Math 32A: General Course Outline
Catalog Description
    32A. Calculus of Several Variables. (4) Lecture, three hours; discussion, one hour. Requisite: course 31B with a grade of C- or better. Introduction to differential calculus of several variables, vector field theory. P/NP or letter grading.
Textbook
    J. Stewart, Calculus, 6th Ed., Thomson Learning.
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
13.1
Three Dimensional Coordinate Systems
2
13.2
Vectors
3
13.3
Dot Product
4
13.4
Cross Product
5
13.5
Equations of Lines and Planes
6
11.1
Curves defined by parametric equations
7
14.1
Vector Functions
8
14.2
Derivatives and Integrals of Vector Functions
9
14.3
Arc-length and curvature
10
14.4

Motion in space (Kepler's Laws)

11
15.1
Functions of several variables
12
13.6
Cylinders and quadric surfaces
13
15.2
Limits and Continuity
14
15.2
Limits and Continuity
15
15.3
Partial Derivatives
16
15.3
Partial Derivatives
17
15.4
Tangent Planes and Linear Approximation
18
15.4
Tangent Planes and Linear Approximation
19
15.5
Chain Rule
20
15.5
Chain Rule
21
15.6
Directional Derivatives and the Gradient Vector
22
15.6
Directional Derivatives and the Gradient Vector
23
15.7
Maximum and Minimum Values
24
15.7
Maximum and Minimum Values
25
15.8
Lagrange Multipliers
26
15.8
Lagrange Multipliers
Comments
1) Some problems may refer to polar coordinates. One only need inform the students that x = r cos q and y = r sin q. Polar coordinates are done in detail in 32B in order to help with areas, double integrals, etc.
2) The first two of Kepler's Laws should be done if at all possible.
3) There are two lectures on limits and continuity, in order to introduce the concepts of open, closed sets, etc.
Outline update: J. Ralston, 8/08
For more information, please contact Student Services, ugrad@math.ucla.edu.
 

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