# MATH 75 - College of Arts and Sciences

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MATH 75 - College of Arts and Sciences

DEPARTMENT OF PHYSICAL SCIENCES AND MATHEMATICS COLLEGE OF ARTS AND SCIENCES UNIVERSITY OF THE PHILIPPINES MANILA Course Code: Mathematics 75 Course Title: Fundamentals of Analysis III Credit: 3 units (2 units lecture / 1 unit laboratory) Hours / week: 2 hrs. lecture / 3 hrs. laboratory Course Description: Vectors and applications, cylinders and quadrics, sequences and series, tests for convergence or divergence, functions of two or more variables, partial differentiation, multiple integration. Learning Outcomes: On the completion of the course, the student should be able to: Learning Outcomes LO1 understand the geometry of lines, planes, and other basic surfaces in three dimensions and apply operations on three dimensional vectors LO2 determine the convergence of infinite sequences and series, and use infinite series to approximate values of transcendental functions LO3 understand the extension of the concepts of limits, derivatives, and integrals to functions of several variables Learning Plan: Week Topic Program/Student Outcomes PO1 (Apply the knowledge of mathematics, science, and engineering) PO1 (Apply the knowledge of mathematics, science, and engineering) PO5 (Communicate effectively in oral and written form) PO1 (Apply the knowledge of mathematics, science, and engineering) Learning Outcome LO1 Teaching-Learning Activities Lecture, Laboratory Exercises, Problem Sets 1 Three-Dimensional Coordinate System Lines and Planes 2 Quadric Surfaces LO1 Lecture, Laboratory Exercises, Problem Sets 3 Operations and Properties of Vectors in R3, Cross Product of Two Vectors LO1 Laboratory Exercises, Problem Sets 4 Calculus of Vector Valued Functions Domain Limits Derivatives Operations LO1 Laboratory Exercises, Problem Sets 5 First Lecture Exam First Laboratory Exam 6 Spheres and Cylinders Cylindrical Coordinate System LO2 Laboratory Exercises, Problem Sets 7 Functions of Several Variables Limits and Continuity LO2 Laboratory Exercises, Problem Sets DEPARTMENT OF PHYSICAL SCIENCES AND MATHEMATICS COLLEGE OF ARTS AND SCIENCES UNIVERSITY OF THE PHILIPPINES MANILA 8 Spherical Coordinates Double and Triple Integrals LO2 Laboratory Exercises, Problem Sets 9 Second Lecture Exam Second Laboratory Exam 10 L’hopitals rule LO3 Laboratory Exercises, Problem Sets 11 Improper Integrals Sequences of Constant Terms LO3 Laboratory Exercises, Problem Sets 12 Series of Constant Terms Tests for Convergence LO3 Laboratory Exercises, Problem Sets 13 Power Series Differentiation and Integration of Power Series LO3 Laboratory Exercises, Problem Sets 14 Taylor Series LO3 Laboratory Exercises, Problem Sets 15 Third Lecture Exam Third Laboratory Exam 16 Final Exam References: The Calculus 7 by Louis Leithold Calculus, Early Transcendentals 9th edition by Anton et.al. Course Requirements: Lecture Component 3 Departmental Exams, 1 Final Exam Non-Departmental Items (Quizzes, Homeworks, Seatworks) Laboratory Component 3 Departmental Exams Laboratory Exercises Grading System: Computation of Grade DEPARTMENT OF PHYSICAL SCIENCES AND MATHEMATICS COLLEGE OF ARTS AND SCIENCES UNIVERSITY OF THE PHILIPPINES MANILA Laboratory Grade = (Average of 3 Laboratory Exams) + (Laboratory Exercises) Lecture Grade = Final Grade = Grading Scale 1.0 1.25 93 - 100 90 - 92 1.5 1.75 2.0 2.25 2.5 2.75 3.0 4.0 5.0 87-89 84 -86 80 – 83 75 – 79 70 – 74 65 – 69 60 – 64 55 – 59 0 – 54 Rules of Conduct / Classroom Policy 1) Attendance is required. A student who is absent for more than 6 times and fails to officially drop the course will automatically be given a grade of 5.0. 2) Cheating is punishable at least with a grade of 5.0. 3) A student is allowed to make up for only one missed exam, provided that the reason is valid. If another exam is missed, the student will get a grade of zero in that exam. The special exam is usually scheduled after the final exam and covers all topics of the entire course. 4) Those who need to take an early or advance exam, provided that the reason is valid, must inform me at least a week before the scheduled exam. 5) No special projects are to be given to compensate for either low or failing grades. 6) Complaints regarding the exam results will only be entertained within a week after the results are released. 7) A student may officially drop the course on or before the deadline for dropping. Only after a dropping slip is accomplished and the instructor’s copy is submitted can a student be considered to have officially dropped the subject.