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Calculus Third Semester (UP)

This document provides information about Math 38 (Mathematical Analysis III), a 3-unit course offered in the second semester of the 2012-2013 academic year. The course covers topics including infinite series, partial differentiation, multiple integration, and their applications. Upon completing the course, students should understand sequences, series, differentiation and integration of functions with more than one variable. The course is divided into four units spanning sequences and series, differential calculus of multivariable functions, applications of partial derivatives, and multiple integration. Student performance will be evaluated through midterm and prefinal exams, recitation exercises, quizzes, and assignments.

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Pau Borlagdan
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230 views2 pages

Calculus Third Semester (UP)

This document provides information about Math 38 (Mathematical Analysis III), a 3-unit course offered in the second semester of the 2012-2013 academic year. The course covers topics including infinite series, partial differentiation, multiple integration, and their applications. Upon completing the course, students should understand sequences, series, differentiation and integration of functions with more than one variable. The course is divided into four units spanning sequences and series, differential calculus of multivariable functions, applications of partial derivatives, and multiple integration. Student performance will be evaluated through midterm and prefinal exams, recitation exercises, quizzes, and assignments.

Uploaded by

Pau Borlagdan
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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STUDENTS GUIDE FOR MATH 38 (Mathematical Analysis III) SECTION X Second Semester, AY 2012-2013

This is a 3-unit course with 2 hours of lecture (TTh) and an hour of recitation (W) in a week. COURSE DESCRIPTION: Infinite series, techniques and applications of partial differentiation and multiple integration COURSE PREREQUISITE: MATH 37 (Mathematical Analysis II) COURSE GOALS: Upon completion of the course, the students should be able to understand the concepts of sequences, series, differentiation and integration of functions of more than one variable and their applications. COURSE OBJECTIVES: At the end of the course, a student must be able to Determine convergence or divergence of infinite series using appropriate tests; Find the interval of convergence of a power series; Find the power series representation of functions; Determine limits and continuity of a function at a point and over a set; Find partial derivatives (explicit, implicit, chain rule and higher order); Find directional derivatives (if they exist); Find equations of tangent plane and normal line to a surface; Find extreme values of functions (constrained or unconstrained case); and Evaluate multiple integrals using rectangular, polar, cylindrical and spherical coordinates. COURSE MATERIALS: Copies of the lecture materials and supplementary exercises shall be uploaded in http://jfrabajante.weebly.com. Other books on Calculus may be used as supplements but these may not be exactly congruent with the course outline in terms of content and sequencing. References: Leithold, L. The Calculus with Analytic Geometry. Leithold, L. TC7. Thomas, G. Calculus. 10th ed. Thomas, Jr G. and Finney, R. Calculus and Analytic Geometry. Peterson, T. Calculus with Analytic Geometry COURSE OUTLINE UNIT I. SEQUENCES AND INFINITE SERIES 1. Sequences and limit of a sequence 2. Monotonic and bounded sequence 3. Infinite series of constant terms 4. Infinite series of positive terms 5. Alternating series 6. Power series 7. Differentiation and Integration of Power Series 8. Taylor and Maclaurin series (10 meetings)

UNIT II. DIFFERENTIAL CALCULUS OF FUNCTIONS OF MORE THAN ONE VARIABLE (5 meetings) 1. Functions of more than one variable 2. Limits and continuity 3. Partial derivatives 4. Chain rule and Higher-order derivatives MIDTERM EXAM UNIT III. APPLICATIONS OF PARTIAL DERIVATIVES 1. Differentiability and the total differential 2. Directional derivatives and gradients 3. Obtaining a function from its gradient 4. Tangent planes and normal to surfaces 5. Extrema of functions of two variables 6. Lagrange multipliers UNIT IV. MULTIPLE INTEGRATION 1. Double integrals in rectangular coordinates 2. Double integrals in polar coordinates 3. Triple integrals in rectangular coordinates 4. Triple integrals in cylindrical coordinates 5. Triple integrals in spherical coordinates 6. Area and volume PREFINAL EXAM (6 meetings)

(6 meetings)

Grading System: Prefinal Standing: Midterm Exam Prefinal Exam Recitation Exercises, Quizzes and Assignments

30% 30% 40%

Exemption Policy: If a student gets 75 or above as Pre-final grade, then the student is exempted from taking the Final Examination. The Pre-final grade shall be the Final grade. However, if the student takes the final exam, the Final Grade shall be computed as follows: Final Grade = 70% Pre-final Grade + 30% Final Exam The grading scale given below shall be used in giving final grades. Grading Scale: Raw Score Equivalent Raw Score Equivalent 96-100 1.0 70-74 2.5 92-95 1.25 65-69 2.75 88-91 1.5 60-64 3.0 84-87 1.75 55-59 4.0 80-83 2 0-54 5.0 75-79 2.25

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