SOCIAL AND LIFE SCIENCES,
BRIEF EDITION
Ninth Edition
By Laurence D. Hoffmann, Salomon Smith Barney, and Gerald L. Bradley,
Claremont Mckenna College
2007 (December 2005) / Hardcover with access card
ISBN-13: 978-0-07-322978-2 / MHID: 0-07-322978-4
(with MathZone)
ISBN-13: 978-0-07-330927-9 / MHID: 0-07-330927-3 (MP)
ISBN-13: 978-0-07-110821-8 / MHID: 0-07-110821-1
[IE with MathZone]
ISBN-13: 978-0-07-110681-8 / MHID: 0-07-110681-2 [IE]
Browse http://www.mhhe.com/hoffmann
Calculus for Business, Economics, and the Social and Life Sciences
introduces calculus in real-world contexts and provides a sound,
intuitive understanding of the basic concepts students need as they
pursue careers in business, the life sciences, and the social sciences.
The new Ninth Edition builds on the straightforward writing style,
practical applications from a variety of disciplines, clear step-by-step
problem solving techniques, and comprehensive exercise sets that
have been hallmarks of Hoffmann/Bradley’s success through the
years.
Contents
Preface
1 Functions, Graphs, and Limits.
1.1 Functions.
1.2 The Graph of a Function.
1.3 Linear Functions.
1.4 Functional Models.
1.5 Limits.
1.6 One-Sided Limits and Continuity.
About It.
2 Differentiation: Basic Concepts.
2.1 The Derivative.
2.2 Techniques of Differentiation.
2.3 Product and Quotient Rules; Higher Order Derivatives.
2.4 The Chain Rule.
2.5 Marginal Analysis and Approximations Using Increments.
2.6 Implicit Differentiation and Related Rates.
About It.
3 Additional Applications of the Derivative.
3.1 Increasing and Decreasing Functions; Relative Extrema.
3.2 Concavity and Points of Inflection.
3.3 Curve Sketching.
3.4 Optimization.
3.5 Additional Applied Optimization.
About It.
4.1 Exponential Functions.
4.2 Logarithmic Functions.
4.3 Differentiation of Logarithmic and Exponential Functions.
4.4 Additional Exponential Models.
Checkup for Chapter 4 Review Problems. Explore! Update. Think
About It.
5 Integration
5.1 Antidifferentiation: The Indefinite Integral.
5.2 Integration by Substitution.
68
5.3 The Definite Integral and the Fundamental Theorem of
Calculus.
5.4 Applying Definite Integration: Area Between Curves and Average
Value.
5.5 Additional Applications to Business and Economics.
5.6 Additional Applications to the Life and Social Sciences
Checkup for Chapter 5. Review Problems Explore! Update. Think
About It.
6 Additional Topics in Integration.
6.1 Integration by Parts; Integral Tables.
6.2 Introduction to Differential Equations.
6.3 Improper Integrals; Continuous Probability
6.4 Numerical Integration.
Checkup for Chapter 6. Review Problems. Explore! Update Think
About It.
7 Calculus of Several Variables.
7.1 Functions of Several Variables.
7.2 Partial Derivatives.
7.3 Optimizing Functions of Two Variables
7.4 The Method of Least-Squares.
7.5 Constrained Optimization: The Method of Lagrange Multipliers
7.6 Double Integrals over Rectangular Regions.
Chapter Summary. Important Terms, Symbols, and Formulas. Checkup
for Chapter 7 Review Problems Explore! Update Think About It.
Appendix A: Algebra Review.
A.1 A Brief Review of Algebra.
A.2 Factoring Polynomials and Solving Systems of Equations
A.3 Evaluating Limits with L’Hôpital’s Rule. Appendix Summary.
Important Terms, Symbols, and Formulas. Review Problems. Think
About It.
Tables
I Powers of e
II The Natural Logarithm (Base e)
Text Solutions
Answers to Odd-Numbered Problems, Chapter Checkup Problems,
and Chapter Review Problems
Index
[email protected]
CALCULUS
Calculus and
Analytic Geometry
BUSINESS CALCULUS DEMYSTIFIED
2006 (December 2005) / 384 pages
ISBN-13: 978-0-07-145157-4 / MHID: 0-07-145157-9
This bestselling author of math titles uses practical business and
mathematical examples to help you relate to essential concepts in
calculus.
Contents
Chapter 1: Algebra Review
The slope and equation of a line
Finding x-intercepts
Solving equations
Quadratic functions
The vertex
The maximum/minimum value of a quadratic function
Increasing/decreasing intervals
Some important exponent properties
Chapter 2: Average rate of change
Limits
Chapter 3: Definition of derivative
Properties of the derivative
Instantaneous rates of change
The tangent line
The Power Rule
The Product Rule
The Quotient Rule
The Chain Rule
Layering different formulas
Chapter 5: Applications
Optimizing functions
Maximizing revenue and profit, minimizing cost, and other optimizing
problems
Chapter 6: The second derivative
Concavity
Another method for optimizing functions
Chapter 7: Implicit differentiation
Chapter 8: Rational functions
Limits and asymptotes
Chapter 9: Using calculus to sketch graphs
Graphs of polynomial functions
Chapter 10: Exponents and Logarithm functions
Using log properties to simplify differentiation
Chapter 11: Integration
The antiderivative
Integration formulas
The area under the curve
More integration formulas
Integration techniques
Chapter 12: Applications of the integral
New
CALCULUS: LATE
TRANSCENDENTAL
FUNCTIONS
Third Edition
By Robert Smith, Millersville University and
Roland Minton, Roanoke College
2008 (January 2007)
ISBN-13: 978-0-07-331270-5 / MHID: 0-07-331270-3
ISBN-13: 978-0-07-110199-8 / MHID: 0-07-110199-3 [IE]
Browse http://www.mhhe.com/smithminton
Students who have used Smith/Minton’s Calculus say it was easier
to read than any other math book they’ve used. That testimony
underscores the success of the authors’ approach which combines the
most reliable aspects of mainstream Calculus teaching with the best
elements of reform, resulting in a motivating, challenging book. Smith/
Minton wrote the book for the students who will use it, in a language
that they understand, and with the expectation that their backgrounds
may have some gaps. Smith/Minton provide exceptional, reality-based
applications that appeal to students’ interests and demonstrate the
elegance of math in the world around us. New features include:
Many new exercises and examples (for a total of 7,000 exercises
and 1000 examples throughout the book) provide a careful balance
of routine, intermediate and challenging exercises
New exploratory exercises in every section that challenge
students to make connections to previous introduced material.
New commentaries (“Beyond Formulas”) that encourage
students to think mathematically beyond the procedures they learn.
New counterpoints to the historical notes, “Today in Mathematics,”
stress the contemporary dynamism of mathematical research and
applications, connecting past contributions to the present.
An enhanced discussion of differential equations and additional
applications of vector calculus.
Exceptional Media Resources: Within MathZone, instructors and
students have access to a series of unique Conceptual Videos that
help students understand key Calculus concepts proven to be most
difficult to comprehend, 248 Interactive Applets that help students
master concepts and procedures and functions, 1600 algorithms,
and 113 e-Professors.
New to this edition
Many new exercises that are written at the intermediate and
rigorous level in response to requests by users of the 2nd Edition.
A more standard organization.
Every chapter was rewritten to be substantially more concise.
New commentaries entitled “Beyond Formulas”.
69
CALCULUS
that stress the contemporary dynamism of mathematical research and
Contents
Chapter 0: Preliminaries
0.1 The Real Numbers and the Cartesian Plane
0.2 Lines and Functions
0.3 Graphing Calculators and Computer Algebra Systems
0.4 Trigonometric Functions
0.5 Transformations of Functions
Chapter 1: Limits and Continuity
1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a
Curve
1.2 The Concept of Limit
1.3 Computation of Limits
1.4 Continuity and its Consequences / The Method of Bisections
1.5 Limits Involving Infinity / Asysmptotes
1.6 The Formal Definition of the Limit
1.7 Limits and Loss-of-Significance Errors / Computer Representation
or Real Numbers
Chaper 2: Differentiation
2.1 Tangent Lines and Velocity
2.2 The Derivative / Alternative Derivative Notations / Numerical
Differentiation
2.3 Computation of Derivatives: The Power Rule / Higher Order
Derivatives / Acceleration
2.4 The Product and Quotient Rules
2.5 The Chain Rule
2.6 Derivatives of the Trigonometric Functions
2.7 Implicit Differentiation
2.8 The Mean Value Theorem
Chapter 3: Applications of Differentiation
3.1 Linear Approximations and Newton’s Method
3.2 Maximum and Minimum Values
3.3 Increasing and Decreasing Functions
3.4 Concavity and the Second Derivative Test
3.5Overview of Curve Sketching
3.6Optimization
3.7 Related Rates
3.8 Rates of Change in Economics and the Sciences
4.1 Antiderivatives
4.2 Sums and Sigma Notation / Principle of Mathematical Induction
4.3 Area under a Curve
4.4 The Definite Integral / Average Value of a Function
4.5 The Fundamental Theorem of Calculus
4.7 Numerical Integration / Error bounds for Numerical Integration
Chapter 5: Applications of the Definite Integral
5.1 Area Between Curves
5.2 Volume: Slicing, Disks, and Washers
5.3 Volumes by Cylindrical Shells
5.4 Arc Length and Srface Area
5.5 Projectile Motion
5.6 Applications of Integration to Physics and Engineering
Chapter 6: Exponentials, Logarithms and other Transcendental
Functions
6.1 The Natural Logarithm
6.3 Exponentials
6.4 The Inverse Trigonometric Functions
6.5 The Calculus of the Inverse Trigonometric Functions
6.6 The Hyperbolic Function
Chapter 7: First-Order Differential Equations
7.1 Modeling with Differential Equations / Growth and Decay Problems
/ Compound Interest
7.2 Separable Differential Equations / Logistic Growth
7.3 Direction Fields and Euler’s Method
7.4 Systems of First-Order Differential Equations / Predator-Prey
Systems
70
7.6 Indeterminate Forms and L’Hopital’s Rule / Improper Integrals /
A Comparison Test
7.8 Probability /
8.1 modeling with Differential Equations / Growth and Decay Problems
/ Compound Interest
8.3 Direction Fields and Euler’s Method / Systems of First Order
Equations
Chapter 9: Infinite Series
9.1 Sequences of Real Numbers
9.2 Infinite Series
9.3 The Integral Test and Comparison Tests
9.4 Alternating Series / Estimating the Sum of an Alternating Series
9.5 Absolute Convergence and the Ratio Test / The Root Test /
Summary of Convergence Test
9.6 Power Series
9.7 Taylor Series / Representations of Functions as Series / Proof of
Taylor’s Theorem
9.8 Applications of Taylor Series / The Binomial Series
9.9 Fourier Series
Chapter 10: Parametric Equations and Polar Coordinates
10.1 Plane Curves and Parametric Equations
10.2 Calculus and Parametric Equations
10.3 Arc Length and Surface Area in Parametric Equations
10.4 Polar Coordinates
10.5 Calculus and Polar Coordinates
10.6 Conic Sections
10.7 Conic Sections in Polar Coordinates
Chapter 11: Vectors and the Geometry of Space
11.1 Vectors in the Plane
11.2 Vectors in Space
11.3 The Dot Product / Components and Projections
11.4 The Cross Product
11.5 Lines and Planes in Space
11.6 Surfaces in Space
Chapter 12: Vector-Valued Functions
12.1 Vector-Valued Functions
12.2 The Calculus Vector-Valued Functions
12.3 Motion in Space
12.4 Curvature
12.5 Tangent and Normal Vectors / Components of Acceleration,
Kepler’s Laws
12.6 Parametric Surfaces
Chapter 13: Functions of Several Variables and Partial
Differentiation
13.2 Limits and Continuity
13.4 Tangent Planes and Linear Approximations / Increments and
Differentials
13.5 The Chain Rule / Implicit Differentiation
13.6 The Gradient and Directional Derivatives
13.7 Extrema of Functions of Several Variables
13.8 Constrained Optimization and Lagrange Multipliers
Chapter 14: Multiple Integrals
14.1 Double Integrals
14.2 Area, Volume, and Center of Mass
14.3 Double Integrals in Polar Coordinates
14.4 Surface Area
14.5 Triple Integrals / Mass and Center of Mass
14.6 Cylindrical Coordinates
14.7 Spherical Coordinates
14.8 Change of Variables in Multiple Integrals
Chapter 15: Vector Calculus
15.1 Vector Fields
15.2 Line Integrals
15.3 Independence of Path and Conservative Vector Fields
15.4 Green’s Theorem
15.5 Curl and Divergence
15.6 Surface Integrals
CALCULUS
15.7 The Divergence Theorem
15.8 Stokes’ Theorem
15.9 Applications of Vector Calculus
Chapter 16: Second-Order Differential Equations
16.1 Second-Order Equations with Constant Coefficients
16.2 Nonhomogeneous Equations: Undetermined Coefficients
16.3 Applications of Second-Order Differential Equations
16.4 Power Series Solutions of Differential Equations
Appendix A: Proofs of Selected Theorems
Appendix B: Answers to Odd-Numbered Exercises
CALCULUS WITH MATHZONE: Early
Transcendental Functions
Third Edition
By Robert T. Smith, Millersville University, and Roland B. Minton,
Roanoke College
2007 (February 2006) / Hardcover with access card
ISBN-13: 978-0-07-330944-6 / MHID: 0-07-330944-3
ISBN-13: 978-0-07-322973-7 / MHID: 0-07-322973-3
(with MathZone)
ISBN-13: 978-0-07-110807-2 / MHID: 0-07-110807-6
[IE with MathZone]
ISBN-13: 978-0-07-110751-8 / MHID: 0-07-110751-7
[IE without MathZone]
underscores the success of the authors’ approach, which combines the
best elements of reform with the most reliable aspects of mainstream
calculus teaching, resulting in a motivating, challenging book. Smith/
Minton also provide exceptional, reality-based applications that appeal
to students’ interests and demonstrate the elegance of math in the
world around us.
Contents
0.1 Polynomials and Rational Functions
0.4 Trigonometric and Inverse Trigonometric Functions
0.5 Exponential and Logarithmic Functions. Hyperbolic Functions.
Fitting a Curve to Data
0.6 Transformations of Functions.
1.1 A First Look at Calculus
1.4 Continuity and its Consequences. The Method of Bisections.
1.5 Limits Involving Infinity. Asymptotes.
1.6 Formal Definition of the Limit. Exploring the Definition of Limit
Graphically
1.7 Limits and Loss-of-Significance Errors. Computer Representation
of Real Numbers.
Chapter 2: Differentiation
2.2 The Derivative Numerical Differentiation
2.3 Computation of Derivatives: The Power Rule. Higher Order
Derivatives. Acceleration.
2.5 The Chain Rule
2.7 Derivatives of the Exponential and Logarithmic Functions
71
2.8 Implicit Differentiation and Inverse Trigonometric Functions
2.9 The Mean Value Theorem.
3.2 Indeterminate Forms and L’Hopital’s Rule
3.6 Overview of Curve Sketching
3.7 Optimization
3.8 Related Rates
3.9 Rates of Change in Economics and the Sciences.
4.1 Antiderivatives
4.2 Sums and Sigma Notation. Principle of Mathematical Induction
4.3 Area
4.4 The Definite Integral. Average Value of a Function
4.7 Numerical Integration. Error Bounds for Numerical Integration
4.8 The Natural Logarithm as an Integral. The Exponential Function
as the Inverse of the Natural Logarithm.
5.4 Arc Length and Surface Area
5.6 Applications of Integration to Economics and the Sciences
5.7 Probability
Chapter 6: Integration Techniques
6.1 Review of Formulas and Techniques
6.2 Integration by Parts
6.3 Trigonometric Techniques of Integration. Integrals Involving
Powers of Trigonometric Functions. Trigonometric Substitution.
6.4 Integration of Rational Functions Using Partial Fractions. General
Strategies for Integration Techniques
6.5 Integration Tables and Computer Algebra Systems
6.6 Improper Integrals. A Comparison Test.
Chapter 7: First Order Differential Equations
7.1 Growth and Decay Problems. Compound Interest. Modeling with
Differential Equations.
7.2 Separable Differential Equations. Logistic Growth
7.4 Systems of First Order Differential Equations. Predator-Prey
Systems
8.2 Infinite Series
8.4 Alternating Series. Estimating the Sum of an Alternating Series
8.5 Absolute Convergence and the Ratio Test. The Root Test.
Summary of Convergence Tests
8.6 Power Series
8.7 Taylor Series. Representations of Functions as Series. Proof of
Taylor’s Theorem.
8.8 Applications of Taylor Series. The Binomial Series.
8.9 Fourier Series.
Chapter 9: Parametric Equations and Polar Coordinates.
9.1 Plane Curves and Parametric Equations.
9.2 Calculus and Parametric Equations.
9.3 Arc Length and Surface Area in Parametric Equations.
9.4 Polar Coordinates.
9.5 Calculus and Polar Coordinates.
9.6 Conic Sections.
9.7 Conic Sections in Polar Coordinates.
Chapter 10: Vectors and the Geometry of Space.
10.1 Vectors in the Plane.
10.3 The Dot Product. Components and Projections
CALCULUS
10.6 Surfaces in Space.
11.2 The Calculus of Vector-Valued Functions
11.4 Curvature
11.5 Tangent and Normal Vectors. Tangential and Normal Components
of Acceleration. Kepler’s Laws
11.6 Parametric Surfaces.
Chapter 12: Functions of Several Variables and Differentiation.
12.4 Tangent Planes and Linear Approximations. Increments and
Differentials.
12.5 The Chain Rule
13.4 Surface Area
13.5 Triple Integrals. Mass and Center of Mass
14.1 Vector Fields
14.2 Line Integrals
14.9 Applications of Vector Calculus.
Chapter 15: Second Order Differential Equations
15.3 Applications of Second Order Equations
15.4 Power Series Solutions of Differential Equations.
Appendix B: Answers to Odd-Numbered Exercises.
72
CALCULUS: Concepts and
Connections
By Robert T Smith, Millersville University and Roland B Minton, Roanoke
College
2006 / 1,312 pages
ISBN-13: 978-0-07-330929-3 / MHID: 0-07-330929-X
ISBN-13: 978-0-07-301607-8 / MHID: 0-07-301607-1
(with MathZone)
ISBN-13: 978-0-07-124902-7 / MHID: 0-07-124902-8
ISBN-13: 978-0-07-111201-7 / MHID: 0-07-111201-4
[IE with MathZone]
http://www.mhhe.com/smithminton
This modern calculus textbook places a strong emphasis on
developing students’ conceptual understanding and on building
connections between key calculus topics and their relevance for the
real world. It is written for the average student—one who is mostly
unfamiliar with the subject and who requires significant motivation. It
follows a relatively standard order of presentation, with early coverage
of transcendentals, and integrates thought-provoking applications,
examples and exercises throughout. The text also provides balanced
guidance on the appropriate role of technology in problem-solving,
including its benefits and its potential pitfalls. Wherever practical,
concepts are developed from graphical, numerical, algebraic and
verbal perspectives (the “Rule of Four”) to give students a complete
understanding of calculus.
Contents
Chapter 0: Preliminaries:
Polynomial and Rational Functions.
Graphing Calculators and Computer Algebra Systems.
Inverse Functions.
Trigonometric and Inverse Trigonometric Functions.
Parametric Equations and Polar Coordinates.
Chapter 1: Limits and Continuity:
Preview of Calculus.
The Concept of Limit.
Computation of Limits.
Continuity and its Consequences.
Method of Bisections.
Limits Involving Infinity.
Limits and Loss-of-Significance Errors.
Chapter 2: Differentiation:
Tangent Lines and Velocity.
The Derivative.
Computation of Derivatives: The Power Rule.
The Product and Quotient Rules.
The Chain Rule.
Derivatives of Trigonometric and Inverse Trigonometric Functions.
Derivatives of Exponential and Logarithmic Functions.
Implicit Differentiation and Related Rates.
The Mean Value Theorem.
Chapter 3: Applications of Differentiation:
Linear Approximations and Newton’s Method.
Indeterminate Forms and L’Hopital’s Rule.
Maximum and Minimum Values.
Increasing and Decreasing Functions.
Concavity and Overview of Curve Sketching.
Optimization.
Rates of Change in Applications.
Chapter 4: Integration:
Area under a Curve.
The Definite Integral.
Average Value of a Function.
Antiderivatives.
The Fundamental Theorem of Calculus.
CALCULUS
Integration by Substitution.
Trigonometric Techniques of Integration.
Integration by Parts.
Other Techniques of Integration.
Integration Tables and Computer Algebra Systems.
Numerical Integration.
Improper Integrals.
Comparison Test.
Chapter 5: Applications of the Definite Integral:
Area Between Curves.
Volume.
Slicing, Disks and Washers.
Arc Length and Surface Area.
Projectile Motion.
Work, Moments, and Hydrostatic Force.
Probability.
Chapter 6: Differential Equations:
Growth and Decay Problems.
Separable Differential Equations.
Euler’s Method.
Second Order Equations with Constant Coefficients.
Nonhomogeneous Equations: Undetermined Coefficients.
Applications of Differential Equations.
Chapter 7: Infinite Series:
Sequences of Real Numbers.
Infinite Series.
The Integral Test and Comparison Tests.
Alternating Series.
Absolute Convergence and the Ratio Test.
Power Series.
Taylor Series.
Taylor’s Theorem.
Applications of Taylor Series.
Fourier Series.
Power Series Solutions of Differential Equations.
Chapter 8: Vectors and the Geometry of Space:
Vectors in the Plane.
Vectors in Space.
The Dot Product.
Components and Projections.
The Cross Product.
Lines and Planes in Space.
Surfaces in Space.
Chapter 9: Vector-Valued Functions:
Vector-Valued Functions.
Parametric Surfaces.
The Calculus of Vector-Valued Functions.
Motion in Space.
Curvature.
Tangent and Normal Vectors.
Components of Acceleration, Kepler’s Laws.
Chapter 10: Functions of Several Variables and Differentiation:
Functions of Several Variables.
Limits and Continuity.
Partial Derivatives.
Tangent Planes and Linear Approximations.
The Chain Rule.
Implicit Differentiation.
The Gradient and Directional Derivatives.
Extrema of Functions of Several Variables.
Constrained Optimization and Lagrange Multipliers.
Chapter 11: Multiple Integrals:
Double Integrals.
Area, Volume and Center of Mass.
Double Integrals in Polar Coordinates.
Surface Area.
Triple Integrals.
Cylindrical Coordinates.
Spherical Coordinates.
Change of Variables in Multiple Integrals.
73
Chapter 12: Vector Calculus:
Vector Fields.
Curl and Divergence.
Line Integrals.
Independence of Path and Conservative Vector Fields.
Green’s Theorem.
Surface Integrals.
Parametric Representation of Surfaces.
The Divergence Theorem.
Stokes’ Theorem.
Applications of Vector Calculus.
Appendices:
A.1 Formal Definition of Limit.
A.2 Complete Derivation of Derivatives of sin x and cos x.
A.3 Natural Logarithm Defined as an Integral; Exponential Defined
A.4 Hyperbolic Functions.
A.5 Conic Sections in Polar Coordinates.
A.6 Proofs of Selected Theorems.
FIVE STEPS TO A 5 AP CALCULUS AB-BC
Second Edition
By William Ma
ISBN-13: 978-0-07-147629-4 / MHID: 0-07-147629-6
A Professional Reference
The AP AB/BC calculus exams have the largest enrollment of any AP
exam. This new edition of the AB/BC guide has been expanded to
cover both the AB and BC calculus tests and includes key updates on
all the material covered in the latest revision of the exams.
Contents
PREFACE
ACKNOWLEDGMENTS
Part I: How to Use This Book
Part II: What You Need to Know About the AP Calculus Exams
Part III: Comprehensive Review
Chapter 3: Graphs of Functions and Derivatives
Chapter 4: Applications of Derivatives
Chapter 5: More Applications of Derivatives
Chapter 7: Definite Integrals
Chapter 8: Areas and Volumes
Chapter 9: More Applications of Definite Integrals
Chapter 10: Series
Part IV: Practice Makes Perfect
APPENDIX I: FORMULAS AND THEOREMS
APPENDIX II: BIBLIOGRAPHY
APPENDIX III: WEBSITES
CALCULUS
Single Variable Calculus
SCHAUM’S OUTLINE OF ADVANCED
CALCULUS
Second Edition
By Robert C Wrede, and Murray R Spiegel (Deceased)
2002 / 356 pages
ISBN-13: 978-0-07-137567-2 / MHID: 0-07-137567-8
New
Contents
Numbers.
Basic Point-Set Topology.
Functions, Limits, and Continuity.
Special Functions (Log, Exp, Circular Trig, Hyperbolics).
Sequences.
Derivative.
Integrals.
Partial Derivatives.
Vectors.
Applications.
Differential Geometry (Curvature, Torsion,).
Multiple Integrals.
Line/Surface Integrals.
Change of Variable.
Infinite Sequences.
Infinite Series.
Improper Integrals.
Gamma and Beta Functions.
Fourier Series.
Fourier Integrals.
Laplace Transforms.
Function of Complex Variables
CALCULUS, SINGLE
VARIABLE: LATE
TRANSCENDENTAL
FUNCTIONS
Third Edition
By Robert Smith, Millersville University and
Roland Minton, Roanoke College
2008 (January 2007)
ISBN-13: 978-0-07-331419-8 / MHID: 0-07-331419-6
ISBN-13: 978-0-07-110198-1 / MHID: 0-07-110198-5 [IE]
elegance of math in the world around us. New features include: • Many
new exercises and examples (for a total of 7,000 exercises and 1000
examples throughout the book) provide a careful balance of routine,
intermediate and challenging exercises • New exploratory exercises in
every section that challenge students to make connections to previous
introduced material. • New commentaries (“Beyond Formulas”) that
encourage students to think mathematically beyond the procedures
they learn. • New counterpoints to the historical notes, “Today in
Mathematics,” stress the contemporary dynamism of mathematical
research and applications, connecting past contributions to the
present. • An enhanced discussion of differential equations and
additional applications of vector calculus. • Exceptional Media
Resources: Within MathZone, instructors and students have access
to a series of unique Conceptual Videos that help students understand
key Calculus concepts proven to be most difficult to comprehend, 248
Interactive Applets that help students master concepts and procedures
and functions, 1600 algorithms , and 113 e-Professors.
New to this edition
A more standard organization.
[email protected]
74
CALCULUS
Contents
Curve
or Real Numbers
Differentiation
2.5 The Chain Rule
3.5Overview of Curve Sketching
3.6Optimization
3.7 Related Rates
4.1 Antiderivatives
Functions
6.3 Exponentials
/ Compound Interest
Systems
A Comparison Test
7.8 Probability
75
/ Compound Interest
Equations
9.2 Infinite Series
9.6 Power Series
9.7 Taylor Series / Representations of Functions as Series / Proof
of Taylor’s Theorem
9.9 Fourier Series
10.6 Conic Sections
12.4 Curvature
Kepler’s Laws
Differentiation
Differentials
14.4 Surface Area
15.1 Vector Fields
15.2 Line Integrals
CALCULUS
CALCULUS: Single Variable: Early
Transcendental Functions
Third Edition
Roanoke College
2007 (December 2005) / Hardcover with access card
ISBN-13: 978-0-07-330943-9 / MHID: 0-07-330943-5
ISBN-13: 978-0-07-321531-0 / MHID: 0-07-321531-7
(with MathZone)
ISBN-13: 978-0-07-110786-0 / MHID: 0-07-110786-X
[IE with MathZone]
world around us. New features include: • A new organization placing
all transcendental functions early in the book and consolidating the
introduction to L’Hôpital’s Rule in a single section. • More concisely
written explanations in every chapter. • Many new exercises (for a
total of 7,000 throughout the book) that require additional rigor not
found in the 2nd Edition. • New exploratory exercises in every section
that challenge students to synthesize key concepts to solve intriguing
projects. • New commentaries (“Beyond Formulas”) that encourage
• New counterpoints to the historical notes, “Today in Mathematics,”
that stress the contemporary dynamism of mathematical research
and applications, connecting past contributions to the present. •
Contents
Fitting a Curve to Data
1.4 Continuity and its Consequences. The Method of Bisections
Graphically
of Real Numbers.
2.2 The Derivative. Numerical Differentiation
76
Derivatives. Acceleration.
2.5 The Chain Rule
Chapter 3: Applications of Differentiation.
3.7 Optimization
3.8 Related Rates
4.1 Antiderivatives
4.2 Sums and Sigma Notation. Principle of Mathematical Induction
4.3 Area
4.7 Numerical Integration. Error Bounds for Numerical Integration
5.6 Applications of Integration to Economics and the Sciences
5.7 Probability.
Powers of Trigonometric Functions. Trigonometric Substitution
7.2 Separable Differential Equations. Logistic Growth.
Systems.
8.2 Infinite Series
8.6 Power Series
Taylor’s Theorem
8.8 Applications of Taylor Series. The Binomial Series
8.9 Fourier Series
9.6 Conic Sections
CALCULUS
10.3 The Dot Product. Components and Projections
10.6 Surfaces in Space.
11.4 Curvature
11.5 Tangent and Normal Vectors. Tangential and Normal.
Components of Acceleration. Kepler’s Laws.
Chapter 12: Functions of Several Variables and Differentiation.
12.2 Limits and Continuity.
Differentials.
12.5 The Chain Rule
12.8 Constrained Optimization and Lagrange Multipliers.
13.4 Surface Area
13.5 Triple Integrals. Mass and Center of Mass.
14.1 Vector Fields
14.2 Line Integrals
15.2 Non-homogeneous Equations: Undetermined Coefficients
Appendix B: Answers to Odd-Numbered Exercises.
77
SCHAUM’S OUTLINE OF CALCULUS
Fifth Edition
By Frank Ayres (deceased) and Elliott Mendelson, Queens College
2009 (July 2008) / 572 pages
ISBN-13: 978-0-07-150861-2 / MHID: 0-07-150861-9
A classic Schaum’s bestseller, thoroughly updated to meet the
emphasis in current courses. The ideal review for the hundreds of
thousands of colleges and high school students who enroll in calculus
courses.
CONTENTS
1. Linear Coordinate Systems. Absolute Value. Inequalities.
2. Rectangular Coordinate Systems
3. Lines
4. Circles
5. Equations and their Graphs
6. Functions
7. Limits
8. Continuity
9. The Derivative
10. Rules for Differentiating Functions
11. Implicit Differentiation
12. Tangent and Normal Lines
13. Law of the Mean. Increasing and Decreasing Functions
14. Maximum and Minimum Values
15. Curve Sketching. Concavity. Symmetry.
16. Review of Trigonometry
17. Differentiation of Trigonometric Functions
18. Inverse Trigonometric Functions
19. Rectilinear and Circular Motion
20. Related Rates
21. Differentials. Newton’s Method
22. Antiderivatives
23. The Definite Integral. Area under a Curve
24. The Fundamental Theorem of Calculus
25. The Natural Logarithm
26. Exponential and Logarithmic Functions
27. L’Hopital’s Rule
28. Exponential Growth and Decay
29. Applications of Integration I: Area and Arc Length
30. Applications of Integration II: Volume
31. Techniques of Integration I: Integration by Parts
32. Techniques of Integration II: Trigonometric Integrands and
Trigonometric Substitutions
33. Techniques of Integration III: Integration by Partial Fractions
34. Miscellaneous Substitutions
35. Improper Integrals
36. Applications of Integration II: Area of a Surface of Revolution
37. Parametric Representation of Curves
38. Curvature
CALCULUS
CALCULUS DEMYSTIFIED
SCHAUM’S OUTLINE OF BEGINNING
CALCULS
Third Edition
By Steven G Krantz, Washington University - St. Louis
2003 / 343 pages
ISBN-13: 978-0-07-139308-9 / MHID: 0-07-139308-0
By Elliott Mendelson, Queens College
2008 (August 2007) / 400 pages
ISBN-13: 978-0-07-148754-2 / MHID: 0-07-148754-9
Contents
The guides that help students study faster, learn better- and get top
grades.
This review of beginning calculus is updated to reflect the latest course
scope and sequences, with expanded explanations of particularly
difficult topics.
Contents
Chapter 1: Coordinate Systems on a Line
Chapter 2: Coordinate Systems in a Plane
Chapter 3: Graphs of Equations
Chapter 4: Straight Lines
Chapter 5: Intersections of Graphs
Chapter 6: Symmetry
Chapter 7: Functions and Their Graphs
Chapter 8: Limits
Chapter 9: Special Limits
Chapter 10: Continuity
Chapter 11: The Slope of a Tangent Line
Chapter 12: The Derivative
Chapter 13: More on the Derivative
Chapter 14: Maximum and Minimum Problems
Chapter 15: The Chain Rule
Chapter 16: Implicit Differentiation
Chapter 17: The Mean-Value Theorem and the Sign of the
Derivative
Chapter 18: Rectilinear Motion and Instantaneous Velocity
Chapter 19: Instantaneous Rate of Change
Chapter 20: Related Rates
Chapter 21: Approximation by Differentials; Newton’s Method
Chapter 22: Higher-Order Derivatives
Chapter 23: Applications of the Second Derivative and Graph
Sketching
Chapter 24: More Maximum and Minimum Problems
Chapter 25: Angle Measure
Chapter 26: Sine and Cosine Functions
Chapter 27: Graphs and Derivatives of Sine and Cosine Functions
Chapter 28: The Tangent and Other Trigonometric Functions
Chapter 29: Antiderivatives
Chapter 30: The Definite Integral
Chapter 31: The Fundamental Theorem of Calculus
Chapter 32: Applications of Integration I: Area and Arc Length
Chapter 33: Applications of Integration II: Volume
Chapter 34: The Natural Logarithm
Chapter 35: Exponential Functions
Chapter 36: L’Hopital’s Rule; Exponential Growth and Decay
Chapter 37: Inverse Trigonometric Functions
Chapter 38: Integration by Parts
Chapter 39: Trigonometric Integrands and Trigonometric
Substitutions
Chapter 40: Integration of Rational Functions; The Method of Partial
Fractions
Appendix A: Trigonometric Formulas
Appendix B: Basic Integration Formulas
Appendix C: Geometric Formulas
Appendix D: Trigonometric Functions
Appendix E: Natural Logarithms
Appendix F: Exponential Functions
Answers to Supplementary Problems
Index
Preface.
Chapter 1: Basics.
Chapter 2: Foundations of Calculus.
Chapter 3: Applications of the Derivative.
Chapter 4: The Integral.
Chapter 5: Indeterminate Forms.
Chapter 6: Transcendental Functions.
Chapter 7: Methods of Integration.
Chapter 8: Applications of the Integral.
Bibliography.
Solutions to Exercises.
Final Exam. Index
How to Solve Word Problems in
Calculus
By Eugene Don and Benay Don
2001 / 226 pages
ISBN-13: 978-0-07-135897-2 / MHID: 0-07-135897-8
ISBN-13: 978-0-07-120383-8 / MHID: 0-07-120383-4 [IE]
(International Edition is not for sale in Japan)
Considered to be the hardest mathematical problems to solve, word
problems continue to terrify students across all math disciplines.
This new title in the World Problems series demystifies these difficult
problems once and for all by showing even the most math-phobic
readers simple, step-by-step tips and techniques. How to Solve
World Problems in Calculus reviews important concepts in calculus
and provides solved problems and step-by-step solutions. Once
students have mastered the basic approaches to solving calculus
word problems, they will confidently apply these new mathematical
principles to even the most challenging advanced problems. Each
chapter features an introduction to a problem type, definitions, related
theorems, and formulas. Topics range from vital pre-calculus review
to traditional calculus first-course content. Sample problems with
solutions and a 50-problem chapter are ideal for self-testing. Fully
explained examples with step-by-step solutions.
78
CALCULUS
SCHAUM’S EASY OUTLINES: Calculus
By Frank Ayres (deceased) and Elliott Mendelson, Queens College
2000 / 135 pages
ISBN-13: 978-0-07-052710-2 / MHID: 0-07-052710-5
Schaum’s Outline of Differential
and Integral Calculus, SI Metric
Third Edition
A Schaum Publication
http://books.mcgraw-hill.com/cgi-bin/getbook.pl?isbn=0070527105&ad
key=W02003
By Frank Ayres, Jr, Dickinson College
1992
ISBN-13: 978-0-07-112531-4 / MHID: 0-07-112531-0 [IE]
Contents
Chapter 1: Functions, Sequences, Limits, and Continuity.
Chapter 2: Differentiation.
Chapter 3: Maxima and Minima.
Chapter 4: Differentiation of Special Functions.
Chapter 5: The Law of the Mean, Indeterminate Forms, Differentials,
and Curve Sketching.
Chapter 6: Fundamental Integration Techniques and Applications.
Chapter 7: The Definite Integral, Plane Areas by Integration, Improper
Integrals.
Appendix A: Differentiation Formulas for Common Mathematical
Functions.
Appendix B: Integration Formulas for Common Mathematical
Functions. Index.
Calculus
By Elliott Mendelson, Queens College
1988 / 442 pages
ISBN-13: 978-0-07-041523-2 / MHID: 0-07-041523-4
ISBN-13: 978-0-07-099148-4 / MHID: 0-07-099148-0 [IE]
SCHAUM’S OUTLINE OF MATHEMATICA
By Eugene Don
2000 / 360 pages
ISBN-13: 978-0-07-135719- 7 / MHID: 0-07-135719-X
This powerful problem-solver gives you 3,000 problems in calculus,
fully solved step-by-step! From Schaum’s, the originator of the solvedproblem guide, and students’ favorite with over 30 million study guides
sold this timesaver helps you master every type of calculus problem
that you will face in your homework and on your tests, from inequalities
to differential equations. Work the problems yourself, then check the
answers, or go directly to the answers you need with a complete
index. Compatible with any classroom text, Schaum’s 3000 Solved
Problems in Calculus is so complete it’s the perfect tool for graduate
or professional exam review!
Contents
Getting Acquainted.
Basic Concepts.
Lists.
Two-Dimensional Graphics.
Three-Dimensional Graphics.
Equations.
Algebra and Trignometry.
Differential Calculus.
Integral Calculus.
Multivariate Calculus.
Ordinary Differential Equations.
Linear Algebra.
Schaum’s Outline of Understanding
Calculus Concepts
By Eli Passow, Temple University
1996 / 224 pages
ISBN-13: 978-0-07-048738-3 / MHID: 0-07-048738-3
Contents
What It’s All About.
The Derivative.
Applications of the Derivative.
The Integral.
Applications of the Integral.
Topics in Integration.
Infinite Series.
79
[email protected]
CALCULUS
Multi-Variable Calculus
New
calculus:
multivariable: late
transcendental
functions
Third Edition
By Robert T. Smith, Millersville University, and
Roland B. Minton, Roanoke College
2008 (January 2007)
ISBN-13: 978-0-07-331420-4 / MHID: 0-07-331420-X
elegance of math in the world around us. New features include: • Many
new exercises and examples (for a total of 7,000 exercises and 1000
examples throughout the book) provide a careful balance of routine,
intermediate and challenging exercises • New exploratory exercises in
every section that challenge students to make connections to previous
introduced material. • New commentaries (“Beyond Formulas”) that
encourage students to think mathematically beyond the procedures
they learn. • New counterpoints to the historical notes, “Today in
Mathematics,” stress the contemporary dynamism of mathematical
research and applications, connecting past contributions to the
present. • An enhanced discussion of differential equations and
additional applications of vector calculus. • Exceptional Media
Resources: Within MathZone, instructors and students have access
to a series of unique Conceptual Videos that help students understand
key Calculus concepts proven to be most difficult to comprehend, 248
Interactive Applets that help students master concepts and procedures
and functions, 1600 algorithms , and 113 e-Professors.
New to this edition
A more standard organization
Contents
80
Curve
or Real Numbers
Differentiation
2.5 The Chain Rule
3.6Optimization
3.8 Related Rates
4.1 Antiderivatives
Functions
6.3 Exponentials
/ Compound Interest
Systems
A Comparison Test
7.8 Probability
/ Compound Interest
Equations
CALCULUS
9.2 Infinite Series
9.6 Power Series
9.7 Taylor Series / Representations of Functions as Series / Proof
of Taylor’s Theorem
9.9 Fourier Series
10.6 Conic Sections
12.4 Curvature
Kepler’s Laws
Differentiation
Differentials
14.4 Surface Area
15.1 Vector Fields
15.2 Line Integrals
81
CALCULUS: Multivariable: EARLY
TRANSCENDENTAL FUNCTIONS
Third Edition
Roanoke College
2007 (February 2006) / Hardcover
ISBN-13: 978-0-07-330937-8 / MHID: 0-07-330937-0
ISBN-13: 978-0-07-321532-7 / MHID: 0-07-321532-5
(with MathZone)
ISBN-13: 978-0-07-110787-7 / MHID: 0-07-110787-8
[IE with MathZone]
world around us. New features include:
A new organization placing all transcendental functions early in
the book and consolidating the introduction to L’Hôpital’s Rule in a
single section.
More concisely written explanations in every chapter.
Many new exercises (for a total of 7,000 throughout the book)
that require additional rigor not found in the 2nd Edition.
New exploratory exercises in every section that challenge
students to synthesize key concepts to solve intriguing projects.
New commentaries (“Beyond Formulas”) that encourage
Contents
Fitting a Curve to Data.
0.6 Transformations of Functions.
1.4 Continuity and its Consequences. The Method of Bisections
Graphically.
of Real Numbers.
2.1 Tangent Lines and Velocity.
2.2 The Derivative. Numerical Differentiation.
Derivatives Acceleration
2.5 The Chain Rule
CALCULUS
3.7 Optimization
3.8 Related Rates
3.9 Rates of Change in Economics and the Sciences.
4.1 Antiderivatives
4.2 Sums and Sigma Notation. Principle of Mathematical Induction.
4.3 Area
4.7 Numerical Integration. Error Bounds for Numerical Integration.
5.6 Applications of Integration to Economics and the Sciences.
5.7 Probability
Powers of Trigonometric Functions. Trigonometric Substitution
7.2 Separable Differential Equations. Logistic Growth.
Systems
8.2 Infinite Series
8.6 Power Series
Taylor’s Theorem
8.8 Applications of Taylor Series. The Binomial Series
8.9 Fourier Series.
9.6 Conic Sections
9.7 Conic Sections in Polar Coordinates.
10.3 The Dot Product. Components and Projections.
82
11.4 Curvature
11.5 Tangent and Normal Vectors. Tangential and Normal Components
of Acceleration. Kepler’s Laws
Chapter 12: Functions of Several Variables and Differentiation
Differentials
12.5 The Chain Rule
Chapter 13: Multiple Integrals.
13.1 Double Integrals.
13.2 Area, Volume, and Center of Mass.
13.3 Double Integrals in Polar Coordinates.
13.4 Surface Area.
13.5 Triple Integrals. Mass and Center of Mass.
13.6 Cylindrical Coordinates.
13.8 Change of Variables in Multiple Integrals.
14.1 Vector Fields
14.2 Line Integrals
14.9 Applications of Vector Calculus.
15.4 Power Series Solutions of Differential Equations.
83
HIGHER
MATHEMATICS
Abstract Algebra................................................................................................101
Advanced Engineering Mathematics...................................................................94
Advanced Geometry..........................................................................................101
Combinatorics.....................................................................................................93
Complex Analysis..............................................................................................101
Differential Equations..........................................................................................85
Differential Equations With Boundary Value Problems........................................87
Dynamical System...............................................................................................95
Graph Theory......................................................................................................95
History Of Mathematics.......................................................................................97
Introductory Analysis...........................................................................................97
Linear Algebra.....................................................................................................90
Logic....................................................................................................................94
Mathematical References..................................................................................105
Number Theory..................................................................................................100
Numerical Analysis..............................................................................................99
Partial Differential Equations...............................................................................88
Topology............................................................................................................104
Transition To Higher Math/Foundations Of Higher Math.....................................89
NEW TITLES
Higher Mathematics
2009
Author
ISBN-13
MHID
Complex Variables And Applications, 8e
Brown
9780073051949
0073051942
101
Brown
9780073051932
0073051934
88
Page
2008
Fourier Series And Boundary Value Problems, 7e
84
HIGHER MATHEMATICS
Differential Equations
DIFFERENTIAL EQUATIONS: Theory,
Technique, and Practice
By George F. Simmons, Colorado College, and Steven G. Krantz,
Washington University-St Louis
2007 (December 2005) / 768 pages / Hardcover
ISBN-13: 978-0-07-286315-4 / MHID: 0-07-286315-3
ISBN-13: 978-0-07-125437-3 / MHID: 0-07-125437-4 [IE]
www.mhhe.com/simmons
This traditional text is intended for mainstream one- or two-semester
differential equations courses taken by undergraduates majoring
in engineering, mathematics, and the sciences. Written by two of
the world’s leading authorities on differential equations, Simmons/
Krantz provides a cogent and accessible introduction to ordinary
differential equations written in classical style. Its rich variety of
modern applications in engineering, physics, and the applied sciences
illuminate the concepts and techniques that students will use through
practice to solve real-life problems in their careers. This text is part of
the Walter Rudin Student Series in Advanced Mathematics.
Contents
Preface
1 What is a Differential Equation?
1.1 Introductory Remarks
1.2 The Nature of Solutions
1.3 Separable Equations
1.4 First-Order Linear Equations
1.5 Exact Equations
1.6 Orthogonal Trajectories and Families of Curves
1.7 Homogeneous Equations
1.8 Integrating Factors
1.9 Reduction of Order
1.9.1 Dependent Variable Missing
1.9.2 Independent Variable Missing
1.10 The Hanging Chain and Pursuit Curves
1.10.1 The Hanging Chain
1.10.2 Pursuit Curves
1.11 Electrical Circuits Anatomy of an Application: The Design of a
Dialysis Machine. Problems for Review and Discovery.
2 Second-Order Equations
2.1 Second-Order Linear Equations with Constant Coefficients
2.2 The Method of Undetermined Coefficients
2.3 The Method of Variation of Parameters
2.4 The Use of a Known Solution to Find Another
2.5 Vibrations and Oscillations
2.5.1 Undamped Simple Harmonic Motion
2.5.2 Damped Vibrations
2.5.3 Forced Vibrations
2.5.4 A Few Remarks About Electricity
2.6 Newton’s Law of Gravitation and Kepler’s Laws
2.6.1 Kepler’s Second Law
2.6.2 Kepler’s First Law
2.6.3 Kepler’s Third Law
2.7 Higher Order Equations. Anatomy of an Application: Bessel
Functions and the Vibrating Membrane. Problems for Review and
Discovery.
3 Qualitative Properties and Theoretical Aspects
3.0 Review of Linear Algebra
3.0.1 Vector Spaces
3.0.2 The Concept Linear Independence
3.0.3 Bases
3.0.4 Inner Product Spaces
3.0.5 Linear Transformations and Matrices
3.0.6 Eigenvalues and Eigenvectors
3.1 A Bit of Theory
85
3.2 Picard’s Existence and Uniqueness Theorem
3.2.1 The Form of a Differential Equation
3.2.2 Picard’s Iteration Technique
3.2.3 Some Illustrative Examples
3.2.4 Estimation of the Picard Iterates
3.3 Oscillations and the Sturm Separation Theorem
3.4 The Sturm Comparison Theorem. Anatomy of an Application: The
Green’s Function. Problems for Review and Discovery.
4 Power Series Solutions and Special Functions
4.1 Introduction and Review of Power Series
4.1.1 Review of Power Series.
4.2 Series Solutions of First-Order Differential Equations.
4.3 Second-Order Linear Equations: Ordinary Points.
4.4 Regular Singular Points.
4.5 More on Regular Singular Points.
4.6 Gauss’s Hypergeometric Equation. Anatomy of an Application:
Steady State Temperature in a Ball. Problems for Review and
Discovery.
5 Fourier Series: Basic Concepts.
5.1 Fourier Coefficients.
5.2 Some Remarks about Convergence.
5.3 Even and Odd Functions: Cosine and Sine Series.
5.4 Fourier Series on Arbitrary Intervals.
5.5 Orthogonal Functions. Anatomy of an Application: Introduction to
the Fourier Transform. Problems for Review and Discovery.
6 Partial Differential Equations and Boundary Value Problems.
6.1 Introduction and Historical Remarks.
6.2 Eigenvalues, Eigenfunctions, and the Vibrating String.
6.2.1 Boundary Value Problems.
6.2.2 Derivation of the Wave Equation.
6.2.3 Solution of the Wave Equation.
6.3 The Heat Equation.
6.4 The Dirichlet Problem for a Disc.
6.4.1 The Poisson Integral
6.5 Sturm-Liouville Problems. Anatomy of an Application: Some Ideas
from Quantum Mechanics. Problems for Review and Discovery.
7 Laplace Transforms.
7.0 Introduction
7.1 Applications to Differential Equations
7.2 Derivatives and Integrals of Laplace Transforms
7.3 Convolutions
7.4 The Unit Step and Impulse Functions. Anatomy of an Application:
Flow Initiated by an Impulsively-Started Flat Plate. Problems for
Review and Discovery.
8 The Calculus of Variations
8.1 Introductory Remarks.
8.2 Euler’s Equation.
8.3 Isoperimetric Problems and the Like.
8.3.1 Lagrange Multipliers
8.3.2 Integral Side Conditions.
8.3.3 Finite Side Conditions. Anatomy of an Application: Hamilton’s
Principle and its Implications. Problems for Review and Discovery.
9 Numerical Methods.
9.2 The Method of Euler.
9.3 The Error Term.
9.4 An Improved Euler Method
9.5 The Runge-Kutta Method. Anatomy of an Application: A
Constant Perturbation Method for Linear, Second-Order Equations.
Problems for Review and Discovery.
10 Systems of First-Order Equations
10.2 Linear Systems
10.3 Homogeneous Linear Systems with Constant Coefficients
10.4 Nonlinear Systems: Volterra’s Predator-Prey Equations.
Anatomy of an Application: Solution of Systems with Matrices and
Exponentials. Problems for Review and Discovery.
11 The Nonlinear Theory.
11.1 Some Motivating Examples
11.2 Specializing Down
11.3 Types of Critical Points: Stability
HIGHER MATHEMATICS
11.4 Critical Points and Stability for Linear Systems
11.5 Stability by Liapunov’s Direct Method
11.6 Simple Critical Points of Nonlinear Systems
11.7 Nonlinear Mechanics: Conservative Systems
11.8 Periodic Solutions: The Poincaré-Bendixson Theorem. Anatomy
of an Application: Mechanical Analysis of a Block on a Spring.
12 Dynamical Systems
12.1 Flows
12.1.1 Dynamical Systems
12.1.2 Stable and Unstable Fixed Points
12.1.3 Linear Dynamics in the Plane
12.2 Some Ideas from Topology
12.2.1 Open and Closed Sets
12.2.2 The Idea of Connectedness
12.2.3 Closed Curves in the Plane
12.3 Planar Autonomous Systems
12.3.1 Ingredients of the Proof of Poincaré-Bendixson. Anatomy
of an Application: Lagrange’s Equations. Problems for Review and
Discovery. Bibliography
DIFFERENTIAL EQUATIONS
By Keng Cheng Ang
2005 (October 2005)
ISBN-13: 978-0-07-125085-6 / MHID: 0-07-125085-9
An Asian Publication
Many books on differential equations assume that the reader has a
fairly sophisticated level of competence in calculus at the university
level. Differential Equations: Models and Methods differs from them
in that it enables a student with some basic knowledge of calculus to
learn about differential equations and appreciate their applications.
The focus of the book is on first order differential equations, their
methods of solution and their use in mathematical models. Methods
include analytic and graphical solutions, as well as numerical
techniques. Readers will not only learn the necessary techniques of
solving first order differential equations, but also how these equations
can be applied in different fields. Examples have been carefully chosen
to provide motivation for new concepts or techniques, and to illustrate
the importance of differential equations. This book was written with
student needs in mind; in particular, pre-university students taking
the new GCE ‘A’ Level H3 Mathematics will find it useful in helping
them through the course.
Contents
Preface
1. Basic Concepts
2. Analytic Solutions
3. Graphical Techniques
4. Numerical Methods
5. Mathematical Models
6. Further Applications
Further Reading
Appendix A: Table of Integrals
Appendix B: Method of Least Squares
Answers to Odd-numbered Problems
Index
86
DIFFERENTIAL EQUATIONS: A Modeling
Approach
By Glenn Ledder, University of Nebraska—Lincoln
2005 / 768 pages
ISBN-13: 978-0-07-242229-0 / MHID: 0-07-242229-7
ISBN-13: 978-0-07-111151-5 / MHID: 0-07-111151-4 [IE]
www.mhhe.com/ledder
Contents
1 Introduction:
1.1 Natural Decay and Natural Growth.
1.2 Differential Equations and Solutions.
1.3 Mathematical Models and Mathematical Modeling. Case Study 1
Scientific Detection of Art Forgery.
2 Basic Concepts and Techniques:
2.1 A Collection of Mathematical Models.
2.2 Separable First-Order Equations.
2.3 Slope Fields.
2.4 Existence of Unique Solutions.
2.5 Euler’s Method.
2.6 Runge-Kutta Methods. Case Study 2 A Successful Volleyball
Serve.
3 Homogeneous Linear Equations.
3.1 Linear Oscillators.
3.2 Systems of Linear Algebraic Equations.
3.3 Theory of Homogeneous Linear Equations.
3.4 Homogeneous Equations with Constant Coefficients.
3.5 Real Solutions from Complex Characteristic Values.
3.6 Multiple Solutions for Repeated Characteristic Values.
3.7 Some Other Homogeneous Linear Equations. Case Study 3 How
Long Should Jellyfish Hold their Food?
4 Nonhomogeneous Linear Equations:
4.1 More on Linear Oscillator Models.
4.2 General Solutions for Nonhomogeneous Equations.
4.3 The Method of Undetermined Coefficients.
4.4 Forced Linear Oscillators.
4.5 Solving First-Order Linear Equations.
4.6 Particular Solutions for Second-Order Equations by Variation of
Parameters. Case Study 4 A Tuning Circuit for a Radio.
5 Autonomous Equations and Systems:
5.1 Population Models.
5.2 The Phase Line.
5.3 The Phase Plane.
5.4 The Direction Field and Critical Points.
5.5 Qualitative Analysis. Case Study 5 A Self-Limiting Population.
6 Analytical Methods for Systems:
6.1 Compartment Models.
6.2 Eigenvalues and Eigenspaces.
6.3 Linear Trajectories.
6.4 Homogeneous Systems with Real Eigenvalues.
6.5 Homogeneous Systems with Complex Eigenvalues.
6.6 Additional Solutions for Deficient Matrices.
6.7 Qualitative Behavior of Nonlinear Systems. Case Study 6 Invasion
by Disease.
7 The Laplace Transform:
7.1 Piecewise-Continuous Functions.
7.2 Definition and Properties of the Laplace Transform.
7.3 Solution of Initial-Value Problems with the Laplace Transform.
7.4 Piecewise-Continuous and Impulsive Forcing.
7.5 Convolution and the Impulse Response Function. Case Study 7
Growth of a Structured Population.
8 Vibrating Strings: A Focused Introduction to Partial Differential
Equations:
8.1 Transverse Vibration of a String.
8.2 The General Solution of the Wave Equation.
8.3 Vibration Modes of a Finite String.
8.4 Motion of a Plucked String.
HIGHER MATHEMATICS
8.5 Fourier Series. Case Study 8 Stringed Instruments and
Percussion.
A Some Additional Topics:
A.1 Using Integrating Factors to Solve First-Order Linear Equations
(Chapter 2).
A.2 Proof of the Existence and Uniqueness Theorem for First-Order
Equations (Chapter 2).
A.3 Error in Numerical Methods (Chapter 2).
A.4 Power Series Solutions (Chapter 3).
A.5 Matrix Functions (Chapter 6).
A.6 Nonhomogeneous Linear Systems (Chapter 6).
A.7 The One-Dimensional Heat Equation (Chapter 8).
A.8 Laplace’s Equation (Chapter 8)
with Boundary
Value Problems
DIFFERENTIAL EQUATIONS: Theory,
Technique, and Practice
By George F. Simmons, Colorado College, and Steven G. Krantz,
2007 (December 2005) / 768 pages / Hardcover
ISBN-13: 978-0-07-286315-4 / MHID: 0-07-286315-3
ISBN-13: 978-0-07-125437-3 / MHID: 0-07-125437-4 [IE]
www.mhhe.com/simmons
This traditional text is intended for mainstream one- or two-semester
differential equations courses taken by undergraduates majoring
in engineering, mathematics, and the sciences. Written by two of
the world’s leading authorities on differential equations, Simmons/
Krantz provides a cogent and accessible introduction to ordinary
differential equations written in classical style. Its rich variety of
modern applications in engineering, physics, and the applied sciences
illuminate the concepts and techniques that students will use through
practice to solve real-life problems in their careers. This text is part of
the Walter Rudin Student Series in Advanced Mathematics.
Differential Equations with
Applications and Historical Notes
Second Edition
By George F. Simmons, Colorado College
1991 / 640 pages
ISBN-13: 978-0-07-057540-0 / MHID: 0-07-057540-1
ISBN-13: 978-0-07-112807-0 / MHID: 0-07-112807-7 [IE]
Contents
Contents
1 The Nature of Differential Equations.
2 First Order Equations.
3 Second Order Linear Equations.
4 Qualitative Properties of Solutions.
5 Power Series Solutions and Special Functions.
6 Fourier Series and Orthogonal Functions.
8 Some Special Functions of Mathematical Physics.
10 Systems of First Order Equations.
11 Nonlinear Equations.
12 The Calculus of Variations.
13 The Existence and Uniqueness of Solutions.
Preface
1 What is a Differential Equation?
1.1 Introductory Remarks
1.2 The Nature of Solutions
1.3 Separable Equations
1.4 First-Order Linear Equations
1.5 Exact Equations
1.6 Orthogonal Trajectories and Families of Curves
1.8 Integrating Factors
1.9 Reduction of Order
1.9.1 Dependent Variable Missing
1.9.2 Independent Variable Missing
1.10 The Hanging Chain and Pursuit Curves
1.10.1 The Hanging Chain
1.10.2 Pursuit Curves
1.11 Electrical Circuits Anatomy of an Application: The Design of a
Dialysis Machine. Problems for Review and Discovery.
2 Second-Order Equations
2.1 Second-Order Linear Equations with Constant Coefficients
2.2 The Method of Undetermined Coefficients
2.3 The Method of Variation of Parameters
2.4 The Use of a Known Solution to Find Another
2.5 Vibrations and Oscillations
2.5.1 Undamped Simple Harmonic Motion
2.5.2 Damped Vibrations
2.5.3 Forced Vibrations
2.5.4 A Few Remarks About Electricity
2.6 Newton’s Law of Gravitation and Kepler’s Laws
2.6.1 Kepler’s Second Law
2.6.2 Kepler’s First Law
2.6.3 Kepler’s Third Law
2.7 Higher Order Equations. Anatomy of an Application: Bessel
Functions and the Vibrating Membrane. Problems for Review and
Discovery.
3 Qualitative Properties and Theoretical Aspects
3.0 Review of Linear Algebra
3.0.1 Vector Spaces
3.0.2 The Concept Linear Independence
3.0.3 Bases
SCHAUM’S OUTLINE OF DIFFERENTIAL
EQUATIONS
Third Edition
By Richard Bronson, Fairleigh Dickinson University-Madison and
Gabriel Costa, US Military Academy
2006 (June 2006) / 384 pages
ISBN-13: 978-0-07-145687-6 / MHID: 0-07-145687-2
Thoroughly updated, this third edition of Schaum’s Outline of
Differential Equations offers you new, faster techniques for solving
differential equations generated by the emergence of high-speed
computers. Differential equations, a linchpin of modern math, are
essential in engineering, the natural sciences, economics, and
business. Includes:
563 fully solved problems
800-plus supplementary problems
New chapter on modeling
87
HIGHER MATHEMATICS
3.0.4 Inner Product Spaces
3.0.5 Linear Transformations and Matrices
3.0.6 Eigenvalues and Eigenvectors
3.1 A Bit of Theory
3.2 Picard’s Existence and Uniqueness Theorem
3.2.1 The Form of a Differential Equation
3.2.2 Picard’s Iteration Technique
3.2.3 Some Illustrative Examples
3.2.4 Estimation of the Picard Iterates
3.3 Oscillations and the Sturm Separation Theorem
3.4 The Sturm Comparison Theorem. Anatomy of an Application: The
Green’s Function. Problems for Review and Discovery.
4 Power Series Solutions and Special Functions
4.1 Introduction and Review of Power Series
4.1.1 Review of Power Series.
4.2 Series Solutions of First-Order Differential Equations.
4.3 Second-Order Linear Equations: Ordinary Points.
4.4 Regular Singular Points.
4.5 More on Regular Singular Points.
4.6 Gauss’s Hypergeometric Equation. Anatomy of an Application:
Steady State Temperature in a Ball. Problems for Review and
Discovery.
5 Fourier Series: Basic Concepts.
5.1 Fourier Coefficients.
5.2 Some Remarks about Convergence.
5.3 Even and Odd Functions: Cosine and Sine Series.
5.4 Fourier Series on Arbitrary Intervals.
5.5 Orthogonal Functions. Anatomy of an Application: Introduction to
the Fourier Transform. Problems for Review and Discovery.
6.1 Introduction and Historical Remarks.
6.2 Eigenvalues, Eigenfunctions, and the Vibrating String.
6.2.1 Boundary Value Problems.
6.2.2 Derivation of the Wave Equation.
6.2.3 Solution of the Wave Equation.
6.3 The Heat Equation.
6.4 The Dirichlet Problem for a Disc.
6.4.1 The Poisson Integral
6.5 Sturm-Liouville Problems. Anatomy of an Application: Some Ideas
from Quantum Mechanics. Problems for Review and Discovery.
7.0 Introduction
7.1 Applications to Differential Equations
7.2 Derivatives and Integrals of Laplace Transforms
7.3 Convolutions
7.4 The Unit Step and Impulse Functions. Anatomy of an Application:
Flow Initiated by an Impulsively-Started Flat Plate. Problems for
Review and Discovery.
8 The Calculus of Variations
8.2 Euler’s Equation.
8.3 Isoperimetric Problems and the Like.
8.3.1 Lagrange Multipliers
8.3.2 Integral Side Conditions.
8.3.3 Finite Side Conditions. Anatomy of an Application: Hamilton’s
Principle and its Implications. Problems for Review and Discovery.
9.2 The Method of Euler.
9.3 The Error Term.
9.4 An Improved Euler Method
9.5 The Runge-Kutta Method. Anatomy of an Application: A
Constant Perturbation Method for Linear, Second-Order Equations.
10 Systems of First-Order Equations
10.2 Linear Systems
10.3 Homogeneous Linear Systems with Constant Coefficients
10.4 Nonlinear Systems: Volterra’s Predator-Prey Equations.
Anatomy of an Application: Solution of Systems with Matrices and
Exponentials. Problems for Review and Discovery.
88
11 The Nonlinear Theory.
11.1 Some Motivating Examples
11.2 Specializing Down
11.3 Types of Critical Points: Stability
11.4 Critical Points and Stability for Linear Systems
11.5 Stability by Liapunov’s Direct Method
11.6 Simple Critical Points of Nonlinear Systems
11.7 Nonlinear Mechanics: Conservative Systems
11.8 Periodic Solutions: The Poincaré-Bendixson Theorem. Anatomy
of an Application: Mechanical Analysis of a Block on a Spring.
12 Dynamical Systems
12.1 Flows
12.1.1 Dynamical Systems
12.1.2 Stable and Unstable Fixed Points
12.1.3 Linear Dynamics in the Plane
12.2 Some Ideas from Topology
12.2.1 Open and Closed Sets
12.2.2 The Idea of Connectedness
12.2.3 Closed Curves in the Plane
12.3 Planar Autonomous Systems
12.3.1 Ingredients of the Proof of Poincaré-Bendixson. Anatomy
of an Application: Lagrange’s Equations. Problems for Review and
Discovery. Bibliography
Partial Differential
Equations
New
FOURIER SERIES AND
BOUNDARY VALUE
PROBLEMS
Seventh Edition
By James Ward Brown, University of MichiganDearborn and Ruel Churchill (deceased)
2008 (August 2006) / 384 pages
ISBN-13: 978-0-07-305193-2 / MHID: 0-07-305193-4
ISBN-13: 978-0-07-125917-0 / MHID: 0-07-125917-1 [IE]
Published by McGraw-Hill since its first edition in 1941, this classic text
is an introduction to Fourier series and their applications to boundary
value problems in partial differential equations of engineering and
physics. It will primarily be used by students with a background in
ordinary differential equations and advanced calculus. There are
two main objectives of this text. The first is to introduce the concept
of orthogonal sets of functions and representations of arbitrary
functions in series of functions from such sets. The second is a
clear presentation of the classical method of separation of variables
used in solving boundary value problems with the aid of those
representations.
New to this edition
Reorganization of Topics: Topics in the text have been realigned
to allow for more focus on each section and to allow for more
HIGHER MATHEMATICS
examples. The chapter on The Fourier Method has been moved earlier
in the book (now Chapter 2). The former Fourier Series chapter has
been split into two chapters (Chapter 3: Orthonormal Sets and Fourier
Series and Chapter 4: Convergence of Fourier Series).
Variational Formulation of Boundary Value Problems.
The Finite Element Method: An Introduction.
Answers to Supplementary Problems.
Problem Sets Revised: Problem sets have been broken up into
more manageable segments to allow for each problem set to be
very focused.
Examples Added: Additional examples have been added in each
chapter to help illustrate important topics.
Contents
Preface
1 Fourier Series
2 Convergence of Fourier Series
3 Partial Differential Equations of Physics
4 The Fourier Method
5 Boundary Value Problems
6 Fourier Integrals and Applications
7 Orthonormal Sets
8 Sturm-Liouville Problems and Applications
9 Bessel Functions and Applications
10 Legendre Polynomials and Applications
11 Verification of Solutions and Uniqueness
Appendixes
Bibliography
Some Fourier Series Expansions
Solutions of Some Regular Sturm-Liouville Problems
Index
Transition to Higher Math
/Foundations of Higher
Math
TRANSITION TO HIGHER MATHEMATICS
Structure and Proof
By Bob A. Dumas, University Of Washington, and John E. McCarthy,
2007 (February 2006) / 416 pages / Hardcover
ISBN-13: 978-0-07-353353-7 / MHID: 0-07-353353-X
ISBN-13: 978-0-07-110647-4 / MHID: 0-07-110647-2 [IE]
This text is intended for the Foundations of Higher Math bridge
course taken by prospective math majors following completion of the
mainstream Calculus sequence, and is designed to help students
develop the abstract mathematical thinking skills necessary for
success in later upper-level majors math courses. As lower-level
courses such as Calculus rely more exclusively on computational
problems to service students in the sciences and engineering,
math majors increasingly need clearer guidance and more rigorous
practice in proof technique to adequately prepare themselves for
the advanced math curriculum. With their friendly writing style Bob
Dumas and John McCarthy teach students how to organize and
structure their mathematical thoughts, how to read and manipulate
abstract definitions, and how to prove or refute proofs by effectively
evaluating them. Its wealth of exercises give students the practice
they need, and its rich array of topics give instructors the flexibility
they desire to cater coverage to the needs of their school’s majors
curriculum. This text is part of the Walter Rudin Student Series in
Advanced Mathematics.
Elements of Partial Differential
Equations
By Sneddon
1985 / 344 pages
ISBN-13: 978-0-07-085740-7 / MHID: 0-07-085740-7 [IE]
Contents
SCHAUM’S OUTLINE OF PARTIAL
DIFFERENTIAL EQUATIONS
By Paul DuChateau, Colorado State University and D W Zachmann,
Colorado State University
1986 / 256 pages
ISBN-13: 978-0-07-017897-7 / MHID: 0-07-017897-6
Contents
Introduction.
Classification and Characteristics.
Qualitative Behavior of Solutions to Elliptic Equations.
Qualitative Behavior of Solutions to Evolution Equations.
First-Order Equations Eigenfunction Expansions and Integral
Transforms: Theory.
Eigenfunction Expansions and Integral Transforms: Applications.
Green’s Functions.
Difference Methods for Parabolic Equations.
Difference and Characteristic Methods for Parabolic Equations.
Difference Methods for Hyperbolic Equations.
Difference Methods for Elliptic Equations.
89
Chapter 0. Introduction.
0.1. Why this book is
0.2. What this book is
0.3. What this book is not
0.4. Advice to the Student
0.5. Advice to the Teacher
0.6. Acknowledgements
Chapter 1. Preliminaries
1.1. “And” “Or”
1.2. Sets
1.3. Functions
1.4. Injections, Surjections, Bijections
1.5. Images and Inverses
1.6. Sequences
1.7. Russell’s Paradox
1.8. Exercises
Chapter 2. Relations
2.1. Definitions
2.2. Orderings
2.3. Equivalence Relations
2.4. Constructing Bijections
2.5. Modular Arithmetic
2.6. Exercises
Chapter 3. Proofs
3.1. Mathematics and Proofs
HIGHER MATHEMATICS
Linear Algebra
3.2. Propositional Logic
3.3. Formulas
3.4. Quantifiers
3.5. Proof Strategies
3.6. Exercises.
Chapter 4. Principle of Induction
4.1. Well-orderings
4.2. Principle of Induction
4.3. Polynomials
4.4. Arithmetic-Geometric Inequality
4.5. Exercises
Chapter 5. Limits
5.1. Limits
5.2. Continuity
5.3. Sequences of Functions
5.4. Exercises
Chapter 6. Cardinality
6.1. Cardinality
6.2. Infinite Sets
6.3. Uncountable Sets
6.4. Countable Sets
6.5. Functions and Computability
6.6. Exercises.
Chapter 7. Divisibility
7.1. Fundamental Theorem of Arithmetic
7.2. The Division Algorithm
7.3. Euclidean Algorithm
7.4. Fermat’s Little Theorem
7.5. Divisibility and Polynomials
7.6. Exercises
Chapter 8. The Real Numbers.
8.1. The Natural Numbers
8.2. The Integers
8.3. The Rational Numbers
8.4. The Real Numbers
8.5. The Least Upper Bound Principle
8.6. Real Sequences
8.7. Ratio Test
8.8. Real Functions
8.9. Cardinality of the Real Numbers
8.10. Exercises
Chapter 9. Complex Numbers
9.1. Cubics
9.2. Complex Numbers
9.3. Tartaglia-Cardano Revisited
9.4. Fundamental Theorem of Algebra
9.5. Application to Real Polynomials
9.6. Further remarks
9.7. Exercises
Appendix A. The Greek Alphabet
Appendix B. Axioms of Zermelo-Fraenkel with the Axiom of Choice
Appendix C. Hints to get started on early exercises.
Bibliography.
Index
LINEAR ALGEBRA WITH APPLICATIONS
Fifth Edition
By Keith Nicholson, University of Calgary
2006 (January 2006) / 512 pages
ISBN-13: 978-0-07-092277-8 / MHID: 0-07-092277-2
ISBN-13: 978-0-07-125353-6 / MHID: 0-07-125353-X [IE]
McGraw-Hill Canada Title
W. Keith Nicholson’s Linear Algebra with Applications, Fifth Canadian
Edition is written for first and second year students at both the college
or university level. Its real world approach challenges students stepby-step, gradually bringing them to a higher level of understanding
from abstract to more general concepts. Real world applications have
been added to the new edition, including: Directed graphs Google
PageRank Computer graphics Correlation and Variance Finite Fields
and Linear Codes In addition to the new applications, the author offers
several new exercises and examples throughout each chapter. Some
new examples include: motivating matrix multiplication (Chapter 2)
a new way to expand a linearly independent set to a basis using an
existing basis While some instructors will use the text for one semester,
ending at Chapter 5 The Vector Space Rn others will continue with
more abstract concepts being introduced. Chapter 5 prepares
students for the transition, acting as the “bridging” chapter, allowing
challenging concepts like subspaces, spanning, independence and
dimension to be assimilated first in the concrete context of Rn. This
“bridging” concept eases students into the introduction of vector
spaces in Chapter 6.
Contents
Chapter 1 Systems of Linear Equations
1.1 Solutions and Elementary Operations
1.2 Gaussian Elimination
1.4 An Application to Network Flow
1.5 An Application to Electrical Networks
1.6 An Application to Chemical Reactions Supplementary Exercises
for Chapter 1
Chapter 2 Matrix Algebra
2.1 Matrix Addition, Scalar Multiplication, and Transposition
2.2 Matrix Multiplication
2.3 Matrix Inverses
2.4 Elementary Matrices
2.5 Matrix Transformations
2.6 LU-Factorization
2.7 An Application to Input-Output Economic Models
2.8 An Application to Markov Chains Supplementary Exercises for
Chapter 2
Chapter 3 Determinants and Diagonalization
3.1 The Cofactor Expansion
3.2 Determinants and Matrix Inverses
3.3 Diagonalization and Eigenvalues
3.5 An Application to Linear Recurrences
3.6 An Application to Population Growth
3.7 Proof of the Cofactor Expansion Supplementary Exercises for
Chapter 3
Chapter 4 Vector Geometry
4.1 Vectors and Lines
4.2 Projections and Planes
4.4 Matrix Transformations II
4.5 An Application to Computer Graphics Supplementary Exercises
for Chapter 4
Chapter 5 The Vector Space Rn
5.1 Subspaces and Spanning
5.2 Independence and Dimension
5.3 Orthogonality
90
HIGHER MATHEMATICS
5.4 Rank of a Matrix
5.5 Similarity and Diagonalization
5.6 An Application to Correlation and Variance
5.7 An Application to Least Squares Approximation Supplementary
Exercises for Chapter 5
Chapter 6 Vector Spaces
6.1 Examples and Basic Properties
6.2 Subspaces and Spanning Sets
6.3 Linear Independence and Dimension
6.4 Finite Dimensional Spaces
6.5 An Application to Polynomials
6.6 An Application to Differential Equations Supplementary Exercises
for Chapter 6
Chapter 7 Linear Transformations
7.1 Examples and Elementary Properties
7.2 Kernel and Image of a Linear Transformation
7.3 Isomorphisms and Composition
7.4 More on Linear Recurrences
Chapter 8 Orthogonality
8.1 Orthogonal Complements and Projections
8.2 Orthogonal Diagonalization
8.3 Positive Definite Matrices
8.4 QR-Factorization
8.5 Computing Eigenvalues
8.6 Complex Matrices
8.7 Best Approximation and Least Squares
8.8 Finite Fields and Linear Codes
8.9 An Application to Quadratic Forms
8.10 An Application to Systems of Differential Equations
Chapter 9 Change of Basis
9.1 The Matrix of a Linear Transformation
9.2 Operators and Similarity
9.3 Invariant Subspaces and Direct Sums
9.4 Block Triangular Form
*9.5 Jordan Canonical Form
Chapter 10 Inner Product Spaces
10.1 Inner Products and Norms
10.2 Orthogonal Sets of Vectors
10.3 Orthogonal Diagonalization
10.4 Isometries
10.5 An Application to Fourier Approximation
[email protected]
91
ELEMENTARY LINEAR ALGEBRA
Second Edition
By Keith Nicholson, University of Calgary
2004 / 608 pages / softcover
ISBN-13: 978-0-07-091142-0 / MHID: 0-07-091142-8
ISBN-13: 978-0-07-123439-9 / MHID: 0-07-123439-X [IE]
www.mcgraw-hill.ca/college/nicholson
McGraw-Hill Canada Title
Contents
Chapter 1 Linear Equations and Matrices:
Matrices.
Linear Equations.
Homogeneous Systems.
Matrix Multiplication.
Matrix Inverses.
Elementary Matrices.
Lu-Factorization.
Application ot Markov Chains.
Chapter 2 Determinants and Eigenvalues:
Cofactor Expansions.
Determinants and Inversees.
Diagonalization and Eigenvalues.
Linear Dynamical Systems.
Complex Eignevalues.
Linear Recurrences.
Polynomial Interpolation.
Systems of Differential Equations.
Chapter 3 Vector Geometry:
Geometric Vectors.
Dot Product and Projections.
Lines and Planes.
Matrix Transformation of R^2.
The Cross Product:
Optional.
Chapter 4 The Vector Space R^n.
Subspaces and Spanning.
Linear Independence.
Dimension.
Rank.
Orthogonality.
Projections and Approximation.
Orthogonal Diagonalization.
Quadratic Forms.
Linear Transformations.
Complex Matrices.
Singular Value Decomposition.
Chapter 5 Vector Spaces:
Examples and Basic Properties.
Independence and Dimension.
Linear Transformations.
Isomorphisms and Matrices.
Linear Operations and Similarity.
Invariant Subspaces.
General Inner Products.
Appendix:
A.1 Basic Trigonometry.
A.2 Induction.
A.3 Polynomials
HIGHER MATHEMATICS
SCHAUM’S OUTLINE OF LINEAR ALGEBRA
Fourth Edition
SCHAUM’S EASY OUTLINES: LINEAR
ALGEBRA
By Seymour Lipschutz, Temple University-Philadelphia and Marc Lipson,
2009 (July 2008) / 480 pages
ISBN-13: 978-0-07-154352-1 / MHID: 0-07-154352-X
By Seymour Lipschutz, Temple University - Philadelphia Marc Lipson,
2003
ISBN-13: 978-0-07-139880-0 / MHID: 0-07-139880-5
latest course scope and sequence. The ideal review for hundreds of
thousands of college and high school students who enroll in linear
algebra courses.
What could be better than the bestselling Schaum’s Outline series?
For students looking for a quick nuts-and-bolts overview, it would have
to be Schaum’s Easy Outline series. Every book in this series is a
pared-down, simplified, and tightly focused version of its predecessor.
With an emphasis on clarity and brevity, each new title features a
streamlined and updated formatº and the absolute essence of the
subject, presented in a concise and readily understandable form.
Graphic elements such as sidebars, reader-alert icons, and boxed
highlights stress selected points from the text, illuminate keys to
learning, and give students quick pointers to the essentials.
CONTENTS
1. Vectors in R and C, Spatial Vectors
2. Algebra of Matrices
3. Systems of Linear Equations
4. Vector Spaces
5. Linear Mappings
6. Linear Mappings and Matrices
7. Inner Product Spaces, Orthogonality
8. Determinants
9. Diagonalization: Eigenvalues and Eigenvectors
10. Canonical Forms
11. Linear Functionals and the Dual Space
12. Bilinear, Quadratic, and Hermitian Forms
13. Linear Operators on Inner Product Spaces
14. Multilinear Products
Linear Algebra
By Seymour Lipschultz, Temple University
1989 / 496 pages
ISBN-13: 978-0-07-038023-3 / MHID: 0-07-038023-6
Contents
LINEAR ALGEBRA DEMYSTIFIED
By David McMahon
2006 (October 2005) / 255 pages
ISBN-13: 978-0-07-146579-3 / MHID: 0-07-146579-0
Taught at junior level math courses at every university, Linear Algebra
is essential for students in almost every technical and analytic
discipline.
Contents
PREFACE
Chapter 2: Matrix Algebra
Chapter 3: Determinants
Chapter 4: Vectors
Chapter 5: Vector Spaces
Chapter 6: Inner Product Spaces
Chapter 7: Linear Transformations
Chapter 8: The Eigenvalue Problem
Chapter 9: Special Matrices
Chapter 10: Matrix Decomposition
Final Exam
Hints And Solutions
References
Index
Vectors in R and C.
Matrix Algebra.
Systems of Linear Equations.
Square Matrices.
Determinants.
Algebraic Structures.
Vector Spaces and Subspaces.
Linear Dependence, Basis, Dimension.
Mappings.
Linear Mappings.
Spaces of Linear Mappings.
Matrices and Linear Mappings.
Change of Basis, Similarity.
Inner Product Spaces, Orthogonality.
Polynomials Over a Field.
Eigenvalues and Eigenvectors.
Diagonalization.
Canonical Forms.
Linear Functional and the Dual Space.
Bilinear, Quadratic, and Hermitian Forms.
Linear Operators on Inner Product Spaces.
Applications to Geometry and Calculus.
92
HIGHER MATHEMATICS
Combinatorics
INTRODUCTION TO ENUMERATIVE
COMBINATORICS
By Miklos Bona, University Of Florida @ Gainesville
2007 (September 2005) / 533 pages / Hardcover
ISBN-13: 978-0-07-312561-9 / MHID: 0-07-312561-X
ISBN-13: 978-0-07-125415-1 / MHID: 0-07-125415-3 [IE]
Written by one of the leading authors and researchers in the
field, this comprehensive modern text is written for one- or twosemester undergraduate courses in General Combinatorics or
Enumerative Combinatorics taken by math and computer science
majors. Introduction to Enumerative Combinatorics features a
strongly-developed focus on enumeration, a vitally important area in
introductory combinatorics crucial for further study in the field. Miklós
Bóna’s text is one of the very first enumerative combinatorics books
written specifically for the needs of an undergraduate audience, with
a lively and engaging style that is ideal for presenting the material to
sophomores or juniors. This text is part of the Walter Rudin Student
Series in Advanced Mathematics.
Contents
Foreword.
Preface.
Acknowledgments.
I How: Methods.
1 Basic Methods.
1.1 When We Add and When We Subtract
1.1.1 When We Add
1.1.2 When We Subtract
1.2 When We Multiply
1.2.1 The Product Principle
1.2.2 Using Several Counting Principles
1.2.3 When Repetitions Are Not Allowed
1.3 When We Divide
1.3.1 The Division Principle
1.3.2 Subsets
1.4 Applications of Basic Counting Principles
1.4.1 Bijective Proofs
1.4.2 Properties of Binomial Coefficients
1.4.3 Permutations With Repetition.
1.5 The Pigeonhole Principle
1.6 Notes
1.7 Chapter Review
1.8 Exercises
1.9 Solutions to Exercises
1.10 Supplementary Exercises.
2 Direct Applications of Basic Methods
2.1 Multisets and Compositions
2.1.1 Weak Compositions
2.1.2 Compositions
2.2 Set Partitions
2.2.1 Stirling Numbers of the Second Kind
2.2.2 Recurrence Relations for Stirling Numbers of the Second
Kind
2.2.3 When the Number of Blocks Is Not Fixed
2.3 Partitions of Integers
2.3.1 Nonincreasing Finite Sequences of Integers
2.3.2 Ferrers Shapes and Their Applications
2.3.3 Excursion: Euler’s Pentagonal Number Theorem
2.4 The Inclusion-Exclusion Principle
2.4.1 Two Intersecting Sets
2.4.2 Three Intersecting Sets
2.4.3 Any Number of Intersecting Sets
2.5 The Twelvefold Way
2.6 Notes
93
2.7 Chapter Review
2.8 Exercises
2.10 Supplementary Exercises
3 Generating Functions
3.1 Power Series
3.1.1 Generalized Binomial Coefficients
3.1.2 Formal Power Series
3.2 Warming Up: Solving Recursions
3.2.1 Ordinary Generating Functions
3.2.2 Exponential Generating Functions
3.3 Products of Generating Functions
3.4 Excursion: Composition of Two Generating Functions
3.5 Excursion: A Different Type of Generating Function
3.6 Notes
3.7 Chapter Review
3.8 Exercises
II What: Topics.
4 Counting Permutations
4.1 Eulerian Numbers
4.2 The Cycle Structure of Permutations
4.2.1 Stirling Numbers of the First Kind
4.2.2 Permutations of a Given Type
4.3 Cycle Structure and Exponential Generating Functions
4.4 Inversions
4.4.1 Counting Permutations with Respect to Inversions
4.5 Notes
4.6 Chapter Review
4.7 Exercises
5 Counting Graphs
5.1 Counting Trees and Forests
5.1.1 Counting Trees
5.2 The Notion of Graph Isomorphisms
5.3 Counting Trees on Labeled Vertices
5.3.1 Counting Forests
5.4 Graphs and Functions
5.4.1 Acyclic Functions
5.4.2 Parking Functions
5.5 When the Vertices Are Not Freely Labeled
5.5.1 Rooted Plane Trees
5.5.2 Binary Plane Trees
5.6 Excursion: Graphs on Colored Vertices
5.6.1 Chromatic Polynomials
5.6.2 Counting k-colored Graphs
5.7 Graphs and Generating Functions
5.7.1 Generating Functions of Trees
5.7.2 Counting Connected Graphs
5.7.3 Counting Eulerian Graphs
5.8 Notes
5.9 Chapter Review
5.10 Exercises
6 Extremal Combinatorics
6.1 Extremal Graph Theory
6.1.1 Bipartite Graphs
6.1.2 Turán’s Theorem
6.1.3 Graphs Excluding Cycles
6.1.4 Graphs Excluding Complete Bipartite Graphs
6.2 Hypergraphs
6.2.1 Hypergraphs with Pairwise Intersecting Edges
6.2.2 Hypergraphs with Pairwise Incomparable Edges
6.3 Something Is More Than Nothing: Existence Proofs
HIGHER MATHEMATICS
Logic
6.3.1 Property B
6.3.2 Excluding Monochromatic Arithmetic Progressions
6.3.3 Codes Over Finite Alphabets
6.4 Notes
6.5 Chapter Review
6.6 Exercises
III What Else: Special Topics.
7 Symmetric Structures
7.1 Hypergraphs with Symmetries
7.2 Finite Projective Planes
7.2.1 Excursion: Finite Projective Planes of Prime Power Order
7.3 Error-Correcting Codes
7.3.1 Words Far Apart
7.3.2 Codes from Hypergraphs
7.3.3 Perfect Codes
7.4 Counting Symmetric Structures
7.5 Notes
7.6 Chapter Review
7.7 Exercises
8 Sequences in Combinatorics
8.1 Unimodality
8.2 Log-Concavity
8.2.1 Log-Concavity Implies Unimodality
8.2.2 The Product Property
8.2.3 Injective Proofs
8.3 The Real Zeros Property
8.4 Notes
8.5 Chapter Review
8.6 Exercises
9 Counting Magic Squares and Magic Cubes
9.1 An Interesting Distribution Problem
9.2 Magic Squares of Fixed Size
9.2.1 The Case of n = 3
9.2.2 The Function Hn(r) for Fixed n
9.3 Magic Squares of Fixed Line Sum
9.4 Why Magic Cubes Are Different
9.5 Notes
9.6 Chapter Review
9.7 Exercises
A The Method of Mathematical Induction.
A.1 Weak Induction
A.2 Strong Induction References
Index
List of Frequently Used Notation
SCHAUM’S EASY OUTLINE OF LOGIC
By John Nolt, University of Tennessee, Dennis Rohatyn, University of San
Diego and Achille Varzi, Columbia University-New York
2006 (September 2005) / 160pages
ISBN-13: 978-0-07-145535-0 / MHID: 0-07-145535-3
Pared-down, simplified, and tightly focused, Schaum’s Easy Outline
of Logic is perfect for anyone turned off by dense text. Cartoons,
sidebars, icons, and other graphic pointers get the material across
fast, and concise text focuses on the essence of logic. This is the
ideal book for last-minute test preparation.
Advanced Engineering
Mathematics
HIGHER ENGINEERING MATHEMATICS
By B.V. Ramana, JNTU College of Engineering-Kakinada
2006 (July 2006) / 1312 pages
MHID: 978-0-07-063419-0 / MHID: 0-07-063419-X
McGraw-Hill India Title
This comprehensive text on Higher Engineering Mathematics
covers the syllabus of all the Mathematics papers offered to the
undergraduate students. The huge chest of solved examples help
the students learn about a variety of problems & the procedure to
solve them. Additional practice problems/exercises facilitate testing
their understanding of the subject.
CONTENTS
Part A: Preliminaries
Chapter 1. Vector Algebra, Theory of Equations, Complex Numbers
Part B: Differential and Integral Calculus
Chapter 2. Differential Calculus
Chapter 3. Partial Differentiation
Chapter 4. Maxima and Minima
Chapter 5. Curve Tracing
Chapter 6. Integral Calculus: Applications
Chapter 7. Multiple Integrals
Part C: Ordinary Differential Equations
Chapter 8. Ordinary Differential Equations: First Order with
Applications
Chapter 9. Ordinary Differential Equations: Second and higher orders
with Applications
Chapter 10. Series Solutions
Chapter 11. Special Functions
Chapter 12. Laplace Transform
Part D: Linear Algebra and Vector Calculus
Chapter 13. Matrices
Chapter 14. Eigen Values and Eigen Vectors
Chapter 15. Vector Differential Calculus
Chapter 16. Vector Integral Calculus
Part E: Fourier Analysis and Partial Differential Equations
Chapter 17. Fourier Series
Chapter 18. Partial Differential Equations
Chapter 19. Applications of PDE
Chapter 20. Fourier Integral and Fourier Transform
Chapter 21. FINITE DIFFERENCES and Z-TRANSFORMS
Part F: Complex Analysis
Chapter 22. Complex Functions
Chapter 23. Complex Integration
Chapter 24. Theory of Residues
94
HIGHER MATHEMATICS
Dynamical System
Chapter 25. Conformal Mapping
Part G: Probability and Statistics
Chapter 26. Probability Theory
Chapter 27. Probability Distributions
Chapter 28. Sampling Distributions (SD)
Chapter 29. Inferences concerning means and proportions
Chapter 30. Line & Curve Fitting, Correlation and Regression
Chapter 31. Joint Probability Distribution and Markov Chains
Part H: Numerical Analysis
Chapter 32. Numerical Analysis
Chapter 33. Numerical Solutions of ODE and PDE
Appendices
A1: Basic Results
A2: Statistical Tables
A3: Bibliography
A4: Index
Schaum’s Outline of Vector Analysis
By Murray R Spiegel, deceased
1968 / 240 pages
ISBN-13: 978-0-07-060228-1 / MHID: 0-07-060228-X
ISBN-13: 978-0-07-099009-8 / MHID: 0-07-099009-3 [IE]
CONTENTS
Vectors and Scalars
The Dot and Cross Product
Vector Differentiation
Gradient, Divergence and Curl
Vector Integration
The Divergence Theorem, Stokes’s Theorem, and Related Integral
Theorems
Curvilinear Coordinates
Tensor Analysis
Schaum’s Outline of Advanced
Mathematics for Engineers and
Scientists, SI Metric
By Murray R Spiegel, Rensselaer Polytechnic Institute
1971 / 416 pages
ISBN-13: 978-0-07-060216-8 / MHID: 0-07-060216-6
(Non SI Metric)
ISBN-13: 978-0-07-099064-7 / MHID: 0-07-099064-6
[IE, SI Metric]
Graph Theory
CONTENTS
Review of Fundamental Concepts
Ordinary Differential Equations
Linear Differential Equations
Laplace Transforms
Vector Analysis
Multiple, Line, and Surface Integrals and Integral Theorems
Fourier Series
Fourier Integrals
Gamma, Beta, and Other Special Functions
Bessel Functions
Lengendre Functions and Other Orthogonal Functions of Partial
Complex Variables and Conformal Mapping
Complex Inversion Formula for Laplace Transforms
Matrices
Calculus of Variations
95
INTRODUCTION TO GRAPH THEORY
By Gary Chartrand, Western Michigan University—Kalamazoo and Ping
Zhang, Western Michigan University—Kalamazoo
2005 (May 2004) / 464 pages
ISBN-13: 978-0-07-320416-1 / MHID: 0-07-320416-1
ISBN-13: 978-0-07-123822-9 / MHID: 0-07-123822-0 [IE]
Contents
1. Introduction:
Graphs and Graph Models. Connected Graphs. Common Classes
of Graphs.
2. Degrees:
The Degree of a Vertex. Regular Graphs. Degree Sequences.
Excursion: Graphs and Matrices. Exploration: Irregular Graphs.
3. Isomorphic Graphs:
The Definition of Isomorphisms. Isomorphism as a Relation.
Excursion: Recognition, Reconstruction, Solvability. Excursion:
Graphs and Groups.
4. Trees:
Bridges. Trees. The Minimum Spanning Tree Problem. Excursion: The
Number of Spanning Trees. Exploration: Comparing Trees.
5. Connectivity:
Cut-Vertices. Blocks. Connectivity. Menger’s Theorem. Exploration:
Geodetic Sets.
6. Traversability:
Eulerian Graphs. Hamiltonian Graphs. Exploration: Hamiltonian Walks
and Numbers. Excursion: The Early Books of Graph Theory.
7. Digraphs:
Strong Digraphs. Tournaments. Excursion: How to Make Decisions.
Exploration: Wine Bottle Problems.
8. Matchings and Factorization:
Matchings. Factorizations. Decompositions and Graceful Labelings.
HIGHER MATHEMATICS
Excursion: Instant Insanity. Excursion: The Petersen Graph.
Exploration: -Labeling of Graphs.
9. Planarity:
Planar Graphs. Embedding Graphs on Surfaces. Excursion: Graphs
Minors. Exploration: Embedding Graphs in Graphs.
10. Coloring Graphs:
The Four Color Problem. Vertex Coloring. Edge Coloring. Excursion:
The Heawood Map-Coloring Theorem. Exploration: Local Coloring.
11. Ramsey Numbers:
The Ramsey Number of Graphs. Turan’s Theorem. Exploration:
Rainbow Ramsey Numbers. Excursion: Erd?umbers.
12. Distance:
The Center of a Graph. Distant Vertices. Excursion: Locating Numbers.
Excursion: Detour Distance and Directed Distance. Exploration:
The Channel Assignment Problem. Exploration: Distance Between
Graphs.
13. Domination:
The Domination Number of a Graph. Exploration: Stratification.
Exploration: Lights Out. Excursion: And Still It Grows More Colorful.
Appendix 1. Sets and Logic.
Appendix 2. Equivalence Relations and Functions.
Appendix 3. Methods of Proof.
Answers and Hints to Odd-Numbered Exercises.
References.
Index of Symbols.
Index of Mathematical Terms
SCHAUM’S OUTLINE OF GRAPH THEORY:
Including Hundreds of Solved
Problems
By V K Balakrishnan, University of Maine
1997 / 288 pages
ISBN-13: 978-0-07-005489-9 / MHID: 0-07-005489-4
Contents
Graphs and Digraphs.
Connectivity.
Eulerian and Hamiltonian Graphs.
Optimization Involving Trees.
Shortest Path Problems.
Flow and Connectivity.
Planarity and Duality.
Graph Colorings.
Additional Topics.
List of Technical Terms and Symbols Used.
Schaum’s Outline of Combinatorics
By V K Balakrishnan, University of Maine
1995 / 320 pages
ISBN-13: 978-0-07-003575-1 / MHID: 0-07-003575-X
CONTENTS
The Sum Rule and the Product Rule.
The Pigeonhole Principle.
Generalized Permutations and Combinations.
Sequences and Selections.
The Inclusion-Exclusion Principle.
Generating Functions and Partitions of Integers.
The Distribution Problem in Combinatorics.
Recurrence Relations.
Group Theory in Combinatorics--Including The Burnside-Froberius
Theorem.
Permutation Groups and Their Cycles Indices and Polya’s
Enumeration Theorems.
Applied and Algorithmic Graph
Theory
By Gary Chartrand, Western Michigan University, and Ortrud
Oellermann, University of Natal, South Africa
1993 / 432 pages
ISBN-13: 978-0-07-557101-8 / MHID: 0-07-557101-3
(Out-of-Print)
ISBN-13: 978-0-07-112575-8 / MHID: 0-07-112575-2 [IE]
Contents
1 An Introduction to Graphs
2 An Introduction to Algorithms
3 Trees
4 Paths and Distance and Graphs
5 Networks
6 Matchings and Factorizations
7 Eulerian Graphs
8 Hamiltonian Graphs
9 Planar Graphs
10 Coloring Graphs
11 Digigraphs
12 Extremal Graph Theory
96
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HIGHER MATHEMATICS
Introductory Analysis
Introduction to Mathematical
Analysis
By William Parzynski, Philip Zipse both of Montclair State College
1982 / 352 pages
ISBN-13: 978-0-07-066467-8 / MHID: 0-07-066467-6 [IE]
CONTENTS
1 Real Numbers and Functions
2 Sequences and Sets of Real Numbers
3 Functions and Limits
4 Continuous Functions
5 Differentiable Functions
6 The Riemann Integral
7 Sequences and Series of Functions
8 Differentiable Functions of Several Variables
9 Multiple Integrals
10 Metric Spaces
Solutions and Hints to Selected Exercises
Index
Section 5.2 Properties of the integral.
Section 5.3 Existence theory.
Section 5.4 The Fundamental Theorem of Calculus.
Section 5.5 Improper integrals.
Chapter 6: Infinite Series:
Section 6.1 Basic theory.
Section 6.2 Absolute convergence.
Section 6.3 Power series.
Section 6.4 Taylor series.
Chapter 7: Sequences and Series of Functions:
Section 7.1 Uniform convergence.
Section 7.2 Consequences of uniform convergence.
Section 7.3 Two examples.
Solutions and Hints for Selected Problems.
Index
History Of Mathematics
THE HISTORY OF MATHEMATICS An
Introduction
Sixth Edition
By David M. Burton, University Of New Hampshire
2007 (November 2005) / 752 pages / Hardcover
ISBN-13: 978-0-07-305189-5 / MHID: 0-07-305189-6
ISBN-13: 978-0-07-125389-5 / MHID: 0-07-125389-0 [IE]
Principles of Mathematical Analysis
Third Edition
The History of Mathematics: An Introduction, Sixth Edition, is written
for the one- or two-semester math history course taken by juniors or
seniors, and covers the history behind the topics typically covered in
an undergraduate math curriculum or in elementary schools or high
schools. Elegantly written in David Burton’s imitable prose, this classic
text provides rich historical context to the mathematics that undergrad
math and math education majors encounter every day. Burton
illuminates the people, stories, and social context behind mathematics’
greatest historical advances while maintaining appropriate focus on
the mathematical concepts themselves. Its wealth of information,
mathematical and historical accuracy, and renowned presentation
make The History of Mathematics: An Introduction, Sixth Edition a
valuable resource that teachers and students will want as part of a
permanent library.
By Walter Rudin, University of Wisconsin-Madison
1976 / 325 pages
ISBN-13: 978-0-07-054235-8 / MHID: 0-07-054235-X
ISBN-13: 978-0-07-085613-4 / MHID: 0-07-085613-3 [IE]
Contents
CHAPTER 1: The Real Numbers:
Section 1.1 Sets.
Section 1.2 Functions.
Section 1.3 Algebraic and order properties.
Section 1.4 The positive integers.
Section 1.5 The least upper bound axiom.
Chapter 2: Sequences:
Section 2.1 Sequences and limits.
Section 2.2 Limit theorems.
Section 2.3 Monotonic sequences.
Section 2.4 Sequences defined inductively.
Section 2.5 Sequences, Cauchy sequences.
Section 2.6 Infinite limits.
Chapter 3: Functions and Continuity:
Section 3.1 Limit of a function.
Section 3.2 Limit theorems.
Section 3.3 Other limits.
Section 3.4 Continuity.
Section 3.5 Intermediate values, extreme values.
Section 3.6 Uniform continuity.
Chapter 4: The Derivative:
Section 4.1 Definition of the derivative.
Section 4.2 Rules for differentiation.
Section 4.3 The Mean Value Theorem.
Section 4.4 Inverse functions.
Chapter 5: The Integral:
Section 5.1 The definition of the integral.
Contents
Preface.
1 Early Number Systems and Symbols
1.1 Primitive Counting. A Sense of Number. Notches as Tally Marks.
The Peruvian Quipus: Knots as Numbers.
1.2 Number Recording of the Egyptians and Greeks. The History
of Herodotus. Hieroglyphic Representation of Numbers. Egyptian
Hieratic Numeration. The Greek Alphabetic Numeral System.
1.3 Number Recording of the Babylonians. Babylonian Cuneiform
Script. Deciphering Cuneiform: Grotefend and Rawlinson. The
Babylonian Positional Number System. Writing in Ancient China.
2 Mathematics in Early Civilizations
2.1 The Rhind Papyrus. Egyptian Mathematical Papyri. A Key To
Deciphering: The Rosetta Stone
2.2 Egyptian Arithmetic. Early Egyptian Multiplication. The Unit
Fraction Table. Representing Rational Numbers
2.3 Four Problems from the Rhind Papyrus. The Method of False
Position. A Curious Problem. Egyptian Mathematics as Applied
Arithmetic.
97
HIGHER MATHEMATICS
2.4 Egyptian Geometry. Approximating the Area of a Circle. The
Volume of a Truncated Pyramid. Speculations About the Great
Pyramid
2.5 Babylonian Mathematics. A Tablet of Reciprocals. The Babylonian
Treatment of Quadratic Equations. Two Characteristic Babylonian
Problems.
2.6 Plimpton. A Tablet Concerning Number Triples. Babylonian Use of
the Pythagorean Theorem. The Cairo Mathematical Papyrus.
3 The Beginnings of Greek Mathematics
3.1 The Geometric Discoveries of Thales. Greece and the Aegean
Area. The Dawn of Demonstrative Geometry: Thales of Miletos.
Measurements Using Geometry.
3.2 Pythagorean Mathematics. Pythagoras and His Followers.
Nichomachus’ Introductio Arithmeticae. The Theory of Figurative
Numbers. Zeno’s Paradox
3.3 The Pythagorean Problem. Geometric Proofs of the Pythagorean
Theorem. Early Solutions of the Pythagorean Equation. The Crisis of
Incommensurable Quantities. Theon’s Side and Diagonal Numbers
Eudoxus of Cnidos.
3.4 Three Construction Problems of Antiquity. Hippocrates and the
Quadrature of the Circle. The Duplication of the Cube. The Trisection
of an Angle.
3.5 The Quadratrix of Hippias. Rise of the Sophists. Hippias of Elis.
The Grove of Academia: Plato’s Academy.
4 The Alexandrian School: Euclid.
4.1 Euclid and the Elements. A Center of Learning: The Museum.
Euclid’s Life and Writings.
4.2 Euclidean Geometry. Euclid’s Foundation for Geometry. Book I of
the Elements. Euclid’s Proof of the Pythagorean Theorem. Book II on
Geometric Algebra. Construction of the Regular Pentagon.
4.3 Euclid’s Number Theory. Euclidean Divisibility Properties. The
Algorithm of Euclid. The Fundamental Theorem of Arithmetic. An
Infinity of Primes.
4.4 Eratosthenes, the Wise Man of Alexandria. The Sieve of
Eratosthenes. Measurement of the Earth. The Almagest of Claudius
Ptolemy. Ptolemy’s Geographical Dictionary.
4.5 Archimedes. The Ancient World’s Genius. Estimating the Value of.
The Sand-Reckoner Quadrature of a Parabolic Segment. Apollonius
of Perga: the Conics.
5 The Twilight of Greek Mathematics: Diophantus.
5.1 The Decline of Alexandrian Mathematics. The Waning of the
Golden Age. The Spread of Christianity. Constantinople, A Refuge
for Greek Learning.
5.2 The Arithmetica. Diophantus’s Number Theory. Problems from
the Arithmetica.
5.3 Diophantine Equations in Greece, India and China. The Cattle
Problem of Archimedes. Early Mathematics in India. The Chinese
Hundred Fowls Problem.
5.4 The Later Commentators. The Mathematical Collection of Pappus.
Hypatia, the First Woman Mathematician. Roman Mathematics:
Boethius and Cassiodorus.
5.5 Mathematics in the Near and Far East. The Algebra of alKhowârizmî. Abû Kamil and Thâbit ibn Qurra. Omar Khayyam The
Astronomers al-Tusi and al-Karashi. The Ancient Chinese Nine
Chapters. Later Chinese Mathematical Works.
6 The First Awakening: Fibonacci.
6.1 The Decline and Revival of Learning. The Carolingian PreRenaissance. Transmission of Arabic Learning to the West. The
Pioneer Translators: Gerard and Adelard.
6.2 The Liber Abaci and Liber Quadratorum. The Hindu-Arabic
Numerals. Libonacci’s Liver Quadratorum. The Works of Jordanus
de Nemore.
6.3 The Fibonacci Sequence. The Liber Abaci’s Rabbit Problem. Some
Properties of Fibonacci Numbers.
6.4 Fibonacci and the Pythagorean Problem. Pythagorean Number
Triples. Fibonacci’s Tournament Problem.
7 The Renaissance of Mathematics: Cardan and Tartaglia.
7.1 Europe in the Fourteenth and Fifteenth Centuries. The Italian
Renaissance. Artificial Writing: The Invention of Printing. Founding
of the Great Universities A Thirst for Classical Learning.
98
7.2 The Battle of the Scholars. Restoring the Algebraic Tradition:
Robert Recorde. The Italian Algebraists: Pacioli, del Ferro and
Tartaglia. Cardan, A Scoundrel Mathematician
7.3 Cardan’s Ars Magna. Cardan’s Solution of the Cubic Equation.
Bombelli and Imaginary Roots of the Cubic.
7.4 Ferrari’s Solution of the Quartic Equation. The Resolvant Cubic.
The Story of the Quintic Equation: Ruffini, Abel and Galois.
8 The Age of Descartes and Newton.
8.1 The Dawn of Modern Mathematics. The 17th Century Spread
of Knowledge. Galileo’s Telescopic Observations. The Beginning
of Modern Notation: Francois Vièta. The Decimal Fractions of
Simon Steven. Napier’s Invention of Logarithms. The Astronomical
Discoveries of Brahe and Kepler.
8.2 Descartes: The Discours de la Méthod. The Writings of Descartes.
Inventing Cartesian Geometry. The Algebraic Aspect of La Géometrie.
Descartes’ Principia Philosophia. Perspective Geometry: Desargues
and Poncelet.
8.3 Newton: The Principia Mathematica. The Textbooks of
Oughtred and Harriot. Wallis’ Arithmetica Infinitorum. The Lucasian
Professorship: Barrow and Newton. Newton’s Golden Years. The
Laws of Motion. Later Years: Appointment to the Mint.
8.4 Gottfried Leibniz: The Calculus Controversy. The Early Work
of Leibniz. Leibniz’s Creation of the Calculus. Newton’s Fluxional
Calculus. The Dispute over Priority. Maria Agnesi and Emilie du
Châtelet.
9 The Development of Probability Theory: Pascal, Bernoulli,
and Laplace.
9.1 The Origins of Probability Theory. Graunt’s Bills of Mortality. James
of Chance: Dice and Cards. The Precocity of the Young Pascal. Pascal
and the Cycloid. De Méré’s Problem of Points.
9.2 Pascal’s Arithmetic Triangle. The Traité du Triangle Arithmétique.
Mathematical Induction. Francesco Maurolico’s Use of Induction.
9.3 The Bernoullis and Laplace. Christiaan Huygens’s Pamphlet on
Probability. The Bernoulli Brothers: John and James. De Moivre’s
Doctrine of Chances The Mathematics of Celestial Phenomena:
Laplace. Mary Fairfax Somerville. Laplace’s Research on Probability
Theory. Daniel Bernoulli, Poisson and Chebyshev.
10 The Revival of Number Theory: Fermat, Euler, and Gauss.
10.1 Martin Mersenne and the Search for Perfect Numbers. Scientific
Societies Marin Mersenne’s Mathematical Gathering. Numbers,
Perfect and Not So Perfect.
10.2 From Fermat to Euler. Fermat’s Arithmetica. The Famous
Last Theorem of Fermat. The Eighteenth Century Enlightenment
Maclaurin’s Treatise on Fluxions. Euler’s Life and Contributions.
10.3 The Prince of Mathematicians: Carl Friedrich Gauss. The
Period of the French Revolution: Lagrange and Monge. Gauss’s
Disquisitiones Arithmeticae. The Legacy of Gauss: Congruence
Theory. Dirichlet and Jacobi.
11 Nineteenth-Century Contributions: Lobachevsky to Hilbert.
11.1 Attempts to Prove the Parallel Postulate. The Efforts of Proclus,
Playfair and Wallis. Saccheri Quadrilaterals. The Accomplishments
of Legendre. Legendre’s Eléments de géometrie.
11.2 The Founders of Non-Euclidean Geometry. Gauss’s Attempt
at a New Geometry. The Struggle of John Bolyai. Creation of NonEuclidean Geometry: Lobachevsky. Models of the New Geometry:
Riemann, Beltrami and Klein. Grace Chisholm Young
11.3 The Age of Rigor. D’Alembert and Cauchy on Limits. Fourier’s
Series. The Father of Modern Analysis, Weierstrass. Sonya
Kovalevsky. The Axiomatic Movement: Pasch and Hilbert
11.4 Arithmetic Generalized. Babbage and the Analytical Engine.
Peacock’s Treatise on Algebra. The Representations of Complex
Numbers. Hamilton’s Discovery of Quaternions. Matrix Algebra:
Cayley and Sylvester. Boole’s Algebra of Logic
12 Transition to the Twenthieth Century
12.1 The Emergence of American Mathematics. Ascendency of the
German Universities. American Mathematics Takes Root: 1800-1900.
The Twentieth Century Consolidation
12.2 Counting the Infinite. The Last Universalist: Poincaré. Cantor’s
Theory of Infinite Sets. Kronecker’s View of Set Theory. Countable
and Uncountable Sets. Transcendental Numbers. The Continuum
Hypothesis
HIGHER MATHEMATICS
12.3 The Paradoxes of Set Theory. The Early Paradoxes. Zermelo and
the Axiom of Choice. The Logistic School: Frege, Peano and Russell.
Hilbert’s Formalistic Approach: Brouwer’s Intuitionism.
13 Extensions and Generalizations: Hardy, Hausdorff, and
Noether.
13.1 Hardy and Ramanujan. The Tripos Examination. The
Rejuvenation of English Mathematics. A Unique Collaboration: Hardy
and Littlewood. India’s Prodigy, Ramanujan
13.2 The Beginnings of Point-Set Topology. Frechet’s Metric Spaces.
The Neighborhood Spaces of Hausdorff. Banach and Normed Linear
Spaces.
13.3 Some Twentieth-Century Developments. Emmy Noether’s
Theory of Rings. Von Neumann and the Computer. Women in
Modern Mathematics. A Few Recent Advances. General Bibliography.
Additional Reading. The Greek Alphabet Solutions to Selected
Problems. Index
Numerical Analysis
Elementary Numerical Analysis
An Algorithmic Approach, Third Edition
By Samuel D. Conte, Purdue University, Carl de Boor, University of
Wisconsin-Madison
1980 / 408 pages
ISBN-13: 978-0-07-066228-5 / MHID: 0-07-066228-2 [IE]
CONTENTS
By Francis Scheid, Boston University
1988 / 471 pages
ISBN-13: 978-0-07-055221-0 / MHID: 0-07-055221-5
Contents
What Is Numerical Analysis?
The Collocation Polynomial.
Finite Differences.
Factorial Polynomials.
Summation.
The Newton Formula.
Operators and Collocation Polynomials.
Unequally-Spaced Arguments.
Splines.
Osculating Polynomials.
The Taylor Polynomial.
Interpolation.
Numerical Differentiation.
Numerical Integration.
Gaussian Integration.
Singular Integrals.
Sums and Series.
Difference Equations.
Differential Problems of Higher Order.
Least-Squares Polynomial Approximation.
Min-Max Polynomial Approximation.
Approximation By Rational Functions.
Trigonometric Approximation.
Nonlinear Algebra.
Linear Systems.
Linear Programming.
Overdetermined Systems.
Boundary Value Problems.
Monte Carlo Methods.
1 Number Systems and Errors
2 Interpolation by Polynomial
3 The Solution of Nonlinear Equations
4 Matrices and Systems of Linear Equations
5 Systems of Equations and Unconstrained Optimization
6 Approximation
7 Differentiation and Integration
8 The Solution of Differential Equations
9 Boundary Value Problems
Appendix: Subroutine Libraries
References
Index
schaum’s Outline of Numerical
Analysis
Second Edition
99
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HIGHER MATHEMATICS
Number Theory
ELEMENTARY NUMBER THEORY
Sixth Edition
By David M. Burton, University Of New Hampshire
2007 (October 2005) / 528 pages / Hardcover
ISBN-13: 978-0-07-305188-8 / MHID: 0-07-305188-8
ISBN-13: 978-0-07-124425-1 / MHID: 0-07-124425-5 [IE]
Elementary Number Theory, Sixth Edition, is written for the onesemester undergraduate number theory course taken by math majors,
secondary education majors, and computer science students. This
contemporary text provides a simple account of classical number
theory, set against a historical background that shows the subject’s
evolution from antiquity to recent research. Written in David Burton’s
engaging style, Elementary Number Theory reveals the attraction that
has drawn leading mathematicians and amateurs alike to number
theory over the course of history.
Contents
Preface. New To This Edition.
1 Preliminaries
1.2 The Binomial Theorem
2 Divisibility Theory in the Integers
2.1 Early Number Theory
2.1 The Division Algorithm
2.2 The Greatest Common Divisor
2.3 The Euclidean Algorithm
2.4 The Diophantine Equation ax + by = c
3 Primes and Their Distribution
3.1 The Fundamental Theorem of Arithmetic
3.2 The Sieve of Eratosthenes
3.3 The Goldbach Conjecture
4 The Theory of Congruences
4.1 Carl Friedrich Gauss
4.2 Basic Properties of Congruence
4.3 Binary and Decimal Representations of Integers
4.4 Linear Congruences and the Chinese Remainder Theorem
5 Fermat’s Theorem
5.1 Pierre de Fermat
5.2 Fermat’s Little Theorem and Pseudoprimes
5.3 Wilson’s Theorem
5.4 The Fermat-Kraitchik Factorization Method
6 Number-Theoretic Functions
6.1 The Sum and Number of Divisors
6.2 The Möbius Inversion Formula
6.3 The Greatest Integer Function
6.4 An Application to the Calendar
7 Euler’s Generalization of Fermat’s Theorem
7.1 Leonhard Euler
7.2 Euler’s Phi-Function
7.3 Euler’s Theorem
7.4 Some Properties of the Phi-Function.
8 Primitive Roots and Indices
8.1 The Order of an Integer Modulo n
8.2 Primitive Roots for Primes
8.3 Composite Numbers Having Primitive Roots
8.4 The Theory of Indices
9 The Quadratic Reciprocity Law
9.1 Euler’s Criterion
9.2 The Legendre Symbol and Its Properties
9.3 Quadratic Reciprocity
9.4 Quadratic Congruences with Composite Moduli
10 Introduction to Cryptography
10.1 From Caesar Cipher to Public Key Cryptography
10.2 The Knapsack Cryptosystem
10.3 An Application of Primitive Roots to Cryptography
11 Numbers of Special Form
11.1 Marin Mersenne
11.2 Perfect Numbers
11.3 Mersenne Primes and Amicable Numbers
11.4 Fermat Numbers
12 Certain Nonlinear Diophantine Equations
12.1 The Equation x2 + y2 = z2
12.2 Fermat’s Last Theorem
13 Representation of Integers as Sums of Squares
13.1 Joseph Louis Lagrange
13.2 Sums of Two Squares
13.3 Sums of More than Two Squares
14 Fibonacci Numbers
14.1 Fibonacci
14.2 The Fibonacci Sequence
14.3 Certain Identities Involving Fibonacci Numbers
15 Continued Fractions
15.1 Srinivasa Ramanujan
15.2 Finite Continued Fractions
15.3 Infinite Continued Fractions
15.4 Pell’s Equation
16 Some Twentieth-Century Developments.
16.1 Hardy, Dickson, and Erdös
16.2 Primality Testing and Factorization
16.3 An Application to Factoring: Remote Coin Flipping
16.4 The Prime Number Theorem and Zeta Function.
Miscellaneous Problems.
Appendixes.
General References.
Suggested Further Reading Tables.
Answers to Selected Problems.
Index.
Elementary Number Theory
Second Edition
By Charles Vanden Eynden, Illinois State University
2001 / 288 pages
ISBN-13: 978-0-07-232571-3 / MHID: 0-07-232571-2 (Out of Print)
ISBN-13: 978-0-07-118193-8 / MHID: 0-07-118193-8 [IE]
Contents
0 What is Number Theory?
1 Divisibility.
2 Prime Numbers.
3 Numerical Functions.
4 The Algebra of Congruence Classes.
5 Congruences of Higher Degree.
6 The Number Theory of the Reals.
7 Diophantine Equations.
100
HIGHER MATHEMATICS
Abstract Algebra
Complex Analysis
SCHAUM’S OUTLINE OF MODERN
ABSTRACT ALGEBRA
By Frank Ayres (deceased)
1965 / 256 pages
ISBN-13: 978-0-07-002655-1 / MHID: 0-07-002655-6
New
Contents
Sets.
Relations and Operations.
The Natural Numbers.
The Integers.
Some Properties of Integers.
The Rational Numbers.
The Real Numbers.
The Complex Numbers.
Groups.
Rings.
Integral Domains.
Division Rings.
Fields.
Polynomials.
Vector Spaces.
Matrices.
Matrix Polynomials.
Linear Algebra.
Boolean Algebra.
Advanced Geometry
SCHAUM’S OUTLINE OF DIFFERENTIAL
GEOMETRY
By Martin M. Lipschutz, Hahnemann Medical College
1969 / 288 pages
ISBN-13: 978-0-07-037985-5 / MHID: 0-07-037985-8
Contents
Vectors.
Vector Functions of Real Variable.
Concept of Curve.
Curvature and Torsion.
Theory of Curves.
Elementary Topology in Euclidean Spaces.
Vector Functions of Vector Variable.
Concept of Curve.
First and Second Fundamental Forms.
Theory of Surfaces.
Tensor Analysis.
Intrinsic Geometry.
Appendix.
Existence Theorem for Curves.
Existence Theorem for Surfaces.
COMPLEX VARIABLES AND
APPLICATIONS
Eighth Edition
By James Ward Brown, University of MichiganDearborn and Ruel V Churchill (deceased)
2009 (January 2008) / 504 pages
ISBN-13: 978-0-07-305194-9 / MHID: 0-07-305194-2
ISBN-13: 978-0-07-126328-3 / MHID: 0-07-126328-4 [IE]
Complex Variables and Applications, 8e will serve, just as the earlier
editions did, as a textbook for an introductory course in the theory
and application of functions of a complex variable. This new edition
preserves the basic content and style of the earlier editions. The text
is designed to develop the theory that is prominent in applications of
the subject. You will find a special emphasis given to the application
of residues and conformal mappings. To accommodate the different
calculus backgrounds of students, footnotes are given with references
to other texts that contain proofs and discussions of the more delicate
results in advanced calculus. Improvements in the text include
extended explanations of theorems, greater detail in arguments, and
the separation of topics into their own sections.
New to this edition
Some sections that can be skipped or postponed without
disruption are more clearly identified. The statements of Taylor’s and
Laurent’s theorems, for example, now appear in sections that are
separate from the sections containing their proofs.
The treatment of the extended form of the Cauchy integral
formula for derivatives has been completely rewritten, with special
attention to its immediate consequences.
Other improvements include more details in arguments involving
mathematical induction, greater emphasis on rules for using complex
exponents, some discussion of residues at infinity, and a clearer
exposition of real improper integrals and their Cauchy principal
values.
Some important material is presented in a more focused way by
placing it in separate sections. For instance, the discussion of upper
bounds of moduli of contour integrals is now entirely in one section,
and there is a separate section devoted to the definition of isolated
singular points.
A revised Student’s Solutions Manual with solutions for a large
number of exercises in Chapters 1-7 is available
CONTENTS
1 Complex Numbers
Sums and Products
Basic Algebraic Properties
Further Properties
Moduli
Complex Conjugates
Exponential Form
Products and Quotients in Exponential Form
Roots of Complex Numbers
101
HIGHER MATHEMATICS
Examples
Regions in the Complex Plane
2 Analytic Functions
Functions of a Complex Variable
Mappings
Mappings by the Exponential Function
Limits
Theorems on Limits
Limits Involving the Point at Infinity
Continuity
Derivatives
Differentiation Formulas
Cauchy–Riemann Equations
Sufficient Conditions for Differentiability
Polar Coordinates
Analytic Functions
Examples
Harmonic Functions
Uniquely Determined Analytic Functions
Reflection Principle
3 Elementary Functions
The Exponential Function
The Logarithmic Function
Branches and Derivatives of Logarithms
Some Identities Involving Logarithms
Complex Exponents
Trigonometric Functions
Hyperbolic Functions
Inverse Trigonometric and Hyperbolic Functions
4 Integrals
Derivatives of Functions w(t)
Definite Integrals of Functions w(t)
Contours
Contour Integrals
Examples
Upper Bounds for Moduli of Contour Integrals
Antiderivatives
Examples
Cauchy–Goursat Theorem
Proof of the Theorem
Simply and Multiply Connected Domains
Cauchy Integral Formula
Derivatives of Analytic Functions
Liouville’s Theorem and the Fundamental Theorem of Algebra
Maximum Modulus Principle
5 Series
Convergence of Sequences
Convergence of Series
Taylor Series
Examples
Laurent Series
Examples
Absolute and Uniform Convergence of Power Series
Continuity of Sums of Power Series
Integration and Differentiation of Power Series
Uniqueness of Series Representations
Multiplication and Division of Power Series
6 Residues and Poles
Residues
Cauchy’s Residue Theorem
Using a Single Residue
The Three Types of Isolated Singular Points
Residues at Poles
Examples
Zeros of Analytic Functions
Zeros and Poles
Behavior of f Near Isolated Singular Points
7 Applications of Residues
Evaluation of Improper Integrals
Example
Improper Integrals from Fourier Analysis
Jordan’s Lemma
Indented Paths
An Indentation Around a Branch Point
Integration Along a Branch Cut
Definite Integrals Involving Sines and Cosines
Argument Principle
Rouché’s Theorem
Inverse Laplace Transforms
Examples
8 Mapping by Elementary Functions
Linear Transformations
The Transformation w = 1/z
Mappings by 1/z
Linear Fractional Transformations
An Implicit Form
Mappings of the Upper Half Plane
The Transformation w = sin z
Mappings by z2 and Branches of z1/2
Square Roots of Polynomials
Riemann Surfaces
Surfaces for Related Functions
9 Conformal Mapping
Preservation of Angles
Scale Factors
Local Inverses
Harmonic Conjugates
Transformations of Harmonic Functions
Transformations of Boundary Conditions
10 Applications of Conformal Mapping
Steady Temperatures
Steady Temperatures in a Half Plane
A Related Problem
Temperatures in a Quadrant
Electrostatic Potential
Potential in a Cylindrical Space
Two-Dimensional Fluid Flow
The Stream Function
Flows Around a Corner and Around a Cylinder
11 The Schwarz–Christoffel Transformation
Mapping the Real Axis onto a Polygon
Schwarz–Christoffel Transformation
Triangles and Rectangles
Degenerate Polygons
Fluid Flow in a Channel Through a Slit
Flow in a Channel with an Offset
Electrostatic Potential about an Edge of a Conducting Plate
12 Integral Formulas of the Poisson Type
Poisson Integral Formula
Dirichlet Problem for a Disk
Related Boundary Value Problems
Schwarz Integral Formula
Dirichlet Problem for a Half Plane
Neumann Problems
Appendixes
Bibliography
Table of Transformations of Regions
Index
102
HIGHER MATHEMATICS
Real and Complex Analysis
Third Edition
By Walter Rudin, University of Wisconsin
1987 / 483 pages
ISBN-13: 978-0-07-054234-1 / MHID: 0-07-054234-1
ISBN-13: 978-0-07-100276-9 / MHID: 0-07-100276-6 [IE]
Contents
Preface.
Prologue: The Exponential Function.
Chapter 1: Abstract Integration:
Set-theoretic notations and terminology. The concept of measurability.
Simple functions. Elementary properties of measures. Arithmetic in
[0, infinity]. Integration of positive functions. Integration of complex
functions. The role played by sets of measure zero. Exercises.
Chapter 2: Positive Borel Measures:
Vector spaces. Topological preliminaries. The Riesz representation
theorem. Regularity properties of Borel measures. Lebesgue measure.
Continuity properties of measurable functions. Exercises.
Chapter 3: L^p-Spaces:
Convex functions and inequalities. The L^p-spaces. Approximation
by continuous functions. Exercises.
Chapter 4: Elementary Hilbert Space Theory:
Inner products and linear functionals. Orthonormal sets. Trigonometric
series. Exercises.
Chapter 5: Examples of Banach Space Techniques:
Banach spaces. Consequences of Baire’s theorem. Fourier series
of continuous functions. Fourier coefficients of L-functions. The
Hahn-Banach theorem. An abstract approach to the Poisson integral.
Exercises.
Chapter 6: Complex Measures:
Total variation. Absolute continuity. Consequences of the RadonNikodym theorem. Bounded linear functionals on L^p. The Riesz
representation theorem. Exercises.
Chapter 7: Differentiation:
Derivatives of measures. The fundamental theorem of Calculus.
Differentiable transformations. Exercises.
Chapter 8: Integration on Product Spaces:
Measurability on cartesian products. Product measures. The Fubini
theorem. Completion of product measures. Convolutions. Distribution
functions. Exercises.
Chapter 9: Fourier Transforms:
Formal properties. The inversion theorem. The Plancherel theorem.
The Banach algebra L. Exercises.
Chapter 10: Elementary Properties of Holomorphic Functions:
Complex differentiation. Integration over paths. The local Cauchy
theorem. The power series representation. The open mapping
theorem. The global Cauchy theorem. The calculus of residues.
Exercises.
Chapter 11: Harmonic Functions:
The Cauchy-Riemann equations. The Poisson integral. The
mean value property. Boundary behavior of Poisson integrals.
Representation theorems. Exercises.
Chapter 12: The Maximum Modulus Principle:
Introduction. The Schwarz lemma. The Phragmen-Lindel’s Method.
An interpolation theorem. A converse of the maximum modulus
theorem. Exercises.
Chapter 13: Approximation by Rational Functions:
Preparation. Runge’s theorem. The Mittag-Leffler theorem. Simply
connected regions. Exercises.
Chapter 14: Conformal Mapping:
Preservation of angles. Linear fractional transformations. Normal
families. The Riemann mapping theorem. The class. Continuity at the
boundary. Conformal mapping of an annulus. Exercises.
Chapter 15: Zeros of Holomorphic Functions:
Infinite Products. The Weierstrass factorization theorem. An
interpolation problem. Jensen’s formula. Blaschke products. The
M’zas theorem. Exercises.
Chapter 16: Analytic Continuation:
Regular points and singular points. Continuation along curves. The
monodromy theorem. Construction of a modular function. The Picard
theorem. Exercises.
Chapter 17: H^p-Spaces:
Subharmonic functions . The spaces H^p and N. The theorem of F.
and M. Riesz. Factorization theorems. The shift operator. Conjugate
functions. Exercises.
Chapter 18: Elementary Theory of Banach Algebras:
Introduction. The invertible elements. Ideals and homomorphisms.
Applications. Exercises.
Chapter 19: Holomorphic Fourier Transforms:
Introduction. Two theorems of Paley and Wiener. Quasi-analytic
classes. The Denjoy-Carleman theorem. Exercises.
Chapter 20: Uniform Approximation by Polynomials:
Introduction. Some lemmas. Mergelyan’s theorem. Exercises.
Appendix:
Hausdorff’s Maximality Theorem. Notes and Comments. Bibliography.
List of Special Symbols. Index
Complex Analysis
Third Edition
By Lars Ahlfors, Harvard University
1979 / 336 pages
ISBN-13: 978-0-07-000657-7 / MHID: 0-07-000657-1
ISBN-13: 978-0-07-085008-8 / MHID: 0-07-085008-9 [IE]
Contents
Chapter 1: Complex Numbers:
1 The Algebra of Complex Numbers.
2 The Geometric Representation of Complex Numbers.
Chapter 2: Complex Functions:
1 Introduction to the Concept of Analytic Function.
2 Elementary Theory of Power Series.
3 The Exponential and Trigonometric Functions.
Chapter 3: Analytic Functions as Mappings:
1 Elementary Point Set Topology.
2 Conformality.
3 Linear Transformations.
4 Elementary Conformal Mappings.
Chapter 4: Complex Integration:
1 Fundamental Theorems.
2 Cauchy’s Theorem for a Rectangle.
3 Local Properties of Analytical Functions.
4 The General Form of Cauchy’s Theorem.
5 The Calculus of Residues.
6 Harmonic Functions.
Chapter 5: Series and Product Developments:
1 Power Series Expansions.
2 Partial Fractions and Factorization.
3 Entire Functions.
4 The Riemann Zeta Function.
5 Normal Families.
Chapter 6: Conformal Mapping, Dirichlet’s Problem:
1 The Riemann Mapping Theorem.
2 Conformal Mapping of Polygons.
3 A Closer Look at Harmonic Functions.
4 The Dirichlet Problem.
5 Canonical Mappings of Multiply Connected Regions.
Chapter 7: Elliptic Functions:
1 Simply Periodic Functions.
2 Doubly Periodic Functions.
3 The Weierstrass Theory.
103
HIGHER MATHEMATICS
Topology
Chapter 8: Global Analytic Functions:
1 Analytic Continuation.
2 Algebraic Functions.
3 Picard’s Theorem.
4 Linear Differential Equations.
Index
TOPOLOGY
Schaum’s Outline of Complex
Variables
By Murray R Spiegel, formerly of Rensselaer Polytechnic Institute
1968 / 320 pages
ISBN-13: 978-0-07-060230-4 / MHID: 0-07-060230-1
ISBN-13: 978-0-07-099010-4 / MHID: 0-07-099010-7
[IE, SI Metric] (Out of Print)
Contents
Complex Numbers.
Functions.
Limits and Continuity.
Complex Differentiation and the Cauchy Riemann Equations.
Complex Integration and Cauchy’s Theorem.
Cauchy’s Integral Formulas and Related Theorems.
Infinite Series.
Taylor’s and Laurent Series.
The Residue Theorem: Evaluation of Integrals and Series.
Conformal Mappings.
Physical Applications of Conformal Mapping.
Special Topics.
By Sheldon W Davis, Miami University—Oxford
2005 / 448 page
ISBN-13: 978-0-07-291006-3 / MHID: 0-07-291006-2
ISBN-13: 978-0-07-124339-1 / MHID: 0-07-124339-9 [IE]
A volume in the Walter Rudin Student Series.
Contents
1 Sets, Functions, Notation:
Cantor-Bernstein Theorem.
Countable Set.
2 Metric Spaces:
Topology Generated by a Metric.
Complete Metric Space.
Cantor Intersection Theorem.
Baire Category Theorem.
3 Continuity:
Banach Fixed Point Theorem.
4 Topological Spaces:
Subspace Topology.
Continuous Function.
Base.
Sorgenfrey Line.
Lindel? Theorem.
5 Basic Constructions:
Products.
Product Topology.
6 Separation Axioms: Hausdorff.
Regular Normal.
Urysohn’s Lemma.
Tietze Extension Theorem.
7 Compactness:
Heine-Borel Theorem.
Tychonoff Theorem.
Lebesgue Number.
8 Local Compactness:
One-Point Compactification.
9 Connectivity:
Intermediate Value Theorem.
Connected Subspaces.
Products of Connected Spaces.
Components.
10 Other Types of Connectivity:
Pathwise Connected.
Locally Pathwise Connected.
Locally Connected.
11 Continua:
Irreducible: Cut Point.
Moore’s Characterization of [0, 1].
12 Homotopy:
Contractible Space.
Fundamental Group.
104
HIGHER MATHEMATICS
Schaum’s Outline of General
Topology
Entering and Plotting a Graph Defined Parametrically
Entering and Graphing a Polar Graph
5. Calculus
Numerical Derivative
Numerical Integral
Turning Points
Drawing Tangent Lines
6. Matrices
The Matrix Menu
Operations on Matrices
7. Complex Numbers
Selecting the Display Format/Rectangular Complex Mode
Polar Complex Mode
Entering expressions involving Complex Numbers
Finding the Argument and Modulus
8. Vectors
Performing Vector Operations
Finding the Magnitude of a Vector
Finding the Scalar Product
Finding the Vector Product
9. Sequences and Series
Sequences on the Home Screen
Defining Sequences Using the Editor
1986 / 256 pages
ISBN-13: 978-0-07-037988-6 / MHID: 0-07-037988-2
Contents
Sets and Relations.
Functions.
Cardinality, Order.
Topology of the Line and Plane.
Topological Spaces.
Definitions.
Bases and Subbases.
Continuity and Topological Equivalence.
Metric and Normed Spaces.
Countability.
Separation Axioms.
Compactness.
Product Spaces.
Connectedness.
Complete Metric Spaces.
Function Spaces.
Appendix.
Properties of the Real Numbers.
GREAT JOBS FOR MATH MAJORS
Second Edition
Mathematical References
By Stephen Lambert and Ruth DeCotis
ISBN-13: 978-0-07-144859-8 / MHID: 0-07-144859-4
GETTING STARTED WITH THE T1-84 PLUS
GRAPHING CALCULATOR
Answers the question “What can I do with a major in math?” It isn’t
always obvious what a math major can offer to the workplace. But
it provides you with valuable skills and training that can be applied
to a wide range of careers. Great Jobs for Math Majors helps you
explore these possibilities.
By Wee Leng Ng
2006 (October 2005) / 84 pages
ISBN-13: 978-0-07-125247-8 / MHID: 0-07-125247-9
An Asian Publication
With the recent introduction of the TI-84 Plus graphing calculator into
the A-level Mathematics curriculum, students can now reduce the time
spent on tedious computations. Getting Started with the TI-84 Plus
Graphing Calculator is an invaluable guide to the basic skills required
to utilize the graphing calculator, and to help students get the most out
of their new tool. Filled with comprehensive key press instructions,
screen-shots and useful tips at almost every step, students as well as
teachers are bound to find this example-based book a rich reference
source and a handy companion to their TI-84 Plus.
MATH PROOFS DEMYSTIFIED
By Stan Gibilisco
2005 / 290 pages / Softcover
ISBN-13: 978-0-07-144576-4 / MHID: 0-07-144576-5
Contents
How to use this book
1. Basic Calculations
The Keys of the TI84+
Entering and Editing Mathematical Expressions
Accessing Menus
Basic Numeric Calculations
2. Basic Features of Function Graphing
Entering and Graphing Functions
Changing the Viewing Window
3. The Equation Solver
Solving Equations Without Parameters
Solving Equations With Parameters
4. Advanced Graphing Features
Defining Functions in Terms of Other Functions
Entering and Graphing a Function with Parameters
Graphing a Family of Functions
Restricting the Domain of a Function
Shading Above/Below a Function
Contents
Part One: The Rules of Reason.
Chapter 1: The Basics of Propositional Logic.
Chapter 2: How Sentences are Put Together.
Chapter 3: Formalities and Techniques.
Chapter 4: Vagaries of Logic.
Test: Part One.
Part Two: Proofs in Action.
Chapter 5: Some Theoretical Geometry.
Chapter 6: Sets and Numbers.
Chapter 7: A Few Historic Tidbits.
Test: Part Two.
Final Exam.
Answers to Quiz, Test and Exam Questions.
Suggested Additional References.
Index
105
HIGHER MATHEMATICS
Schaum’s Easy OutlineS:
Mathematical Handbook of
Formulas and Tables
PRE-CALCULUS DEMYSTIFIED
ISBN-13: 978-0-07-143927-5 / MHID: 0-07-143927-7
By Murray R Spiegel, Rensselaer Polytechnic Institute, and John Liu,
Temple University
2001 / 144 pages
ISBN-13: 978-0-07-136974-9 / MHID: 0-07-136974-0
Contents
Preface
Chapter 1: The Slope and Equation of a Line
Chapter 2: Introduction to Functions
Chapter 3: Functions and Their Graphs
Chapter 4: Combinations of Functions and Inverse Functions
Chapter 5: Translations and Special Functions
Chapter 6: Quadratic Functions
Chapter 7: Polynomial Functions
Chapter 8: Rational Functions
Chapter 9: Exponents and Logarithms
Chapter 11: Matrices
Chapter 12: Conic Sections
Chapter 13: Trigonometry
Chapter 14: Sequences and Series Appendix. Final Exam
CONTENTS
Part 1: Formulas.
Section 1: Elementary Constants, Products, Formulas.
Section 2: Geometry.
Section 3: Elementary Transcendental Functions.
Section 4: Calculus.
Section 5: Differential Equations.
Section 6: Series.
Section 7: Vector Analysis.
Part 2: Tables.
Section 8: Factorial n.
Section 9: Conversion of Radians to Degrees, Minutes, and
Seconds.
Section 10: Conversion of Degrees, Minutes, and Seconds to
Radians.
Section 11: Sin x.
Section 12: Cos x.
Section 13: Tan x.
Section 14: Natural or Naperian Logarithms log x or In x.
Section 15: Exponential Functions e.
DIFFERENTIAL EQUATIONS DEMYSTIFIED
By Steven G Krantz, Washington University-St Louis
ISBN-13: 978-0-07-144025-7 / MHID: 0-07-144025-9
Contents
Preface.
Chapter 1: What Is a Differential Equation?
Chapter 2: Second-Order Equations
Chapter 3: Power Series Solutions and Special Functions
Chapter 4: Fourier Series: Basic Concepts
Chapter 5: Partial Differential Equations and Boundary Value
Problems
Chapter 6: Laplace Transforms
Chapter 7: Numerical Methods
Chapter 8: Systems of First-Order Equations. Final Exam. Solutions
to Exercises. Bibliography Index.
Schaum’s Outline of Mathematical
Handbook of Formulas and Tables
Second Edition
By Murray R Spiegel, Rensselaer Polytechnic Institute, and John Liu,
Temple University
1999 / 278 pages
ISBN-13: 978-0-07-038203-9 / MHID: 0-07-038203-4
ISBN-13: 978-0-07-116765-9 / MHID: 0-07-116765-X [IE]
Contents
mCgRAW-HILL DICTIONARY of
Mathematics
Second Edition
By McGraw-Hill
2003 / 336 pages
ISBN-13: 978-0-07-141049-6 / MHID: 0-07-141049-X
Derived from the content of the respected McGraw-Hill Dictionary
of Scientific and Technical Terms Sixth Edition, each title provides
thousands of definitions of words and phrases encountered in a
specific discipline. All include:
Section I: Elementary Constants, Products, Formulas.
Section II: Geometry. Geometric Formulas.
Section III: Elementary Transcendental Functions.
Section IV: Calculus. Derivatives.
Section V: Differential Equations and Vector Analysis.
Section VI: Series.
Section VII: Special Functions and Polynomials.
Section VIII: Laplace and Fourier Transforms.
Section IX: Elliptic and Miscellaneous Special Functions.
Section X: Inequalities and Infinite Products.
Section XI: Probability and Statistics.
Section XII: Numerical Methods.
Pronunciation guide for every term
Acronyms, cross-references, and abbreviations
Append-ices with conversion tables; listings of scientific,
technical, and mathematical notation; tables of relevant data; and more
A convenient, quick-find format
106
107
STATISTICS AND
PROBABILITY
Advanced Statistics...........................................................................................125
Applied Statistics – Engineering........................................................................117
Applied Statistics – Eduction, Psychology And Soical Science.........................116
Applied Statistics – Science, Health And Biostatistics.......................................115
Business Statistics............................................................................................119
Statistics And Probability (Calculus)..................................................................114
Statistics And Probability (Non-Calculus)..........................................................109
NEW TITLES
Statistics and Probability
2009
Author
ISBN-13
MHID
Complete Business Statistics With Student CD, 7e
Aczel
9780077239695
0077239695
119
Business Statistics In Practice, 5e
Bowerman
9780073373591
0073373591
119
Bluman
9780073534961
007353496X
109
Essentials Of Business Statistics With Student CD, 2e
Bowerman
9780073319889
0073319880
119
Basic Statistics For Business And Economics With Lind
9780077230968
0077230965
120
Lind
9780073030265
0073030260
120
Statistical Techniques In Business And Economics, 3e
Lind
9780073272962
0073272965
120
Statistics For Engineers And Scientists, 2e
Navidi
9780073309491
0073309494
117
Page
2008
Student CD, 6e
Basic Statistics Using Excel To Accompany Statistical
Techniques In Business And Economics, 13e
108
STATISTICS AND PROBABILITY
Statistics And Probability
(Non-calculus)
New
ELEMENTARY STATISTICS:
A BRIEF VERSION
Fourth Edition
By Allan G Bluman, Community College of
Allegheny County-South
ISBN-13: 978-0-07-353496-1 / MHID: 0-07-353496-X
ISBN-13: 978-0-07-331267-1 / MHID: 0-07-331265-7
(with Math Zone)
ISBN-13: 978-0-07-334714-1 / MHID: 0-07-334714-0
(with Data Disk)
ISBN-13: 978-0-07-128610-7 / MHID: 0-07-128610-1
[IE with formula card and MathZone]
Browse http://www.mhhe.com/bluman
Elementary Statistics: A Brief Version, 4th Edition is a shorter version
of Allan Bluman’s popular text Elementary Statistics: A Step by
Step Approach, 6th edition. This softcover edition includes all the
features of the longer book, but is designed for a course in which
the time available limits the number of topics covered. The book is
written for general beginning statistics courses with a basic algebra
prerequisite. The book use a non-theoretical approach, explaining
concepts intuitively and teaching problem solving through worked
examples step-by-step.
New to this edition
Applying the Concepts--This new feature has been added to each
section and gives students an opportunity to think about the concepts
and apply them to hypothetical examples and scenarios similar to
those found in newspapers, magazines, and news programs.
More Examples and Exercises!--Over 200 new exercises
have been added, most using real data, and many questions now
incorporate thought-provoking questions requiring students to
interpret their results.
Fresh New Look--The text layout and color palette have been
redesigned to help increase the readability and ease of use by
students and instructors.
The text has been updated throughout with current data and
statistics including new Unusual Stats and Interesting Facts; new
Speaking of Statistics; new Critical Thinking Challenges; new
Statistics Today openers; new worked examples; new Data Analysis
Exercises; and new Data Sets.
Contents
Preface
1: The Nature of Probability and Statistics
1.1 Introduction
1.2 Descriptive and Inferential Statistics
1.3 Variables and Types of Data
1.4 Data Collection and Sampling Techniques
1.5 Observational and Experimental Studies
1.6 Uses and Misuses of Statistics
1.7 Computers and Calculators
1.8 Summary
2: Frequency Distributions and Graphs
2.1 Introduction
2.2 Organizing Data
2.3 Histograms, Frequency Polygons, and Ogives
2.4 Other Types of Graphs
2.5 Paired Data and Scatter Plots Ana
2.6 Summary
3: Data Description
3.1 Introduction
3.2 Measures of Central Tendency
3.3 Measures of Variation
3.4 Measures of Position
3.5 Exploratory Data Analysis
3.6 Summary
4: Probability and Counting Rules
4.1 Introduction
4.2 Sample Spaces and Probability
4.3 The Addition Rules for Probability
4.4 The Multiplication Rules and Conditional Probability
4.5 Counting Rules
4.6 Probability and Counting Rules
4.7 Summary
5: Discrete Probability Distributions
5.1 Introduction
5.2 Probability Distributions
5.3 Mean, Variance, Standard Deviation, and Expectation
5.4 The Binomial Distribution
5.5 Summary
6: The Normal Distribution
6.1 Introduction
6.2 Properties of the Normal Distribution
6.3 The Standard Normal Distribution
6.4 Applications of the Normal Distribution
6.5 The Central Limit Theorem
6.6 The Normal Approximation to the Binomial Distribution
6.7 Summary
7: Confidence Intervals and Sample Size
7.1 Introduction
7.2 Confidence Intervals for the Mean (Sigma Known or n > 30) and
Sample Size
7.3 Confidence Intervals for the Mean (Sigma Unknown and n < 30)
7.4 Confidence Intervals and Sample Size for Proportions
7.5 Confidence Intervals for Variances and Standard Deviations
7.6 Summary
8: Hypothesis Testing
8.1 Introduction
8.2 Steps in Hypothesis Testing – Traditional Method
8.3 z Test for a Mean
8.4 t Test for a Mean
8.5 z Test for a Proportion
8.6 Chi-Square Test for a Variance or Standard Deviation
8.7 Additional Topics Regarding Hypothesis Testing
8.8 Summary
9: Testing the Difference Between Two Means, Two Variances,
and Two Proportions
9.1 Introduction
9.2 Testing the Difference Between Two Means: Large Samples
9.3 Testing the Difference Between Two Variances
9.4 Testing the Difference Between Two Means: Small Independent
Samples
9.5 Testing the Difference Between Two Means: Small Dependent
Samples
9.6 Testing the Difference Between Two Proportions
9.7 Summary
10: Correlation and Regression
10.1 Introduction
10.2 Correlation
10.3 Regression
109
10.4 Coefficient of Determination and Standard Error of the Estimate
10.5 Summary
11: Chi-Square and Analysis of Variance (ANOVA)
11.1 Introduction
11.2 Test for Goodness of Fit
11.3 Tests Using Contingency Tables
11.4 Analysis of Variance (ANOVA)
11.5 Summary
Appendix B-1: Writing the Research Report
Appendix B-2: Alternate Approach to the Standard Normal
Distribution
Appendix C: Tables
Appendix D: Data Bank
Appendix E: Glossary
Appendix F: Bibliography
Appendix G: Photo Credits
Appendix H: Selected Answers
ELEMENTARY STATISTICS: A Step by
Step Approach
Sixth Edition
By Allan G. Bluman, Community College Of Allegheny County-South
ISBN-13: 978-0-07-330543-1 / MHID: 0-07-330543-X
ISBN-13: 978-0-07-325163-9 / MHID: 0-07-325163-1
(with MathZone)
ISBN-13: 978-0-07-110838-6 / MHID: 0-07-110838-6
[IE with MathZone]
ISBN-13: 978-0-07-126703-8 / MHID: 0-07-126703-4
Browse http://www.mhhe.com/bluman
ELEMENTARY STATISTICS: A STEP BY STEP APPROACH is for
general beginning statistics courses with a basic algebra prerequisite.
The book is non-theoretical, explaining concepts intuitively and
teaching problem solving through worked examples and step-bystep instructions. This edition places more emphasis on conceptual
understanding and understanding results. This edition also features
increased emphasis on Excel, MINITAB, and the TI-83 Plus and TI
84-Plus graphing calculators, computing technologies commonly
used in such courses.
Contents
1 The Nature of Probability and Statistics
1-1 Introduction
1-2 Descriptive and Inferential Statistics
1-3 Variables and Types of Data
1-4 Data Collection and Sampling Techniques
1-5 Observational and Experimental Studies
1-6 Uses and Misuses of Statistics
1-7 Computers and Calculators
1-8 Summary
2 Frequency Distributions and Graphs
2-1 Introduction
2-2 Organizing Data
2-3 Histograms, Frequency Polygons, and Ogives
2-4 Other Types of Graphs
2-5 Summary
3 Data Description
3-1 Introduction
3-2 Measures of Central Tendency
3-3 Measures of Variation
3-4 Measures of Position
3-5 Exploratory Data Analysis
3-6 Summary
4 Probability and Counting Rules
4-1 Introduction
4-3 The Addition Rules for Probability
4-4 The Multiplication Rules and Conditional Probability
4-5 Counting Rules
4-6 Probability and Counting Rules
4-7 Summary
5 Discrete Probability Distributions
5-1 Introduction
5-2 Probability Distributions
5-3 Mean, Variance, Standarddeviation, and Expectation
5-4 The Binomial Distribution
5-5 Other Types of Distributions (Optional)
5-6 Summary
6 The Normal Distribution
6-1 Introduction
6-2 Properties of the Normal Distribution
6-3 The Standard Normal Distribution
6-4 Applications of the Normal Distribution
6-5 The Central Limit Theorem
6-6 The Normal Approximation to the Binomial Distribution
6-7 Summary
7 Confidence Intervals and Sample Size
7-1 Introduction
7-2 Confidence Intervals for the Mean (s Known or n©30)
7-3 Confidence Intervals for the Mean (s Unknown or n<30)
7-4 Confidence Intervals and Sample Size for Proportions
7-5 Confidence Intervals for Variances and Standard Deviations
7-6 Summary
8 Hypothesis Testing
8-1 Introduction
8-2 Steps in Hypothesis Testing–Traditional Method
8-3 z Test for a Mean
8-4 t Test for a Mean
8-5 z Test for a Proportion
8-6 Chi Square test for a Variance or Standard Deviation
8-7 Additional Topics Regarding Hypothesis Testing
8-8 Summary
9 Testing the Difference Between Two Means, Two Variances,
and Two Proportions
9-1 Introduction
9-2 Testing the Difference Between Two Means: Large Samples
9-3 Testing the Difference Between Two Variances
9-4 Testing the Difference Between Two Means: Small Independent
Samples
9-5 Testing the Difference Between Two Means: Small Dependent
Samples
9-6 Testing the Difference Between Proportions
9-7 Summary
10 Correlation and Regression
10-1 Introduction
10-2 Scatter Plots
10-3 Correlation
10-4 Regression
10-5 Coefficient of Determination and Standard Error of the
Estimate
10-6 Multiple Regression (Optional)
10-7 Summary
11 Other Chi-Square Tests.
11-1 Introduction
11-2 Test for Goodness of Fit
11-3 Tests Using Contingency Tables
11-4 Summary
12 Analysis of Variance
12-1 Introduction
12-2 One-Way Analysis of Variance
12-3 The Scheffé Test and the Tukey Test
110
READY, SET, GO! A STUDENT GUIDE TO
SPSS ® 13.0 AND 14.0 FOR WINDOWS
Second Edition
By Thomas Pavkov and Kent Price of Purdue University-Calumet-Hammond
2007 (February 2006) / 96 pages
ISBN-13: 978-0-07-312665-4 / MHID: 0-07-312665-9
ISBN-13: 978-0-07-125297-3 / MHID: 0-07-125297-5 [IE]
9 Describing the Linear Relationship Between Two Variables
Assignment
10 Assessing the Association Between Two Categorical Variables
Appendix Entering Data Using Programs Other Than SPSS
RESEARCH PROJECTS IN STATISTICS
By Joseph Kincaid, Blue Cross and Blue Shield of Kansas City
ISBN-13: 978-0-07-294681-9 / MHID: 0-07-294681-4
http://www.mhhe.com/kincaid
Contents
Overview: Motivation for the project.
Schedule for the project.
Group Communication: Purpose of the communication plan.
Contents of the communication plan.
Project Ideas: Purpose of the list of ideas.
Generating research questions.
Requirements for the research project.
Example of a list of ideas.
The Research Proposal: Purpose of the research proposal.
Contents of the research proposal.
Examples of research proposals.
Data Collection: Purpose of the data collection stage.
Characteristics of good data: Integrity.
Characteristics of good data: Accuracy.
Collecting the data.
That data collection report.
Examples of data collection.
Data Analysis: Purpose of the data analysis.
Types of data analysis.
Preparing the data for analysis.
Examples of data analysis.
Presenting the Results: The overall presentation.
The oral presentation.
The written report.
Examples of written reports.
Comments on Student Examples: Comments on the list of ideas.
Comments on the research proposals.
Comments on the data collection.
Comments on the written reports
This guide features concise instructions for accessing and using
SPSS for Windows. Ready, Set, Go! is more than a reference book
for versions 13.0 and 14.0; through ten guided assignments, students
learn about statistical analysis of data while also learning the steps in
the research process. The students are guided through assignments
such as using frequency distributions, performing the t test, using the
one-way ANOVA procedure, computing a correlation, and computing
chi-square function.
12-4 Two-Way Analysis of Variance
12-5 Summary
13 Nonparametric Statistics
13-1 Introduction
13-2 Advantages and Disadvantages of Nonparametric Methods
13-3 The Sign Test
13-4 The Wilcoxon Rank Sum Test
13-5 The Wilcoxon Signed-Rank Test
13-6 The Kruskal-Wallis Test
13-7 The Spearman Rank Correlation Coefficient and the Runs
Test
13-8 Summary
14 Sampling and Simulation
14-1 Introduction
14-2 Common Sampling Techniques
14-3 Surveys and Questionnaire Design
14-4 Simulation Techniques
14-5 The Monte Carlo Method
14-6 Summary
Appendix B-1: Writing the Research Report.
Appendix B-2: Bayes’s Theorem.
Appendix B-3: Alternate Method for the Standard Normal
Distribution.
Appendix C: Tables.
Appendix D: Data Bank.
Appendix E: Glossary.
Appendix F: Bibliography.
Appendix G: Photo Credits.
Appendix H: Selected Answers
Contents
Preface / Assignment
1 Learning the Basics of SPSS Assignment
2 Looking at Frequency Distributions and Descriptive Statistics
Assignment
3 Presenting Data in Graphic Form Assignment
4 Testing Research Hypotheses for Two Independent Samples
Assignment
5 Testing Research Hypotheses About Two Related Sampled
Assignment
6 Comparing Independent Samples with One-Way ANOVA
Assignment
7 Comparing Related Samples with One-Way ANOVA Assignment
8 Measuring the Simple Relationship Between Two Variables
Assignment
111
[email protected]
LECTURES IN ELEMENTARY PROBABILITY
THEORY AND STOCHASTIC PROCESSES
Statistics: A First Course
Sixth Edition
By Jean-Claude Falmagne
2003 / 288 pages
ISBN-13: 978-0-07-244890-0 / MHID: 0-07-244890-3
ISBN-13: 978-0-07-122975-3 / MHID: 0-07-122975-2 [IE]
By Donald H. Sanders, Education Consultant and Robert Smidt,
California Polytechnic State University - San Luis Obispo
2000 / 736 pages
ISBN-13: 978-0-07-233217-9 / MHID: 0-07-233217-4
(with CD-ROM)
ISBN-13: 978-0-07-116984-4 / MHID: 0-07-116984-9
[IE with CD-ROM]
Contents
1 Preliminaries.
2 Sample Space and Events.
3 Probability and Area.
4 Probability Measures.
5 Basic Rules of Probability Calculus.
6 Sampling.
7 Counting Subsets.
8 Discrete Distributions.
9 Conditional Probabilities.
10 Independence and Bayes Theorem.
11 The Principle of Maximum Likelihood.
12 Random Variables.
13 Distribution Functions.
14 Continuous Random Variables.
15 Expectation and Moments.
16 Covariance and Correlation.
17 The Law of Large Numbers.
18 Moment Generating Functions.
19 Multivariate Distributions.
20 Bivariate Normal Distributions.
21 Finite Markov Chains, Basic Concepts.
22 Homogeneous Markov Chains.
23 Random Walks.
24 Poisson Processes.
Solutions and Hints for Selected Problems.
Glossary of Symbols.
Index. Bibliography
Contents
Let’s Get Started.
Looking Ahead.Looking Back
Review Exercises
Topics For Review And Discussion
Projects
Issues To Consider
Computer Exercises.
Descriptive Statistics.
Probability Concepts.
Probability Distributions.
Sampling Concepts.
Estimating Parameters.
Testing Hypotheses: One Sample Procedures.
Inference: Two-Sample Procedures.
Analysis of Variance.
Chi-Square Tests: Goodness-of-Fit and Contingency Table
Methods.
Linear Regression and Correlation.
Nonparametric Statistical Methods.
Appendices.
Selected Values of the Binomial Probability Distribution.
Areas under the Standard Normal Probability Distribution.
A Brief Table of Random Numbers.
Areas for t Distributions.
F Distribution Tables.
Chi-Square Distribution.
Critical Values of T for Level of Significance = .05 and Level of
Significance = .01 in the Wilcoxon Signed Rank Test.
Distribution of U in the Mann-Whitney Test.
Critical Values for r in the Runs Test for Randomness.
Selected Values of the Poisson Probability Distribution.
Entering and Editing Data in Minitab.
Answers to Odd-Numbered Exercises.
SCHAUM’S OUTLINE OF STATISTICS
Fourth Edition
By Murray Spiegel (deceased) and Larry J Stephens, University of
Nebraska, Omaha
2008 (November 2007) / 544 pages
ISBN-13: 978-0-07-148584-5 / MHID: 0-07-148584-8
The guides that help students study faster, learn better-and get
top grades.
Updated to match the latest developments in the field of statistics, this
new edition includes dozens of new problems showing output from
EXCEL, SAS, SPSS, STATISTIX, and MINITAB, all of which are in
general use for in college courses on statistics.
112
Schaum’s Outline of Elements of
Statistics II
Inferential Statistics
Schaum’s Outline of Elements of
Statistics I
Differential Statistics and Probability
By Stephen Bernstein and Ruth Bernstein, University of Colorado
2000 / 480 pages
ISBN-13: 978-0-07-134637-5 / MHID: 0-07-134637-6
By Stephen Bernstein and Ruth Bernstein, University of Colorado
1999 / 368 pages
ISBN-13: 978-0-07-005023-5 / MHID: 0-07-005023-6
Contents
Schaum’s Outline of Probability
Second Edition
2000 / 224 pages
ISBN-13: 978-0-07-135203-1 / MHID: 0-07-135203-1
ISBN-13: 978-0-07-118356-7 / MHID: 0-07-118356-6 [IE]
Mathematics Required for Statistics.
Characteristics of the Data.
Populations, Samples, and Statistics.
Descriptive Statistics: Organizing the Data Into Tables.
Descriptive Statistics: Graphing the Data.
Descriptive Statistics: Measures of Central Tendency, Average Value,
and Location.
Descriptive Statistics: Measures of Dispersion.
Probability: The Classical, Relative Frequency, Set Theory, and
Subjective Interpretations.
Probability: Rules for Multiplication and Division, Marginal Probabilities
and Bayes’ Theorem, Tree Diagrams and Counting Rules.
Random Variables, Probability Distributions, Cumulative Distribution
Functions, and Expected Values.
Contents
Set Theory.
Techniques of Counting.
Introduction to Probability.
Conditional Probability and Independence.
Random Variables.
Binomial, Normal and Poisson Distributions.
Markov Chains.
Appendices: Descriptive Statistics.
Schaum’s Outline of Introduction
to Probability and Statistics
By Seymour Lipschutz and Jack Schiller, Temple University
1998 / 384 pages
ISBN-13: 978-0-07-038084-4 / MHID: 0-07-038084-8
Contents
SCHAUM’S EASY OUTLINES: Statistics
By Murray R Spiegel (Deceased) and David P. Lindstrom
2000 / 138 pages
ISBN-13: 978-0-07-116984-6 / MHID: 0-07-052712-1
Contents
Variables and Graphs.
Measures of Central Tendency and Dispersion.
Elementary Probability Theory.
The Binomial, Normal, and Poisson Distributions.
Elementary Sampling Theory.
Statistical Estimation Theory.
Statistical Decision Theory.
Small Sampling Theory.
The Chi-Square Test.
Curve Fitting and the Method of Least Squares.
Correlation Theory.
Multiple and Partial Correlation.
Analysis of Variance.
Nonparametric Tests.
Appendices:
A: Areas Under the Standard Normal Curve.
B: Student’s t Distribution.
C: Chi-Square Distribution.
D: 99th Percentile Values for the F Distribution
Part I: Descriptive Statistics and Probability.
Preliminary: Descriptive Statistics.
Sets and Counting.
Basic Probability.
Conditional Probability and Independence.
Random Variables.
Binomial and Normal Distributions.
Part II: Inferential Statistics.
Sampling Distributions.
Confidence Intervals for A Single Population.
Hypotheses Tests for A Single Population.
Inference for Two Populations.
Chi-Square Tests and Analysis of Variance.
113
Schaum’s Outline of Set Theory and
Related Topics
Second Edition
1998 / 200 pages
ISBN-13: 978-0-07-038159-9 / MHID: 0-07-038159-3
ISBN-13: 978-0-07-116494-8 / MHID: 0-07-116494-4 [IE]
Contents
Sets and Subsets.
Basic Set Operators.
Sets of Numbers.
Functions.
Product Sets and Graphs of Functions.
Relations.
Further Theory of Sets.
Further Theory of Functions, Operations.
Cardinal Numbers.
Partially and Totally Ordered Sets.
Well-Ordered Sets/Ordinal Numbers.
Axiom of Choice.
Paradoxes in Set Theory.
Algebra of Propositions.
Quantifiers.
Boolean Algebra.
Logical Reasoning.
Statistics And Probability
(Calculus)
INTRODUCTION TO PROBABILITY
AND STATISTICS: Principles and
Applications for Engineering and
the Computing Sciences
Fourth Edition
By J Susan Milton, Emeritus, Radford University and Jesse C Arnold,
Virginia Polytechnic Institute
2003 / 816 pages
ISBN-13: 978-0-07-246836-6 / MHID: 0-07-246836-X
ISBN-13: 978-0-07-124248-6 / MHID: 0-07-124248-1
[IE, 2-colour Text]
ISBN-13: 978-0-07-119859-2 / MHID: 0-07-119859-8 [IE]
http://www.mhhe.com/miltonarnold
Contents
1 Introduction to Probability and Counting:
Interpreting Probabilities.
Sample Spaces and Events.
2 Some Probability Laws.
Axioms of Probability.
Conditional Probability.
Independence and the Multiplication Rule.
Bayes’ Theorem.
Random Variables.
Discrete Probablility Densities.
Expectation and Distribution Parameters.
Geometric Distribution and the Moment Generating Function.
Binomial Distribution.
Negative Binomial Distribution.
Hypergeometric Distribution.
Poisson Distribution.
4 Continuous Distributions.
Continuous Densities.
Gamma Distribution.
Normal Distri-bution.
Normal Probability Rule and Chebyshev’s Inequality.
Normal Approximation to the Binomial Distribution.
Weibull Distribution and Reliability.
Transformation of Variables.
Simulating a Continuous Distribution.
5 Joint Distributions.
Joint Densities and Independence.
Expectation and Covariance.
Correlation.
Conditional Densities and Regression.
6 Descriptive Statistics.
Random Sampling.
Picturing the Distribution.
Sample Statistics.
Boxplots.
7 Estimation.
Point Estimation.
The Method of Moments and Maximum Likelihood.
Functions of Random Variables - Distribution of X.
Interval Estimation and the Central Limit Theorem.
8 Inferences on the Mean and Variance of a Distribution.
Interval Estimation of Variability.
Estimating the Mean and the Student-t Distribution.
Hypothesis Testing.
Significance Testing.
Hypothesis and Significance Tests on the Mean.
Hypothesis Tests.
Alternative Nonparametric Methods.
9 Inferences on Proportions.
Estimating Proportions.
Testing Hypothesis on a Proportion.
Comparing Two Proportions: Estimation.
Coparing Two Proportions: Hypothesis Testing.
10 Comparing Two Means and Two Variances.
Point Estimation.
Comparing Variances: The F Distribution.
Comparing Means: Variances Equal (Pooled Test).
Comparing Means: Variances Unequal.
Compairing Means: Paried Data.
A Note on Technology.
11 Sample Linear Regression and Correlation.
Model and Parameter Estimation.
Properties of Least-Squares Estimators.
Confidence Interval Estimation and Hypothesis Testing.
Repeated Measurements and Lack of Fit.
Residual Analysis.
Correlation.
12 Multiple Linear Regression Models.
Least-Squares Procedures for Model Fitting.
A Matrix Approach to Least Squares.
Properties of the Least-Squares Estimators.
Interval Estimation.
Testing Hypotheses about Model Parameters.
Use of Indicator or “Dummy” Variables.
114
Criteria for Variable Selection.
Model Transformation and Concluding Remarks.
13 Analysis of Variance.
One-Way Classification Fixed-Effects Model.
Comparing Variances.
Pairwise Comparison.
Testing Contrasts.
Randomized Complete Block Design.
Latin Squares.
Random-Effects Models.
Design Models in Matrix Form.
14 Factorial Experiments.
Two-Factor Analysis of Variance.
Extension to Three Factors.
Random and Mixed Model Factorial Experiments.
2^k Factorial Experiments.
2^k Factorial Experiments in an Incomplete Block Design.
Fractional Factorial Experiments.
15 Categorical Data.
Multinomial Distribution.
Chi-Squared Goodness of Fit Tests.
Testing for Independence.
Comparing Proportions.
16 Statistical Quality Control.
Properties of Control Charts.
Shewart Control Charts for Measurements.
Shewart Control Charts for Attributes.
Tolerance Limits.
Acceptance Sampling.
Two-Stage Acceptance Sampling.
Extensions in Quality Control.
Appendix A Statistical Tables.
Appendix B Answers to Selected Problems.
Appendix C Selected Derivations
SCHAUM’S OUTLINE OF PROBABILITY AND
STATISTICS
Third Edition
By John J Schiller, R Alu Srinivasan, Temple University
2009 (July 2008) / 399 pages
ISBN-13: 978-0-07-154425-2 / MHID: 0-07-154425-9
A classic Schaum’s bestseller, thoroughly updated to match the latest
course scope and sequence. The ideal review for the hundreds of
thousands of college and high school students who enroll in probability
and statistics courses.
CONTENTS
Part I: Probability
1. Basic Probability
2. Random Variables and Probability Distributions
3. Mathematical Expectation
4. Special Probability Distributions
Part II: Statistics
5. Sampling Theory
6. Estimation Theory
7. Tests of Hypotheses and Significance
8. Curve Fitting, Regression, and Correlation
9. Analysis of Variance
10. Nonparametric Tests
Applied Statistics –
Science, Health And
Biostatistics
Introduction to the Theory of
Statistics
Third Edition
By Alexander M. Mood, University of California, Irvine Franklin A.
Graybill, Duane C. Boes, both of Colorado State University
1974 / 480 pages
ISBN-13: 978-0-07-042864-5 / MHID: 0-07-042864-6
(Out-of-Print)
ISBN-13: 978-0-07-085465-9 / MHID: 0-07-085465-3 [IE]
INTRODUCTION TO BIOSTATISTICS
By Thomas Glover, Hobart & Wm Smith College and Kevin Mitchell,
Hobart & Wm Smith College
2002 / 432 pages
ISBN-13: 978-0-07-241841-5 / MHID: 0-07-241841-9
(Out of Print)
ISBN-13: 978-0-07-123743-7 / MHID: 0-07-123743-7 [IE]
http://www.mhhe.com/biosci/pae/zoology/glover/index.mhtml
Contents
1 Introduction to Data Analysis.
2 Introduction to Probability.
3 Probability Distributions.
4 Sampling Distributions.
5 Introduction to Hypothesis Testing.
6 One-Sample Tests of Hypothesis.
7 Tests of Hypothesis Involving Two Samples.
8 k-Sample Tests of Hypothesis: The Analysis of Variance.
9 Two-Factor Analysis.
10 Linear Regression and Correlation.
11 Goodness of Fit Tests for Categorical Data.
Appendixes: A Proofs of Selected Results.
B Answers to Even-Numbered Problems.
C Tables of Distributions and Critical Values
115
Eduction, Psychology and
Soical Science
STATISTICS FOR THE UTTERLY CONFUSED
Second Edition
By Lloyd R. Jaisingh
ISBN-13: 978-0-07-146193-1 / MHID: 0-07-146193-0
When it comes to understanding statistics, even good students can be
confused. Perfect for students in any introductory non-calculus-based
statistics course, and equally useful to professionals working in the
world, Statistics for the Utterly Confused is your ticket to success.
Statistical concepts are explained step-by-step and applied to such
diverse fields as business, economics, finance, and more. The
message of Statistics for the Utterly Confused is simple: you don’t
have to be confused anymore. Updated and expanded to give you the
latest changes in the field, this up-to-the-minute edition includes many
new examples of Excel output, the most widely used of all statistics
programs; a new chapter on Analysis of Variance (ANOVA); and 200
additions to the 700 self-testing questions and answers. The expert
author’s Web site also gives you tons of fresh examples, practice
problems, and strategies--so you can go from utterly confused to
totally prepared in no time!
Inside, you’ll discover how to:
Grasp the meaning of everyday statistical concepts
Find out what’s probable and what isn’t
Read, understand, and solve statistics problems
Improve your scores on exams
Use your skills in any field
SPSS SURVIVAL MANUAL
Third Edition
By Julie Pallant, University of Melbourn
2007 (August 2007) / 352 pages
ISBN-13: 978-0-335-22366-4 / MHID: 0-335-22366-4
Open University Press Titles
In this fully revised edition of her bestselling text, Julie Pallant guides
you through the entire research process, helping you choose the
right data analysis technique for your project. From the formulation
of research questions, to the design of the study and analysis of
data, to reporting the results, Julie discusses basic and advanced
statistical techniques. She outlines each technique clearly, with
step-by-step procedures for performing the analysis, a detailed guide
to interpreting SPSS output and an example of how to present the
results in a report. For both beginners and experienced SPSS users
in psychology, sociology, health sciences, medicine, education,
business and related disciplines, the SPSS Survival Manual is an
essential guide. Illustrated with screen grabs, examples of output and
tips, it is supported by a website with sample data and guidelines on
report writing. In this third edition all chapters have been updated to
accommodate changes to SPSS procedures, screens and output in
version 15. A new flowchart is included for SPSS procedures, and
factor analysis procedures have been streamlined. It also includes
more examples and material on syntax. Additional data files are
available on the books’s supporting website.
Contents
[email protected]
Preface
Data files and website
Introduction & overview
Part One: Getting Started
Designing a study
Preparing a codebook
Getting to know SPSS
Part Two: Preparing The Data File
Creating a data file and entering data
Screening and cleaning the data
Part Three: Preliminary Analyses
Descriptive statistics
Using graphs to describe and explore the data
Manipulating the data
Checking the reliability of a scale
Choosing the right statistic
Part Four: Statistical Techniques To Explore Relationships
Among Variables
Correlation
Partial correlation
Multiple regression
Logistic regression
Factor analysis
Part Five: Statistical Techniques To Compare Groups
Non-parametric statistics
T-tests
One-way analysis of variance
Two-way between-groups ANOVA
Mixed between-within subjects analysis of variance
Multivariate analysis of variance
Analysis of covariance
Appendix: Details of data files
Recommended reading
References
Index
116
Engineering
Over 180 new homework problems have been added
throughout.
Contents
1 Sampling and Descriptive Statistics
2 Probability
3 Propagation of Error
4 Commonly Used Distributions
5 Confidence Intervals
6 Hypothesis Testing
7 Correlation and Simple Linear Regression
8 Multiple Regression
9 Factorial Experiments
10 Statistical Quality Control
A Tables
B Partial Derivatives
C Suggestions for Further Reading Answers to Selected Exercises
Index
New
STATISTICS FOR
ENGINEERS AND
SCIENTISTS
Second Edition
By William Navidi, Colorado School of Mines
2008 (Janurary 2007) / 675 pages
ISBN-13: 978-0-07-330949-1 / MHID: 0-07-330949-4
ISBN-13: 978-0-07-110022-3 / MHID: 0-07-110222-1 [IE]
Browse http://www.mhhe.com/navidi2
The second edition of this book is intended to extend the strengths
of the first. Some of the changes are:
More than 200 new exercises have been added.
A new section on point estimation has been added to Chapter 4.
The material on histograms in Chapter 1 has been completely
revised.
Chapter 2 now contains a discussion of Chebyshev’s
inequality.
Chapter 4 now contains a discussion of the uniform
distribution.
The section on the normal distribution contains a discussion on
linear functions of normal random variables.
Chapter 7 contains additional material on the correlation
coefficient.
Chapter 10 contains a discussion of the relationship between
control charts and hypothesis tests.
The exposition has been improved in a number of places.
Also new for this edition is the ARIS online course management
system. ARIS provides automatic grading of student assignments
and keeps a record of students’ grades. In addition, ARIS contains
problems for student practice, along with Java applets that allow
students to interactively explore ideas in the text. Customizable
PowerPoint lecture notes for each chapter are available as well, along
with suggested syllabi, and other features. More information can be
found at aris.mhhe.com. About the Author William Navidi is Professor
of Mathematical and Computer Sciences at the Colorado School of
Mines. He received the B.A. degree in mathematics from New College,
the M.A. in mathematics from Michigan State University, and the Ph.D.
in statistics from the University of California at Berkeley. Professor
Navidi has authored more than 50 research papers both in statistical
theory and in a wide variety of applications includingcomputer
networks, epidemiology, molecular biology, chemical engineering,
and geophysics.
New to this edition
McGraw-Hill’s ARIS online Homework Manager has been added
to this edition and features algorithmic problems and gradebook
capability. Instructors will have access to data sets, solutions, lecture
powerpoints, and images from the text.
INTRODUCTION TO PROBABILITY AND
STATISTICS
Principles and Applications for Engineering
and the Computing Sciences, Fourth Edition
By J Susan Milton, Emeritus, Radford University and Jesse C Arnold,
Virginia Polytechnic Institute
2003 / 816 pages
ISBN-13: 978-0-07-246836-6 / MHID: 0-07-246836-X
ISBN-13: 978-0-07-124248-6 / MHID: 0-07-124248-1
[IE, 2-colour Text]
ISBN-13: 978-0-07-119859-2 / MHID: 0-07-119859-8 [IE]
http://www.mhhe.com/miltonarnold
Contents
1 Introduction to Probability and Counting:
Interpreting Probabilities.
Sample Spaces and Events.
2 Some Probability Laws.
Axioms of Probability.
Conditional Probability.
Independence and the Multiplication Rule.
Bayes’ Theorem.
Random Variables.
Discrete Probablility Densities.
Geometric Distribution and the Moment Generating Function.
Binomial Distribution.
Negative Binomial Distribution.
Hypergeometric Distribution.
4 Continuous Distributions.
Con-tinuous Densities.
Gamma Distribution.
Normal Distri-bution.
Normal Probability Rule and Chebyshev’s Inequality.
Normal Approximation to the Binomial Distribution.
Weibull Distribution and Reliability.
Simulating a Continuous Distribution.
5 Joint Distributions.
Joint Densities and Independence.
117
Expectation and Covariance.
Correlation.
Conditional Densities and Regression.
6 Descriptive Statistics.
Random Sampling.
Picturing the Distribution.
Sample Statistics.
Boxplots.
7 Estimation.
Point Estimation.
The Method of Moments and Maximum Likelihood.
Functions of Random Variables - Distribution of X.
Interval Estimation and the Central Limit Theorem.
8 Inferences on the Mean and Variance of a Distribution.
Interval Estimation of Variability.
Estimating the Mean and the Student-t Distribution.
Hypothesis Testing.
Significance Testing.
Hypothesis and Significance Tests on the Mean.
Hypothesis Tests.
9 Inferences on Proportions.
Estimating Proportions.
Testing Hypothesis on a Proportion.
Comparing Two Proportions: Estimation.
Coparing Two Proportions: Hypothesis Testing.
10 Comparing Two Means and Two Variances.
Point Estimation.
Comparing Variances: The F Distribution.
Comparing Means: Variances Equal (Pooled Test).
Comparing Means: Variances Unequal.
Compairing Means: Paried Data.
A Note on Technology.
11 Sample Linear Regression and Correlation.
Model and Parameter Estimation.
Properties of Least-Squares Estimators.
Confidence Interval Estimation and Hypothesis Testing.
Repeated Measurements and Lack of Fit.
Residual Analysis.
Correlation.
12 Multiple Linear Regression Models.
Least-Squares Procedures for Model Fitting.
A Matrix Approach to Least Squares.
Properties of the Least-Squares Estimators.
Interval Estimation.
Testing Hypotheses about Model Parameters.
Use of Indicator or “Dummy” Variables.
Criteria for Variable Selection.
Model Transformation and Concluding Remarks.
13 Analysis of Variance.
One-Way Classification Fixed-Effects Model.
Comparing Variances.
Pairwise Comparison.
Testing Contrasts.
Randomized Complete Block Design.
Latin Squares.
Random-Effects Models.
Design Models in Matrix Form.
14 Factorial Experiments.
Two-Factor Analysis of Variance.
Extension to Three Factors.
Random and Mixed Model Factorial Experiments.
2^k Factorial Experiments.
2^k Factorial Experiments in an Incomplete Block Design.
Fractional Factorial Experiments.
15 Categorical Data.
Multinomial Distribution.
Chi-Squared Goodness of Fit Tests.
Testing for Independence.
Comparing Proportions.
16 Statistical Quality Control.
Properties of Control Charts.
Shewart Control Charts for Measurements.
Shewart Control Charts for Attributes.
Tolerance Limits.
Acceptance Sampling.
Two-Stage Acceptance Sampling.
Extensions in Quality Control.
Appendix A Statistical Tables.
Appendix B Answers to Selected Problems.
Appendix C Selected Derivations
ENGINEERING STATISTICS DEMYSTIFIED
By Larry J Stephens, University of Nebraska, Omaha
ISBN-13: 978-0-07-146272-3 / MHID: 0-07-146272-4
Clueless? Feel Like a Dummy? Get Demystified!
This versatile reference offers solid coverage of the basics of
traditional engineering statistics and also incorporates examples
from the most popular statistical software programs, making it equally
valuable to professionals.
Contents
Preface
Acknowledgments
Chapter 1: Treatment of Data Using EXCEL, MINITAB, SAS, SPSS,
and STATISTIX
Chapter 2: Probability
Chapter 3: Probability Distributions for Discrete Random Variables
Chapter 4: Probability Densities for Continuous Random Variables
and Introduction to MAPLE
Chapter 5: Sampling Distributions
Chapter 6: Inferences Concerning Means
Chapter 7: Inferences Concerning Variances
Chapter 8: Inferences Concerning Proportions
Final Examinations
Solutions To Chapter Exercises
Bibliography
Index
118
MULTIVARIATE STATISTICAL METHODS IN
QUALITY MANAGEMENT
New
By Kai Yang and Jayant Trewn
2004 / Hardcover / 299 pages
ISBN-13: 978-0-07-143208-5 / MHID: 0-07-143208-6
essentials of business
statistics with student
cd
Second Edition
Contents
Chapter 1: Multivariate Statistical Methods and Quality.
Chapter 2: Graphical Multivariate Data Display and Data
Stratification.
Chapter 3: Introduction to Multivariate Random Variables, Normal
Distribution, and Sampling Properties.
Chapter 4: Multivariate Analysis of Variance.
Chapter 5: Principal Component Analysis and Factor Analysis.
Chapter 6: Discriminant Analysis.
Chapter 7: Cluster Analysis.
Chapter 8: Mahalanobis Distance and Taguchi Method.
Chapter 9: Path Analysis and the Structural Method.
Chapter 10: Multivariate Statistical Process Control.
Appendix: Probability Distribution Tables.
References.
Index
Business Statistics
By Bruce Bowerman and Richard O’Connell
of Miami University University, Oxford and J
Burdeane Orris, Butler University
ISBN-13: 978-0-07-331988-9 / MHID: 0-07-331988-0
ISBN-13: 978-0-07-128605-3 / MHID: 0-07-128605-5 [IE]
Browse http://www.mhhe.com/bowermaness2e
The new edition of Essentials of Business Statistics delivers clear and
understandable explanations of core business statistics concepts,
making it ideal for a one term course in business statistics. Containing
continuing case studies that emphasize the theme of business
improvement, the text offers real applications of statistics that are
relevant to today’s business students. The authors motivate students
by showing persuasively how the use of statistical techniques in
support of business decision-making helps to improve business
processes. A variety of computer centered examples and exercises,
and a robust, technology-based ancillary package are designed to
help students master this subject.
New to this edition
Business Improvement – ‘Business Improvement’ theme,
connecting statistical analysis and business decision making, is
highlighted and called out with BI icons in the book.
New
COMPLETE BUSINESS STATISTICS WITH
STUDENT CD
Seventh Edition
By Aczel
ISBN-13: 978-0-07-723969-5 / MHID: 0-07-723969-5
ISBN-13: 978-0-07-128753-1 / MHID: 0-07-128753-1
New
BUSINESS STATISTICS IN PRACTICE
Fifth Edition
By Bruce L Bowerman and Richard T O’Connell of Miami University of
OH-Oxford
2009 (February 2008) / 896 pages
ISBN-13: 978-0-07-337359-1 / MHID: 0-07-337359-1
ISBN-13: 978-0-07-724253-4 / MHID: 0-07-724253-X
(with Student CD)
http://www.mhhe.com/bowerman5e
The Z versus T Decision--The Z versus T decision is governed
by sigma known-unknown rather than by sample size. This is a
reasonably significant change reflecting a new and widely accepted
direction in this course area.
Hypothesis Testing – Hypothesis testing is approached using a
new stepped method, which makes the material easier to learn. This
new method received outstanding reviews.
Internet Tutorials and Exercises highlight real work applications
and give students practice in gathering and using real data.
Contents
Chapter 1: An Introduction to Business Statistics
Chapter 2: Descriptive Statistics
Chapter 4: Discrete Random Variables
Chapter 5: Continuous Random Variables
Chapter 6: Sampling Distributions
Chapter 7: Confidence Intervals
Chapter 8: Hypothesis Testing
Chapter 9: Statistical Inferences Based on Two Samples
Chapter 10: Experimental Design and Analysis of Variance
Chapter 11: Chi Square Tests
Chapter 12: Simple Linear Regression Analysis
Chapter 13: Multiple Regression and Model-Building
Chapter 14: Process Improvement Using Control (On CD ROM)
Appendix A. Statistical Tables
Appendix B. Covariance and Correlation
Appendix C (1) Counting Rules
Appendix C (2) The Hypergeometric Distribution
Appendix D The Normal Probability Plot
Appendix E Two-Way Analysis of Variance (On CD ROM)
119
New
New
BASIC STATISTICS USING EXCEL TO
ACCOMPANY STATISTICAL TECHNIQUES
IN BUSINESS AND ECONOMICS
Thirteenth Edition
BASIC STATISTICS FOR BUSINESS AND
ECONOMICS WITH STUDENT CD
Sixth Edition
By Douglas A Lind, Coastal Carolina University, William G Marchal,
University of Toledo and Samuel A Wathen, Coastal Carolina University
ISBN-13: 978-0-07-723096-8 / MHID: 0-07-723096-5
ISBN-13: 978-0-07-126365-8 / MHID: 0-07-126365-9 [IE]
By Douglas Lind, Coasta Carolina University
2008 (October 2006)
ISBN-13: 978-0-07-303026-5 / MHID: 0-07-303026-0
http://www.mhhe.com/lindbasic6e
Lind/Marchal/Wathen: Basic Statistics for Business and Economics,
Sixth edition is a derivative of the best-selling Statistical Techniques
in Business and Economics, offering the essential topics of statistical
tools and methods delivered in a student friendly, step-by-step
format. The text is non-threatening and presents concepts clearly
and succinctly with a conversational writing style. All statistical
concepts are illustrated with solved applied examples immediately
upon introduction. Modern computing tools and applications are
introduced, but the text maintains a focus on presenting statistics
content as opposed to technology or programming methods, and the
sixth edition continues as a “students” text with increased emphasis
on interpretation of data and results.
New
STATISTICAL TECHNIQUES
IN BUSINESS AND
ECONOMICS
Thirteenth Edition
New to this edition
Basic Statistics for Business and Economics provides a short and
understandable, step by step approach. Based on the more complete
Statistical Techniques for Business and Economics, Basic has the
same style and content coverage, just fewer chapters and optional
topics in a shorter, less expensive text. Reading and homework
assignments will be less intimidating to beginning students and
students will be more motivated to use a text that looks and feels
easier to use.
More real world data and scenarios are used in exercises
and examples, providing students with more realistic and relevant
applications and motivation. Optional computer exercises and webbased exercise allow students to use technology and the World Wide
Web for very current information and data for projects at the direction
of the instructor.
CONTENTS
1 What Is Statistics?
2 Describing Data: Frequency Distributions and Graphic
Presentation
3 Describing Data: Numerical Measures
4 Describing Data: Displaying and Exploring Data
5 A Survey of Probability Concepts
6 Discrete Probability Distributions
7 Continuous Probability Distributions
8 Sampling Methods and the Central Limit Theorem
9 Estimation and Confidence Intervals
10 One-Sample Tests of Hypothesis
11 Two-Sample Tests of Hypothesis
13 Linear Regression and Correlation
14 Multiple Regression and Correlation Analysis
15 Chi-Square Applications
MegaStat for Excel
Visual Statistics
Appendixes, Tables, Data Sets, Solutions
Photo Credits
Index
By Douglas Lind, Coastal Carolina University,
William Marchal, University of Toledo and
Samuel Wathen, Coastal Carolina University
2008 (October 2006)
ISBN-13: 978-0-07-327296-2 / MHID: 0-07-327296-5
(with Student CD)
ISBN-13: 978-0-07-128575-9 / MHID: 0-07-128575-X
[IE with Student CD]
Browse http://www.mhhe.com/lind13e
The new edition of Lind’s Statistical Techniques in Business and
Economics is a perennial market best seller due to its comprehensive
coverage of statistical concepts and methods delivered in a studentfriendly, step-by-step format. The text is non-threatening and presents
concepts clearly and succinctly with a conversational writing style.
All statistical concepts are illustrated with solved applied examples
immediately upon introduction. Self reviews and exercises for each
section, and review sections for groups of chapters also support
the student learning steps. Modern computing applications (Excel,
Minitab, and MegaStat) are introduced, but the text maintains a focus
on presenting statistics concepts as applied in business as opposed to
technology or programming methods. The thirteenth edition continues
as a students’ text with increased emphasis on interpretation of data
and results.
New to this edition
Z Versus T: The division between the z and t distributions is based
sigma known or unknown rather than on sample sizes
Multiple Regression: Treatment now includes an investigation of
the theory behind the linear model along with tests for the violation
of each assumption.
Robust Technology Package: Lind 13e features additional
detail in the software sections, is available with Homework Manager/
Homework Manager Plus, and is available as a Zinio eBook. Excel,
MegaStat, and Minitab are integrated throughout the text, in enough
detail to support students. The comprehensive, user-friendly Student
CD includes MegaStat, Visual Statistics, ScreenCam tutorials and
additional study resources.
120
Contents
Chapter 1: What Is Statistics?
Chapter 2: Describing Data: Frequency Tables, Frequency
Distributions, and Graphic Presentation
Chapter 3: Describing Data: Numerical Measures
Chapter 4: Describing Data: Displaying and Exploring Data
Chapter 5: A Survey of Probability Concepts
Chapter 6: Discrete Probability Distributions
Chapter 7: Continuous Probability Distributions
Chapter 8: Sampling Methods and the Central Limit Theorem
Chapter 9: Estimation and Confidence Intervals
Chapter 10: One-Sample Tests of Hypothesis
Chapter 11: Two-Sample Tests of Hypothesis
Chapter 12: Analysis of Variance
Chapter 13: Linear Regression and Correlation
Chapter 14: Multiple Regressions and Correlation Analysis
Chapter 15: Index Numbers
Chapter 16: Time Series and Forecasting
Chapter 17: Nonparametric Methods: Chi-Square Application
Chapter 18: Nonparametric Methods: Analysis of Ranked Data
Chapter 19: Statistical Process Control and Quality Management
Chapter 20: An Introduction to Decision Theory / MegaStat for Excel
/ Visual Statistics 2.0 / Appendixes / Photo Credits / Index
11. Simple Linear Regression Analysis
12. Multiple Regression and Model Building.
13. Time Series Forecasting.
14. Process Improvement Using Control Charts.
15. Nonparametric Methods.
16. Chi-Square Tests
17. Decision Theory
Appendix A: Statistical Tables
Appendix B: Covariance and Correlation
Appendix C: • Part I: Counting Rules • Part II The Hypergeometric
Distribution
Appendix D: The Normal Probability Plot
Appendix E: • Part I: Properties of the Mean and the Variance of a
Random Variable, and Covariance
Appendix F: • Part I: Stratified Random Sampling. Answers to Most
Odd-Numbered Exercises. References. Index.
Appendix E: (Part 2) Derivations of the Mean and Variance of x and
p On CD-ROM.
Appendix F: (Part 2) Cluster Sampling and Ratio Estimation On
CD-ROM.
Appendix G: Using Matrix Algebra to Perform Regression Calculations
On CD-ROM
BUSINESS FORECASTING WITH FORECAST
X SOFTWARE
Fifth Edition
BUSINESS STATISTICS IN PRACTICE
Fourth Edition
By Bruce L. Bowerman, and Richard T. O’Connell, both of Miami
University Of Ohio-Oxford
ISBN-13: 978-0-07-325291-9 / MHID: 0-07-325291-3
(with Student CD)
ISBN-13: 978-0-07-126118-0 / MHID: 0-07-126118-4
By J. Holton Wilson, Central Michigan University, Barry Keating,
University Of Notre Dame, and John Galt Solutions Inc.
ISBN-13: 978-0-07-320398-0 / MHID: 0-07-320398-X
(with Student CD)
ISBN-13: 978-0-07-124494-7 / MHID: 0-07-124494-8 [IE with CD]
The new edition of Business Statistics in Practice delivers clear and
understandable explanations of business statistics concepts through
the use of continuing case studies and an emphasis on business
improvement. The cases and examples show real applications of
statistics relevant to today’s business students. The authors motivate
students by showing persuasively how the use of statistical techniques
in support of business decision-making helps to improve business
processes. A variety of computer centered examples and exercises,
and a robust, technology-based ancillary package are designed to
help students master this subject. Acknowledging the importance of
spreadsheets and statistical software in their statistical instruction,
the authors continue to integrate Excel and Minitab output throughout
the text. In addition, a new enhanced version of MegaStat, an Excel
add-in program designed to optimize Excel for statistical application,
is available free on the Student CD. For students and instructors who
want to explore statistical concepts from a graphical perspective,
Visual Statistics is again available on the Student CD. New Business
Improvement icons are integrated throughout the text to illustrate
the ‘BI’ theme.
The Fifth Edition of Business Forecasting is the most practical
forecasting book on the market with the most powerful software—
Forecast X. This new edition presents a broad-based survey of
business forecasting methods including subjective and objective
approaches. As always, the author team of Wilson and Keating
deliver practical how-to forecasting techniques, while theory and
math are held to a minimum. This edition focuses on the most proven,
acceptable methods used commonly in business and government
such as regression, smoothing, decomposition, and Box-Jenkins.
This new edition continues to integrate the most comprehensive
software tool available in this market, Forecast X. With the addition
of ForeCastX, this text provides the most complete and up-to-date
coverage of forecasting concepts with the most technologically
sophisticated software package on the market. This Excel-based tool
(which received a 4 point out 5 rating from PC Magazine, Oct. 2, 2000
issue) effectively uses wizards and many tools to make forecasting
easy and understandable.
Contents
Chapter 1 Introduction to Business Forecasting
Chapter 2 The Forecast Process, Data Considerations, and Model
Selection
Chapter 3 Moving Averages and Exponential Smoothing
Chapter 4 Introduction to Forecasting with Regression Methods
Chapter 5 Forecasting with Multiple Regressions
Chapter 6 Times-Series Decomposition
Chapter 7 ARIMA (Box-Jenkins) – Type Forecasting Models
Chapter 8 Combining Forecast Results
Chapter 9 Forecast Implications
1. An Introduction to Business Statistics.
2. Descriptive Statistics.
3. Probability
4. Discrete Random Variables.
5. Continuous Random Variables.
6. Sampling Distributions
7. Confidence Intervals.
8. Hypothesis Testing.
9. Statistical Inferences Based on Two Samples
10. Experimental Design and Analysis of Variance.
Browse http://www.mhhe.com/business/opsci/wilson5e
Contents
121
15. Nonparametric Methods: Chi-Square Applications
16. Nonparametric Methods: Analysis of Ranked Data
17. Statistical Quality Control
18. Index Numbers
19. Time Series and Forecasting
20. An Introduction to Decision Theory
Appendixes
Answers to Odd-Numbered Chapter Exercises
Answers to Odd-Numbered Review Exercises
Photo Credits
Index
COMPLETE BUSINESS STATISTICS
Sixth Edition
By Amir D. Aczel , Bentley College
2006 / Hardcover
ISBN-13: 978-0-07-312698-2 / MHID: 0-07-312698-5
(with Student CD)
Browse http://www.mhhe.com/aczel6e
Statistical integrity with a complete Excel solution, this new edition of
Complete Business Statistics offers revised sections on regression
analysis and updated cases highlighting companies across the
globe.
Contents
0. Working with Templates
1. Introduction and Descriptive Statistics
2. Probability
3 Random Variables
4. The Normal Distribution
5. Sampling and Sampling Distributions
6. Confidence Intervals
7. Hypothesis Testing
8. The Comparison of Two Populations
10. Simple Linear Regression and Correlation
11. Multiple Regression and Correlation
12. Time Series, Forecasting, and Index Numbers
13. Quality Control and Improvement
14. Nonparametric Methods and Chi-Square Test
15. Bayesian Statistics and Decision Analysis
Appendices
A: References
B: Answers to Most Odd-Numbered Problems
C: Statistical Tables On the CD
16. Sampling Methods
17. Multivariate Analysis
Applied Linear Regression Models
Fourth Edition
By Michael H Kutner, Emory University; Christopher J Nachtsheim,
University of Minnesota and John Neter, University of Georgia
2004 / 672 pages
ISBN-13: 978-0-07-301466-1 / MHID: 0-07-301466-4
(with Student CD)
ISBN-13: 978-0-07-123252-4 / MHID: 0-07-123252-4 (IE)
http://www.mhhe.com/kutnerALRM4e
Contents
Part 1 Simple Linear Regression:
1 Linear Regression with One Predictor Variable.
2 Inferences in Regression and Correlation Analysis.
3 Diagnostics and Remedial Measures.
4 Simultaneous Inferences and Other Topics in Regression
Analysis.
5 Matrix Approach to Simple Linear Regression Analysis.
Part 2 Multiple Linear Regression:
6 Multiple Regression I.
7 Multiple Regression II.
8 Building the Regression Model I: Models for Quantitative and
Qualitative Predictors.
9 Building the Regression Model II: Model Selection and Validation.
10 Building the Regression Model III: Diagnostics.
11 Remedial Measures and Alternative Regression Techniques.
12 Autocorrelation in Time Series Data.
Part 3 Nonlinear Regression:
13 Introduction to Nonlinear Regression and Neural Networks.
14 Logistic Regression, Poisson Regression, and Generalized Linear
Models
BASIC STATISTICS USING EXCEL FOR
OFFICE XP
Twelve Edition
By Douglas Lind, Coasta Carolina University, William Marchal,
University of Toledo and Robert Mason
2005
ISBN-13: 978-0-07-286828-9 / MHID: 0-07-286828-7
CONTENTS
1. What is Statistics?
2. Describing Data: Frequency Distributions and Graphic
Presentation
3. Describing Data: Numerical Measures
4. Describing Data: Displaying and Exploring Data
5. A Survey of Probability Concepts
6. Discrete Probability Distributions
7. Continuous Probability Distributions
8. Sampling Methods and the Central Limit Theorem
9. Estimation and Confidence Intervals
10. One-Sample Tests of Hypothesis
11.Two-Samples Tests of Hypothesis
12. Analysis of Variance
13. Linear Regression and Correlation
14. Multiple Regression and Correlation Analysis
122
Introductory Mathematics and
Statistics For Business
Fourth Edition
Practical Business Statistics
Fifth Edition
By John Croucher, Macquarie University, NSW, Australia
2002 / 784 pages
ISBN-13: 978-0-07-471042-5 / MHID: 0-07-471042-7
By Andrew F Siegel, University of Washington
2003 / 816 pages / hardcover
ISBN-13: 978-0-07-282125-3 / MHID: 0-07-282125-6
(with Student CD)
ISBN-13: 978-0-07-121338-7 / MHID: 0-07-121338-4
Contents
http://www.mhhe.com/siegel5e
Contents
PART I: INTRODUCTION: DEFINING THE ROLE OF STATISTICS
IN BUSINESS.
1 Introduction: Defining the Role of Statistics in Business.
2 Data Structures: Classifying the Various Types of Data Sets.
3 Histograms: Looking at the Distribution of Data.
4 Landmark Summaries: Interpreting Typical Values and
Percentiles.
5 Variabilty: Dealing With Diversity.
PART II: PROBABILITY.
6 Probability: Understanding Random Situations.
7 Random Variables: Working With Uncertain Numbers.
PART III: STATISTICAL INFERENCE.
8 Random Sampling.
9 Confidence Intervals: Admitting That Estimates Are Not Exact.
10 Hypothesis Testing: Deciding Between Reality And Coincidence.
PART IV: REGRESSION AND TIME SERIES.
11 Correaltion And Regression: Measuring And Predicting
Relationships.
12 Multiple Regression: Predicting One Factor From Several
Others.
13 Report Writing: Communicating The Results Of A Multiple
Regression.
14 Time Series: Understanding Changes Over Time.
PART V: METHODS AND APPLICATIONS.
15 Anova: Testing For Differences Among Many Samples, And Much
More.
16 Nonparametrics: Testing With Ordinal Data Or Nonnormal
Distributions.
17 Chi-Squared Analysis: Testing For Patterns In Qualitive Data.
18 Quality Control: Recognizing And Managing Variation.
Appendix A: Employee Database.
Appendix B: Donations Database.
Appendix C: Self-Test: Solutions To Selected Problems And Database
Exercises.
Appendix D: Statistical Tables.
Appendix E: Statpad Quick Reference Guide
Preface.
Guided tour.
MATHEMATICS:
Chapter 1 Basics Mathematics.
Chapter 2 Percentages.
Chapter 3 Algebra.
Chapter 4 Ratios And Proportions.
Chapter 5 Simple Interest.
Chapter 6 Compound Interest.
Chapter 7 Annuities.
Chapter 8 Depreciation.
Chapter 9 Graphing.
APPENDIXES:
A: A test of basic mathematics.
B: Trial examination.
TABLES:
1 Amount at compound interest tables.
2 Present value at compound interest tables.
3 Future value of an annuity tables.
4 Table of common logarithms.
Summary Of Useful Mathematical Formulae.
Solutions To Selected Exercises.
STATISTICS:
Chapter 1 Introduction To Statistics.
Chapter 2 Visual Presentation Of Data.
Chapter 3 Measures Of Central Tendency.
Chapter 4 Measures Of Dispersion.
Chapter 5 Sampling.
Chapter 6 Elementary Probability.
Chapter 7 The Normal Distribution.
Chapter 8 Correlation.
Chapter 9 Regression Analysis.
Chapter 10 Index Numbers.
Chapter 11 Time Series And Trend Analysis.
Chapter 12 Hypothesis Testing.
Chapter 13 Analysis Of Frequency Data.
APPENDIXES:
A: A note on summation notation.
B: A note on calculators.
C: A note on computer packages Minitab, SPSS, Microsoft Excel
for Windows.
D: Trial examinations.
TABLES:
1 Areas under the standard normal curve.
2 Critical values for the t-distribution.
3 Critical values for the rank correlation coefficient.
4 Critical values for the chi-square distribution.
A Summary Of Useful Statistical Formulae.
Solutions To Selected Exercises.
Glossary.
Index
123
Statistics
Making Business Decisions
By John Croucher, Macquarie University, NSW, Australia
2002 / 528 pages
ISBN-13: 978-0-07-471041-8 / MHID: 0-07-471041-9
Schaum’s Outline of Business
Statistics
Fourth Edition
Contents
Preface.
Guided Tour.
Chapter 1 Introduction to Statistics.
Chapter 2 Visual Presentation of Data.
Chapter 3 Measures of Central Tendency.
Chapter 4 Measures of Dispersion.
Chapter 5 Sampling.
Chapter 6 Elementary Probability.
Chapter 7 The Normal Distribution.
Chapter 8 Correlation.
Chapter 9 Regression Analysis.
Chapter 10 Index Numbers.
Chapter 11 Time Series And Trend Analysis.
Chapter 12 Hypothesis Testing.
Chapter 13 Analysis of Frequency Data.
APPENDIXES:
A: A note on summation notation.
B: A note on calculators.
C: A note on computer packages — Minitab, SPSS®, Microsoft Excel
for Windows.
D: Trial examinations.
TABLES:
1 Areas under the standard normal curve.
2 Critical values for the t-distribution.
3 Critical values for the rank correlation coefficient.
4 Critical values for the chi-square distribution.
A Summary of Useful Statistical Formulae.
Solutions to Selected Exercises.
Glossary.
Index
SCHAUM’S OUTLINE OF BEGINNING
STATISTICS
Second Edition
By Larry Stephens, University of Nebraska, Omaha
ISBN-13: 978-0-07-145932-7 / MHID: 0-07-145932-4
This study tool is ideal if you wish to master the basics for an
introductory course or solo study. This new edition includes output
from Excel, SAS, SPSS, STATISTIX, and MINITAB, all of which are
now in general use for college courses on statistics at this level. It
will also include up-to-date statistical examples taken from the latest
media sources.
By Leonard J. Kazmier, Arizona State University
2004 / 432 pages
ISBN-13: 978-0-07-141080-9 / MHID: 0-07-141080-5
ISBN-13: 978-0-07-123679-9 / MHID: 0-07-123679-1 [IE]
(International Edition is not for sale in Japan)
Conforming to the current business statistics curriculum, this fourth
edition of Schaum’s Outline of Business Statistics reflects recent
changes in the course as well as in general practice, including new
sections in each chapter on the application of Excel—the most used
program in offices throughout the world—making this the first book
to address this change in the curriculum. The fourth edition continues
to provide a direct and effective tool for learning the fundamentals of
business statistics without the technical verbiage.
SCHAUM’S EASY OUTLINE OF BUSINESS
STATISTICS
By Leonard J. Kazmier, Arizona State University
2003 / 160 pages
ISBN-13: 978-0-07-139876-3 / MHID: 0-07-139876-7
CONTENTS
Chapter 1: Analyzing Business Data
Chapter 2: Statistical Presentations and Graphical Analysis
Chapter 3: Describing Business Data: Measures of Location
Chapter 4: Describing Business Data: Measures of Variability
Chapter 6: Probability Distributions for Discrete Random Variables
Chapter 7: Probability Distributions for Continuous Random
Variables
Chapter 8: Sampling Distributions and Confidence Intervals for the
Mean
Chapter 9: Other Confidence Intervals
Chapter 10: Testing Hypotheses Concerning the Value of the
Population Mean
Chapter 11: Testing Other Hypotheses
Chapter 12: The Chi-Square Test
Chapter 13: Analysis of Variance
Chapter 14: Linear Regression and Correlation Analysis
Chapter 15: Multiple Regression and Correlation
Chapter 16: Time Series Analysis and Business Forecasting
Chapter 17: Index Numbers for Business and Economic Data
Chapter 18: Decision Analysis: Payoff Tables And Decision Trees
Chapter 19: Decision Analysis: The Use of the Sample Information
Chapter 20: Statistical Process Control
Chapter 21: Nonparametric Statistics
Appendices
124
Advanced Statistics
SCHAUM’S OUTLINE OF STATISTICS AND
ECONOMETRICS
Second Edition
By Dominick Salvatore, Fordham University—Bronx and Derrick Reagle
2002 / 256 pages
ISBN-13: 978-0-07-134852-2 / MHID: 0-07-134852-2
CONTENTS
Introduction.
Descriptive Statistics.
Probability and Probability Distributions.
Statistics Inference: Estimation.
Statistical Inference: Testing Hypothesis.
Statistics Examination.
Simple Regression Analysis.
Multiple Regression Analysis.
Problems in Regression Analysis.
Further Techniques and Applications in Regression Analysis.
Simultaneous-Equations Methods.
Time Series Econometrics.
Statistics Examination.
Bionomial Distribution.
Standard Normal Distribution.
Table of Random Numbers.
Student t Distribution.
F Distribution.
Durbin-Watson Statistics.
Critical Values of Runs in the Run Tests.
[email protected]
APPLIED LINEAR STATISTICAL MODELS
Fifth Edition
By Michael H Kutner, Emory University; Christopher J Nachtsheim,
University of Minnesota; John Neter, University of Georgia and William
Li, University of Minnesota
2005 / 1,200 pages
ISBN-13: 978-0-07-310874-2 / MHID: 0-07-310874-X (with CD)
CONTENTS
Part 1 Simple Linear Regression:
1 Linear Regression with One Predictor Variable.
2 Inferences in Regression and Correlation Analysis.
3 Diagnostic and Remedial Measures.
4 Simultaneous Inferences and Other Topics in Regression
Analysis.
5 Matrix Approach to Simple Linear Regression Analysis.
Part 2 Multiple Linear Regression:
6 Multiple Regression I.
7 Multiple Regression II.
8 Regression Models for Quantitative and Qualitative Predictors.
9 Building the Regression Model I: Model Selection and Validation.
10 Building the Regression Model II: Diagnostics.
11 Building the Regression Model III: Remedial Measures.
12 Autocorrelation in Time Series Data.
Part 3 Nonlinear Regression:
13 Introduction to Nonlinear Regression and Neural Networks.
14 Logistic Regression, Poisson Regression, and Generalized Linear
Models.
Part 4 Design and Analysis of Single-Factor Studies:
15 Introduction to the Design of Experimental and Observational
Studies.
16 Single Factor Studies.
17 Analysis of Factor-Level Means.
18 ANOVA Diagnostics and Remedial Measures.
Part 5 Multi-Factor Studies:
19 Two Factor Studies with Equal Sample Sizes.
20 Two Factor Studies-One Case per Treatment.
21 Randomized Complete Block Designs.
22 Analysis of Covariance.
23 Two Factor Studies with Unequal Sample Sizes.
24 MultiFactor Studies.
25 Random and Mixed Effects Models.
Part 6 Specialized Study Designs:
26 Nested Designs, Subsampling, and Partially Nested Designs.
27 Repeated Measures and Related Designs.
28 Balanced Incomplete Block, Latin Square, and Related Designs.
29 Exploratory Experiments: Two-Level Factorial and Fractional
Factorial Designs.
30 Response Surface Methodology.
Appendix A: Some Basic Results in Probability and Statistics.
Appendix B: Tables.
Appendix C: Data Sets.
Appendix D: Rules for Develping ANOVA Models and Tables for
Balanced Designs.
Appendix E: Selected Bibliography
125
TITLE INDEX
A
Algebra Demystified
Huettenmueller 16
Algebra for College Students
Miller
36
Algebra for College Students, 5e
Dugopolski
34
Applied and Algorithmic Graph Theory
Chartrand
96
Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition, 9e
Hoffmann
67
Applied Linear Regression Models, 4e
Kutner
122
Applied Linear Statistical Models, 5e
Kutner
125
Applied Mathematics for Business, Economics and the Social Science, 4e
Budnick
42
B
Basic College Mathematics
Miller
6
Basic College Mathematics, 2e
Bello
6
Basic Mathematical Skills with Geometry, 7e
Hutchison
5
Basic Statistics for Business and Economics with Student CD, 6e
Lind
120
Basic Statistics Using Excel for Office XP, 12e
Lind
122
Basic Statistics Using Excel to Accompany Statistical Techniques in Business and Economics, 13e
Lind
120
Miller
14
Hutchison
13
Beginning and Intermediate Algebra, 2e
Hall
20
Messersmith
18
Miller
24
Beginning and Intermediate Algebra: A Unified Worktext
Streeter
26
Bob Miller’s Algebra for the Clueless, 2e
Miller
16
Bob Miller’s Geometry for the Clueless, 2e
Miller
40
Business Calculus Demystified
Huettenmueller
69
Business Forecasting with Forecast X Software, 5e
Wilson
121
Business Math Demystified
Bluman
42
Business Statistics in Practice, 4e
Bowerman
121
Bowerman
119
C
Calculus Demystified
Krantz
78
Calculus for Business, Economics, and the Social and Life Sciences, Brief Edition, 9e
Hoffmann
68
Calculus with Mathzone: Early Transcendental Functions, 3e
Smith
71
Smith
74
Calculus: Concepts and Connections
Smith
72
Smith
69
Calculus: Multivariable: Early Transcendental Functions, 3e
Smith
81
Smith
80
Calculus: Single Variable: Early Transcendental Functions, 3e
Smith
76
126
TITLE INDEX
College Algebra with Trigonometry, 8e
Barnett
56
College Algebra with Trigonometry: Graphs and Models
Barnett
57
College Algebra
Coburn
53
College Algebra, 8e
Barnett
52
College Algebra: Graphs and Models, 3e
Barnett
51
Complete Business Statistics with Student CD, 7e
Aczel
119
Complete Business Statistics, 6e
Aczel
122
Complex Analysis, 3e
Ahlfors
103
Complex Variables and Applications, 8e
Brown
101
Differential Equations Demystified
Krantz
106
Differential Equations with Applications and Historical Notes, 2e
Simmons
87
Ang
86
Differential Equations: A Modeling Approach
Ledder
86
Differential Equations: Theory, Technique, and Practice
Simmons
Discrete Mathematics and its Applications, 6e
Rosen
45
Simpson
46
Dugopolski
12
Elementary and Intermediate Algebra, 3e
Dugopolski
16
Hutchison
21
Elementary and Intermediate Algebra, Alternate Hardcover Edition, 3e
Hutchinson
23
Elementary Linear Algebra, 2e
Nicholson
91
Elementary Number Theory, 2e
Eynden
100
Burton
100
Elementary Numerical Analysis: An Algorithmic Approach, 3e
Conte
99
Bluman
109
Elementary Statistics: A Step by Step Approach, 6e
Bluman
110
Elements of Partial Differential Equations
Sneddon
89
Engineering Statistics Demystified
Stephens
118
Essentials of Business Statistics with Student CD, 2e
Bowerman
119
Everyday Math Demystified
Gibilisco D
85, 87
E
8
F
Five Steps to a 5 AP Calculus AB-BC, 2e
Ma
73
Fourier Series and Boundary Value Problems, 7e
Brown
88
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Hvidsten
39
Getting Started with the T1-84 Plus Graphing Calculator
Ng
105
Great Jobs for Math Majors, 2e
Lambert
105
G
127
TITLE INDEX
H
Higher Engineering Mathematics
Ramana
94
History of Mathematics an Introduction (The), 6e
Burton
97
How to Solve Word Problems in Arithmetic
Pullman
How to Solve Word Problems in Calculus
Don How to Solve Word Problems in Mathematics
Wayne
8
78
8
I
Hutchison
29
Bello
33
Miller
31
Dugopolski
27
Intermediate Algebra: The Language and Symbolism of Mathematics
Hall
32
Introduction to Biostatistics
Glover
Introduction to Enumerative Combinatorics
Bona
93
Introduction to Graph Theory
Chartrand
95
Introduction to Mathematical Analysis
Parzynski
97
Introduction to Probability and Statistics: Principles and Applications for Engineering and the
Milton
114, 117
Introduction to the Theory of Statistics, 3e
Mood
115
Miller
15
Bello
11
Introductory Mathematics and Statistics for Business, 4e
Croucher
123
Lectures in Elementary Probability Theory and Stochastic Processes
Falmagne 112
Linear Algebra Demystified
McMahon
92
Linear Algebra with Applications, 5e
Nicholson
90
115
Computing Sciences, 4e
L
M
Math for the Anxious
Proga Math Proofs Demystified
Gibilisco
105
Math Word Problems Demystified
Bluman
27
Mathematics for Elementary Teachers: A Conceptual Approach, 7e
Bennett
43
Mathematics for Elementary Teachers: An Activity Approach, 7e
Bennett
44
Mathematics for Technicians, 5e
Alldis
7
Alldis
46
Mathematics in Our World
Bluman
41
McGraw-Hill Dictionary of Mathematics, 2e
McGraw-Hill
McGraw-Hill’s Conquering GRE/GMAT Math
Moyer
42
Multivariate Statistical Methods in Quality Management
Yang
119
128
7
106
TITLE INDEX
P
Practical Business Statistics, 5e
Siegel
123
Prealgebra, 2e
Hutchison
Pre-Algebra, 3e
Bach
Pre-Calculus Demystified
Huettenmueller Precalculus with Limits, 6e
Barnett
60
Precalculus with Mathzone, 6e
Barnett
61
Precalculus: Concepts, Connections and Applications
Coburn
62
Precalculus: Graphs and Models, 3e
Barnett
58
Principles of Mathematical Analysis, 3e
Rudin
97
9
10
106
R
Ready, Set, Go! a Student Guide to SPSS ® 13.0 and 14.0 for Windows, 2e
Pavkov
111
Real and Complex Analysis, 3e
Rudin
103
Research Projects in Statistics
Kincaid
111
S
Schaum’s 2,000 Solved Problems in Discrete Mathematics
Lipschutz
46
Schaum’s 3,000 Solved Problems in Calculus
Mendelson
79
Schaum’s 3,000 Solved Problems in Linear Algebra
Lipschultz
92
Schaum’s A-Z Mathematics
Berry
Schaum’s Easy Outline Intermediate Algebra
Steege
34
Schaum’s Easy Outline of Business Statistics
Kazmier
124
Schaum’s Easy Outline of Logic
Nolt
94
Schaum’s Easy Outline: College Algebra
Spiegel
54
Schaum’s Easy Outlines: Calculus
Ayres
79
Schaum’s Easy Outlines: Geometry
Rich
40
Schaum’s Easy Outlines: Linear Algebra
Lipschutz
92
Schaum’s Easy Outlines: Mathematical Handbook of Formulas and Tables
Spiegel
106
Schaum’s Easy Outlines: Statistics
Spiegel
113
Schaum’s Outline of Advanced Calculus, 2e
Wrede
74
Schaum’s Outline of Advanced Mathematics for Engineers and Scientists, SI Metric
Spiegel
95
Schaum’s Outline of Beginning Calculs, 3e
Mendelson
78
Schaum’s Outline of Beginning Finite Mathematics
Lipschutz
44
Schaum’s Outline of Beginning Statistics, 2e
Stephens
124
Schaum’s Outline of Business Statistics, 4e
Kazmier
124
Schaum’s Outline of Calculus, 5e
Ayres
77
Schaum’s Outline of College Algebra, 3e
Moyer
54
Balakrishnan
96
Schaum’s Outline of Complex Variables
Spiegel
Schaum’s Outline of Differential and Integral Calculus, SI Metric, 3e
Ayres
79
Schaum’s Outline of Differential Equations, 3e
Bronson
87
Schaum’s Outline of Differential Geometry
Lipschutz
101
129
7
104
TITLE INDEX
Schaum’s Outline of Discrete Mathematics, 3e
Lipschutz
46
Schaum’s Outline of Elementary Algebra, 3e
Rich
16
Schaum’s Outline of Elements of Statistics I: Differential Statistics and Probability
Bernstein
113
Schaum’s Outline of Elements of Statistics II: Inferential Statistics
Bernstein
113
Schaum’s Outline of General Topology
Lipschutz
105
Schaum’s Outline of Geometry, 3e
Rich
40
Rich
40
Schaum’s Outline of Graph Theory: Including Hundreds of Solved Problems
Balakrishnan
96
Schaum’s Outline of Intermediate Algebra
Steege
34
Schaum’s Outline of Introduction to Mathematical Economics, 3e
Dowling
43
Schaum’s Outline of Introduction to Probability and Statistics
Lipschutz
113
Schaum’s Outline of Linear Algebra, 4e
Lipschutz
92
Schaum’s Outline of Mathematica
Don
79
Schaum’s Outline of Mathematical Handbook of Formulas and Tables, 2e
Spiegel
106
Schaum’s Outline of Mathematical Methods for Business and Economics
Dowling
43
Schaum’s Outline of Modern Abstract Algebra
Ayres
101
Schaum’s Outline of Numerical Analysis, 2e
Scheid
99
Schaum’s Outline of Partial Differential Equations
DuChateau
89
Schaum’s Outline of Precalculus, 2e
Safier
63
Schaum’s Outline of Probability and Statistics, 3e
Schiller
115
Schaum’s Outline of Probability, 2e
Lipschutz
113
Schaum’s Outline of Review of Elementary Mathematics, 2e
Rich
Schaum’s Outline of Set Theory and Related Topics, 2e
Lipschutz
114
Schaum’s Outline of Statistics and Econometrics, 2e
Salvatore
125
Schaum’s Outline of Statistics, 4e
Spiegel
112
Schaum’s Outline of Trigonometry, 4e
Moyer
56
Schaum’s Outline of Understanding Calculus Concepts
Passow
79
Spiegel
95
Solving Business Problems Using a Calculator, 6e
Polisky 41
SPSS Survival Manual, 3e
Pallant
116
Statistical Techniques in Business and Economics, 13e
Lind
120
Statistics for Engineers and Scientists, 2e
Navidi
117
Statistics for the Utterly Confused, 2e
Jaisingh 116
Statistics: A First Course, 6e
Sanders
112
Statistics: Making Business Decisions
Croucher
124
Technical Math Demystified
Gibilisco
47
Topology
Davis
Transition to Higher Mathematics: Structure and Proof
Dumas
89
Trigonometry with Mathzone
Coburn
54
Trigonometry, Revised 3e
Baley
55
8
T
130
104
AUTHOR INDEX
A
Aczel
Complete Business Statistics with Student CD, 7e
119
Aczel
Complete Business Statistics, 6e
122
Ahlfors
Complex Analysis, 3e
103
Alldis
7
Alldis
46
Ang
86
Ayres
Schaum’s Easy Outlines: Calculus
79
Ayres
Schaum’s Outline of Calculus, 5e
77
Ayres
Schaum’s Outline of Differential and Integral Calculus, SI Metric, 3e
79
Ayres
Schaum’s Outline of Modern Abstract Algebra
101
B
Bach
Pre-Algebra, 3e
10
Balakrishnan
96
Balakrishnan
Schaum’s Outline of Graph Theory: Including Hundreds of Solved Problems
96
Baley
Trigonometry, Revised 3e
55
Barnett
College Algebra with Trigonometry, 8e
56
Barnett
College Algebra with Trigonometry: Graphs and Models
57
Barnett
College Algebra, 8e
52
Barnett
College Algebra: Graphs and Models, 3e
51
Barnett
Precalculus with Limits, 6e
60
Barnett
Precalculus with Mathzone, 6e
61
Barnett
Precalculus: Graphs and Models, 3e
58
Bello
Basic College Mathematics, 2e
Bello
33
Bello
11
Bennett
Mathematics for Elementary Teachers: A Conceptual Approach, 7e
43
Bennett
Mathematics for Elementary Teachers: An Activity Approach, 7e
44
Bernstein
Schaum’s Outline of Elements of Statistics I: Differential Statistics and Probability
113
Bernstein
Schaum’s Outline of Elements of Statistics II: Inferential Statistics
113
Berry
Schaum’s A-Z Mathematics
7
Bluman
Business Math Demystified
42
Bluman
109
Bluman
Elementary Statistics: A Step by Step Approach, 6e
110
Bluman
Math Word Problems Demystified
27
Bluman
Mathematics in Our World
41
Bona
Introduction to Enumerative Combinatorics
93
Bowerman
121
Bowerman
119
Bowerman
Essentials of Business Statistics with Student CD, 2e
119
Bronson
Schaum’s Outline of Differential Equations, 3e
6
131
87
AUTHOR INDEX
Brown
Complex Variables and Applications, 8e
101
Brown
Fourier Series and Boundary Value Problems, 7e
88
Budnick
Applied Mathematics for Business, Economics and the Social Science, 4e
42
Burton
Burton
The History of Mathematics an Introduction, 6e
97
Chartrand
Applied and Algorithmic Graph Theory
96
Chartrand
Introduction to Graph Theory
95
Coburn
College Algebra
53
Coburn
Precalculus: Concepts, Connections and Applications
62
Coburn
Trigonometry with Mathzone
54
Conte
Elementary Numerical Analysis: An Algorithmic Approach, 3e
99
Croucher
Introductory Mathematics and Statistics for Business, 4e
123
Croucher
Statistics: Making Business Decisions
124
Davis
Topology
104
Don How to Solve Word Problems in Calculus
78
Don
Schaum’s Outline of Mathematica
79
Dowling
Schaum’s Outline of Introduction to Mathematical Economics, 3e
43
Dowling
Schaum’s Outline of Mathematical Methods for Business and Economics
43
DuChateau
Schaum’s Outline of Partial Differential Equations
89
Dugopolski
Algebra for College Students, 5e
34
Dugopolski
12
Dugopolski
16
Dugopolski
27
Dumas
Transition to Higher Mathematics: Structure and Proof
89
100
C
D
E
Eynden
100
Lectures in Elementary Probability Theory and Stochastic Processes
112
F
Falmagne G
Gibilisco Everyday Math Demystified
8
Gibilisco
Math Proofs Demystified
Gibilisco
Technical Math Demystified
47
Glover
Introduction to Biostatistics
115
105
H
Hall
20
Hall
Intermediate Algebra: The Language and Symbolism of Mathematics
32
Hoffmann
Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition, 9e
67
132
AUTHOR INDEX
Hoffmann
Calculus for Business, Economics, and the Social and Life Sciences, Brief Edition, 9e
68
Huettenmueller Pre-Calculus Demystified
Huettenmueller
Algebra Demystified
16
Huettenmueller
Business Calculus Demystified
69
Hutchinson
Elementary and Intermediate Algebra, Alternate Hardcover Edition, 3e
23
Hutchison
Basic Mathematical Skills with Geometry, 7e
Hutchison
13
Hutchison
21
Hutchison
29
Hutchison
Prealgebra, 2e
Hvidsten
Geometry with Geometry Explorer
106
5
9
39
J
Jaisingh Statistics for the Utterly Confused, 2e
116
Kazmier
Schaum’s Easy Outline of Business Statistics
124
Kazmier
Schaum’s Outline of Business Statistics, 4e
124
Kincaid
Research Projects in Statistics
111
Krantz
Calculus Demystified
Krantz
Differential Equations Demystified
106
Kutner
Applied Linear Regression Models, 4e
122
Kutner
Applied Linear Statistical Models, 5e
125
Lambert
Great Jobs for Math Majors, 2e
105
Ledder
Differential Equations: A Modeling Approach
Lind
Basic Statistics for Business and Economics with Student CD, 6e
120
Lind
Basic Statistics Using Excel for Office XP, 12e
122
Lind
Basic Statistics Using Excel to Accompany Statistical Techniques in Business and Economics, 13e
120
Lind
Statistical Techniques in Business and Economics, 13e
120
Lipschultz
Schaum’s 3,000 Solved Problems in Linear Algebra
92
Lipschutz
Schaum’s 2,000 Solved Problems in Discrete Mathematics
46
Lipschutz
Schaum’s Easy Outlines: Linear Algebra
92
Lipschutz
Schaum’s Outline of Beginning Finite Mathematics
44
Lipschutz
Schaum’s Outline of Differential Geometry
Lipschutz
Schaum’s Outline of Discrete Mathematics, 3e
Lipschutz
Schaum’s Outline of General Topology
105
Lipschutz
Schaum’s Outline of Introduction to Probability and Statistics
113
Lipschutz
Schaum’s Outline of Linear Algebra, 4e
Lipschutz
Schaum’s Outline of Probability, 2e
113
Lipschutz
Schaum’s Outline of Set Theory and Related Topics, 2e
114
K
78
L
86
101
46
92
133
AUTHOR INDEX
M
Ma
Five Steps to a 5 AP Calculus AB-BC, 2e
73
McGraw-Hill
McGraw-Hill Dictionary of Mathematics, 2e
McMahon
Linear Algebra Demystified
92
Mendelson
Schaum’s 3,000 Solved Problems in Calculus
79
Mendelson
Schaum’s Outline of Beginning Calculs, 3e
78
Messersmith
18
Miller
Algebra for College Students
36
Miller
Basic College Mathematics
Miller
14
Miller
24
Miller
Bob Miller’s Algebra for the Clueless, 2e
16
Miller
Bob Miller’s Geometry for the Clueless, 2e
40
Miller
31
Miller
15
106
6
Milton
Introduction to Probability and Statistics: Principles and Applications for Engineering and the
Computing Sciences, 4e
114, 117
Mood
Introduction to the Theory of Statistics, 3e
115
Moyer
McGraw-Hill’s Conquering GRE/GMAT Math
42
Moyer
Schaum’s Outline of College Algebra, 3e
54
Moyer
Schaum’s Outline of Trigonometry, 4e
56
N
Navidi
Statistics for Engineers and Scientists, 2e
117
Ng
Getting Started with the T1-84 Plus Graphing Calculator
105
Nicholson
Elementary Linear Algebra, 2e
91
Nicholson
Linear Algebra with Applications, 5e
90
Nolt
Schaum’s Easy Outline of Logic
94
P
Pallant
SPSS Survival Manual, 3e
116
Parzynski
Introduction to Mathematical Analysis
97
Passow
Schaum’s Outline of Understanding Calculus Concepts
79
Pavkov
Ready, Set, Go! a Student Guide to SPSS ® 13.0 and 14.0 for Windows, 2e
Polisky Solving Business Problems Using a Calculator, 6e
Proga Math for the Anxious
7
Pullman
How to Solve Word Problems in Arithmetic
8
111
41
R
Ramana
Higher Engineering Mathematics
94
Rich
Schaum’s Easy Outlines: Geometry
40
Rich
Schaum’s Outline of Elementary Algebra, 3e
16
Rich
40
Rich
40
134
AUTHOR INDEX
Rich
Schaum’s Outline of Review of Elementary Mathematics, 2e
8
Rosen
Discrete Mathematics and its Applications, 6e
45
Rudin
Principles of Mathematical Analysis, 3e
97
Rudin
Real and Complex Analysis, 3e
103
S
Safier
Schaum’s Outline of Precalculus, 2e
63
Salvatore
Schaum’s Outline of Statistics and Econometrics, 2e
125
Sanders
Statistics: A First Course, 6e
112
Scheid
Schaum’s Outline of Numerical Analysis, 2e
Schiller
Schaum’s Outline of Probability and Statistics, 3e
115
Siegel
Practical Business Statistics, 5e
123
Simmons
Differential Equations with Applications and Historical Notes, 2e
Simmons
Differential Equations: Theory, Technique, and Practice
Simpson
46
Smith
Calculus with Mathzone: Early Transcendental Functions, 3e
71
Smith
74
Smith
Calculus: Concepts and Connections
72
Smith
69
Smith
Calculus: Multivariable: Early Transcendental Functions, 3e
81
Smith
80
Smith
Calculus: Single Variable: Early Transcendental Functions, 3e
76
Sneddon
Elements of Partial Differential Equations
89
Spiegel
Schaum’s Easy Outline: College Algebra
54
Spiegel
Schaum’s Easy Outlines: Mathematical Handbook of Formulas and Tables
106
Spiegel
Schaum’s Easy Outlines: Statistics
113
Spiegel
Schaum’s Outline of Advanced Mathematics for Engineers and Scientists, SI Metric
Spiegel
Schaum’s Outline of Complex Variables
104
Spiegel
Schaum’s Outline of Mathematical Handbook of Formulas and Tables, 2e
106
Spiegel
Schaum’s Outline of Statistics, 4e
112
Spiegel
95
Steege
Schaum’s Easy Outline Intermediate Algebra
34
Steege
Schaum’s Outline of Intermediate Algebra
34
Stephens
Engineering Statistics Demystified
118
Stephens
Schaum’s Outline of Beginning Statistics, 2e
124
Streeter
Beginning and Intermediate Algebra: A Unified Worktext
99
87
85, 87
95
26
W
Wayne
How to Solve Word Problems in Mathematics
Wilson
Business Forecasting with Forecast X Software, 5e
Wrede
Schaum’s Outline of Advanced Calculus, 2e
8
121
74
Y
Yang
Multivariate Statistical Methods in Quality Management
135
119
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Nursing
n
Allied Health (Medical Assisting, Radiology Technician,
Surgical Technician, Massage Therapy, Medical Billing,
Medical Insurance, Medical Coding)
n Public Safety (Paramedic & Emergency Medical
Technician)
21/11/07 11:34:59
www.blackboard.com
/
www.webct.com
course management systems
Course Management Systems like Blackboard and WebCT offer you another way to integrate
digital McGraw-Hill content into your class. McGrawHill Online Learning Center content is formatted to
save you hours of computer inputting.
How instructors use it
Load McGraw-Hill content into your
platform and you will have a fully populated
course online. You can then customize the
content to match your syllabus. You will
also be able to assign specific exercises,
quizzes, or readings to your students.
Grades are posetd automatically to let you
know how students are doing as a whole,
or individually. Built-in communication
allows you to conduct live chats, oversee
bulletin board topics, and e-mail students
who might need more help than others.
How students use it
Students can visit your online course via
the Internet to check the coursework you
have assigned. The platform will record the
students’ progress through your course,
which will enable you to see where they
are studying most. Self-grading quizzes
also indicate exactly where students
need further review. The platform’s
communicaiton
system
encourages
student collaboration with features such
as live chat rooms, asynchronous bulletin
boards, or traditional e-mail.
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- McGraw

Transcription

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