Math 32B: General Course Outline
Catalog Description
    32B. Calculus of Several Variables. (4) Lecture, three hours; discussion, one hour. Requisite: courses 31B & 32A with a grade of C- or better. Introduction to integral calculus of several variables, line and surface integrals. P/NP or letter grading.
Textbook
Comment
    The following schedule, with textbook sections and topics, is based on 26 lectures. The remaining classroom meetings are for leeway, reviews, and two midterm exams. These are scheduled by the individual instructor.
Schedule of Lectures

Lecture
Sections
Topics
1
16.1
Integration in the Variables
2
16.1
Integration in the Variables
3
16.2
More General Regions
4
16.3
Triple Integrals
5
12.3
Polar Coordinates
6
16.4
Integration in Polar Coordinates
7
16.4
Integration in Polar Coordinates
8
16.5
Applications of Multiple Integrals
9
16.6
Change of Variables
10
16.6
Change of Variables
11
17.1
Vector Fields
12
17.1
Vector Fields
13
17.2
Line Integrals
14
17.2
Line Integrals
15
17.3
Conservative Vector Fields
16
17.3
Conservative Vector Fields
17
17.4
Parametrized Surface
18
17.4
Parametrized Surface
19
17.5
Surface Integrals
20
18.1
Green's Theorem
21
18.1
Green's Theorem
22
18.2
Strokes' Theorem
23
18.2
Stokes' Theorem
24
18.2,3
Stokes' Theorem, Divergence Theorem
25
18.3
The Divergence Theorem
26
18.3
The Divergence Theorem

Comments

1) The section on polar coordinates should be used to emphasize areas inside polar curves, as a preview of polar double integrals and cylindrical coordinates, and not arcane polar coordinate curves.

2) The sections on Green's Theorem, Stokes' Theorem, and the Divergence Theorem are extremely important. Time must be left to cover these sections in detail.

Outline update: R. Brown, 8/12
For more information, please contact Student Services, ugrad@math.ucla.edu.
 

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