Math 33B: General Course Outline

(Math 31C has been renumbered to Math 33B effective Fall 1998)

Catalog description

33B. Infinite Series. Lecture, three hours; discussion, one hour. Requisite: course 33A (C- or better). Infinite sequences and series; applications.

Textbook

Murray H. Protter and Charles B. Morrey, Jr., Intermediate Calculus,, 2nd Edition, Springer-Verlag (1985)

Reviews and Exams

The following schedule, with textbook sections and topics, is based on 26 lectures. The pace of the schedule below is moderate and can easily be adjusted. The remaining three classroom meetings (only two in Winter Quarter) are for reviews and midterm exams. These are scheduled by the individual instructor. Often there are midterm exams during the fourth and eighth weeks of instruction. The course covers Chapters 3 and 6. Section 3.14 is on double series and can easily be eliminated. The text minimizes or ignores such things as the Limit Comparison Test and Root Test and a few other items of a similar nature. This may be covered if wished as well as the generalized p-test. Note also that solving differential equations with power or Fourier series is not formalized, but it is mentioned briefly in places.

Schedule of Lectures

Lecture	Sections	Topics
1	3.1	Indeterminate Forms
2	3.2	Convergent and Divergent Series
3-4	3.3	Series of Positive Terms
5-6	3.4	Series of Positive and Negative Terms
7	3.5	Power series
8	3.6	Taylor series
9	3.7	Taylor series with remainder
10	3.8	Differentiation and Integration of Series
11	3.9	Validity of Taylor Expansions and Computations with Series
12	3.10	Algebraic Operation with Series
13-14	3.11	Uniform Convergence: Sequences of Functions
15	3.12	Uniform Convergence of Series
16	3.13	Integration and Differentiation of Power series
17-18	3.15	Complex Functions: Complex Series
19-21	6.1-6.3	Fourier Series, Half-range Expansions, Expansions on Other Intervals
22-24	6.4	Convergence Theorem. Differentiation and Integration of Fourier Series.
25-26	6.5	The Complex Form of Fourier Series

Outline update: P. Petersen, 8/98

Class Home Page

Andrea Brose's Home

Department of Mathematics

UCLA

UCLA Department of Mathematics
6363 Math Sciences, Los Angeles, CA 90095-1555
Phone: (310) 206-1286 Fax: (310) 206-6673