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UCLA Department of Mathematics
32A. Calculus of Several Variables
. Lecture, three hours; discussion, one hour. Requisite: course 31B (C- or better). Introduction to differential calculus of several variables and vector field theory.J. Marsden & A. Tromba, Vector Calculus, 4th Ed., Freeman
The following schedule, with textbook sections and topics, is based on 24 lectures. The remaining five classroom meetings (only four in Winter Quarter) are for leeway, reviews, and midterm exams. These are scheduled by the individual instructor. Often there are reviews and midterm exams about the beginning of the fourth and eighth weeks of instruction, plus reviews for the final exam.
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Lecture |
Section |
Topics |
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1-6 |
1.1,2,3, 5 |
Vectors, Determinants, Cross Products & Inner Products |
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7 |
2.1 |
Functions of Several Variables |
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8-10 |
2.2,3 |
Limits and Differentiability |
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11 |
1.1-1.3,1.5,2.1-2.3 |
Review |
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12 |
1.1-1.3,1.5,2.1-2.3 |
Midterm 1 |
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13 |
2.4 |
Paths |
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14 |
2.5 |
Properties of the Derivative |
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15 |
2.6 |
Gradients & Directional Derivatives |
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16 |
3.1 |
Iterated Partials |
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17 |
3.2 |
Taylor's Theorem |
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18,20 |
3.3 |
Max/Min |
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21-22 |
3.4 (3.6) |
Constrained Max/Min and possibly Applications |
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23 |
2.4-2.6,3.1-3.4(3.6) |
Review |
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24 |
2.4-2.6,3.1-3.4(3.6) |
Midterm 2 |
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25 |
4.1 |
Acceleration |
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26 |
4.2 |
Arc Length (look at exercises for further material) |
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27 |
4.3 |
Vector Fields |
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28-29 |
4.4 |
Divergence and Curl |
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30 |
all |
Review |
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* Can be omitted if instructor feels that more time is needed to cover chapter 1 and chapter 2.2-3.
Outline update: P. Petersen, 6/00; modified by Andrea Brose, 12/00
Class Home Page |
Andrea Brose's Home |
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UCLA |
NOTE: Have TA cover polar coordinates during first discussion section.