Math 32A: General Course Outline
Catalog Description
    32A. Calculus of Several Variables. (4) Lecture, three hours; discussion, one hour. Requisite: course 31A with a grade of C- or better. Introduction to differential calculus of several variables, vector field theory. 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
13.1
Vectors in the Plane
2
13.2
Vectors in Three Dimensions
3
13.3
Dot Product
4
13.4
Cross Product
5
13.5
Planes in Three-Space
6
12.1
Curves Defined by Parametric equations
7
14.1
Vector-Valued Functions
8
14.2
Calculus of Vector-Valued Functions
9
14.3,4
Arc-Length and Speed; Curvature
10
14.4,5

Motion in Three-Space; Planetary Motion

11
15.1
Functions of Two or More Variables
12
13.6
A Survey of 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
Differentiability and Tangent Planes
18
15.4
Differentiability and Tangent Planes
19
15.5
Gradient and Directional Derivatives
20
15.5
Gradient and Directional Derivatives
21
15.6
Chain Rule
22
15.6
Chain Rule
23
15.7
Optimization
24
15.7
Optimization
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: R. Brown, 8/12
For more information, please contact Student Services, ugrad@math.ucla.edu.
 

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