Math 131B: General Course Outline
Catalog Description
    131B. Analysis. (4) Lecture, three hours; discussion, one hour. Requisites: courses 33B, 115A, 131A. Derivatives, Riemann integral, sequences and series of functions, power series, Fourier series.
Textbook
    Stall, Intro to Real Analysis, Addison Wesley.
Reviews & Exams
    The following schedule, with textbook sections and topics, is based on 26 lectures. The remaining classroom meetings are for leeway, reviews, and midterm exams. These are scheduled by the individual instructor. Often there are midterm exams about the beginning of fourth and eighth weeks of instruction, plus reviews for the final exam.
Schedule of Lectures

Lecture
Section
Topics
1
.
Review of Math 131A
2-3
4.6
Functions of two variables
4
5.1
Pointwise and uniform convergence
5-6
5.2
Limit theorems
7-8
5.3
The supremum norm
9-10
5.6
Metric spaces
11-12
5.7
The contraction mapping principle (including integral equations)
13-14
5.8
Normed linear spaces
15
6.1
Lim sup and Lim inf
16-17
6.2
Series of real constants
18-19
6.3
Weierstrass M-test
20
6.4
Power series
21
6.5
Complex numbers
22
9.1
The heat equation
23
9.2
Definitions and examples
24-25
9.3
Pointwise convergence
26
9.4
Mean-square convergence

Comments

If time permits, the instructor may discuss 5.5 and 7.1-7.3 or parts thereof.

Outline update: V.S. Varadarajan, 12/99

For more information, please contact Student Services, ugrad@math.ucla.edu.

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