THE COLLEGE OF STATEN ISLAND, CUNY
DEPARTMENT OF MATHEMATICS
MATH 233 -- CALCULUS III
COURSE OUTLINE
Text: Rogawski, Calculus -- Early Transcendentals,
W. H. Freeman & Co. (2008)
ISBN-13: 978-1-4292-1073-7
ISBN-10: 1-4292-1073-7
Note: Below, each lesson corresponds to a one-hour class. Homework problems in bold correspond to similar WeBWorK problems, which must be submitted online.
Note: Students are also required to complete four MATLAB projects listed below.
|
Lesson |
Section |
Topic |
Homework Problems |
|
1
|
12.1 12.2 |
Review: Vectors
|
12.1/ 35, 39, 49, 51 12.2/ 13, 25, 39, 51 |
|
2
|
12.3 12.4 |
Review: Dot product Review: Cross product |
12.3/ 25, 35, 43, 49, 61 12.4/ 15, 19, 23, 27, 47 |
|
3 |
12.5 |
Review: Planes in three-space |
3, 13, 15, 21, 31 |
|
|
12.6
|
Quadric surfaces
|
15, 17, 21, 33, 35 |
|
5 |
13.1 |
Vector-valued functions |
11, 15, 18, 22, 27, 31, 37 |
|
6 |
13.2 |
Calculus of vector-valued functions |
11, 13, 19, 27, 29, 44, 45, 49, 55 |
|
7
|
13.3 13.4 |
Arc length and speed Curvature |
13.3/ 1, 3, 9, 11, 16, 17, 19, 20 13.4/ 1, 7, 11, 17, 34, 49 |
|
8
|
13.5
|
Motion in three-space
|
3, 5, 8, 15, 16, 17, 19, 31, 48 MATLAB Project 2 |
|
9 |
14.1 |
Functions of several variables |
3, 6, 7, 15, 19, 21 |
|
10
|
14.2
|
Limits and continuity in several variables |
1, 6, 9, 13, 17, 32 |
|
11 |
14.3 |
Partial derivatives |
3, 19, 22, 24, 25, 41, 47, 53, 64 |
|
12 |
14.3 cont'd |
|
|
|
13 |
|
Review |
|
|
14 |
|
Review |
|
|
15 |
|
Exam 1 |
|
|
16 |
|
Exam 1 |
|
|
17
|
14.4
|
Differentiability and tangent planes
|
1, 5, 6, 15, 17, 19, 23, 31, 35, 39 MATLAB Project 3 |
|
18 |
14.5 |
Gradient and directional derivatives |
1, 5, 7, 23, 25, 35 |
|
19 |
14.5 cont'd |
|
|
|
20 |
14.6 |
Chain rule in several variables |
1, 2, 5, 9, 19, 25, 33, 35, |
|
21 |
14.6 cont'd |
|
|
|
22 |
14.7 |
Optimization in several variables |
5, 15, 19, 25, 29, 30, 39, 42 |
|
23 |
14.7 cont'd |
|
|
|
24 |
14.8 |
Lagrange multipliers |
5, 11, 15, 17, 19, 21, 26, 35 |
|
25 |
14.8 cont'd |
|
|
|
26 |
15.1 |
Integration in several variables |
1, 7, 19, 25, 31, 39, 42, 44 |
|
27 |
15.1 cont'd |
|
|
|
28 |
15.2 |
Double integrals over general regions |
1, 7, 17, 29, 36, 41, 46, 55 |
|
29 |
15.2 cont'd |
|
MATLAB Project 4 |
|
30 |
15.3 |
Triple integrals |
3, 7, 16, 19, 23, 29, 37 |
|
31 |
15.3 cont'd |
|
|
|
32 |
12.7 |
Cylindrical and spherical coordinates |
1, 7, 21, 27, 31, 37, 45 |
|
33
|
15.4
|
Integration in polar, cylindrical, spherical coordinates |
3, 15, 23, 27, 31, 42 |
|
34 |
15.5 |
Change of variables |
3, 4, 13, 17, 21, 25, 29 |
|
35 |
15.5 cont'd |
|
|
|
36 |
|
Review |
|
|
37 |
|
Review |
|
|
38 |
|
Exam 2 |
|
|
39 |
|
Exam 2 |
|
|
40 |
16.1 |
Vector fields |
1, 3, 15, 17, 26, 27, 29 |
|
41 |
16.2 |
Line integrals |
1, 5, 13, 17, 21, 25, 33, 40, 41 |
|
42 |
16.2 cont'd |
|
|
|
43 |
16.3 |
Conservative vector fields |
5, 9, 13, 17, 21, 23, 24 |
|
44 |
16.3 cont'd |
|
|
|
45
|
16.4
|
Parametrized surfaces and surface integrals |
3, 14, 19, 23, 27, 31, 36, 41 |
|
46 |
16.4 cont'd |
|
|
|
47 |
16.5 |
Surface integrals of vector fields |
3, 7, 11, 15, 18, 23, 28 |
|
48 |
16.5 cont'd |
|
|
|
49 |
17.1 |
Green's Theorem |
3, 9, 13, 22, 23, 27, 28 |
|
50 |
17.1 cont'd |
|
|
|
51 |
17.2 |
Stokes' Theorem |
3, 7, 13, 17, 19, 21, 23 |
|
52 |
17.2 cont'd |
|
|
|
53 |
17.3 |
Divergence Theorem |
3, 7, 11, 15, 22, 25 |
|
54 |
17.3 cont'd |
|
|
|
55 |
|
Review |
|
|
56 |
|
Review |
|