Mathematics 13
Winter 2005
tentative
Syllabus
| Day |
Date |
Topic
|
Sections and pages in text |
Homework
(Do not hand in the starred problems.) |
| 1 | 1-5 |
Review matrices, determinants and derivatives;
general derivative |
1.6 (57-61), 2.3 (126-127) |
p. 41: 10, 18; p. 62: 11*, 12; p. 132:
20, 22, 25 |
| 2 | 1-7 |
Review chain rule; general chain rule |
2.5 (143-153) |
pp. 154-156: 2, 3ab, 5, 17, 19, 20, 22 |
| 3 | 1-10 |
Review directional derivatives and gradient |
2.6 (158-166) |
pp. 171-172: 1*, 3, 4, 11, 12; p. 181: 28ab |
| 4 |
1-12 |
Vector fields, Start Divergence, Curl, Gradient |
3.3 (216-220); 3.4 (222-227) |
pp. 173-174: 17, 22, 23, 31; p. 180: 20; pp.
220-221: 4, 8, 17 |
| 5 |
1-14 |
More Divergence, Curl, Gradient |
3.4 |
pp. 229-231: 3, 4, 9, 11, 13, 14, 15, 17, 20, 28ab |
No class Monday the 17th, and no
tutorial Sunday the 16th.
Instead,
class meets Tuesday the 18th during X-hour, and there
is a tutorial on Monday the 17th.
| 6 | 1-18 |
Introduction to volumes, Start double integrals |
5.1 (299-301) |
p. 302: 2, 5, 8, 10, 12 and problem 1 |
| 7 |
1-19 |
Double integrals |
5.2 (302-308) |
p. 318: 2, 4, 6, 8, 26(a), 27 and
problem 2 |
| 8 |
1-21 |
More double integrals (including areas in polar coordinates) |
5.2 (308-313) |
p. 319: 12, 13, 14, 15, 16; p. 76: 1, 6,
20(a) |
| 9 |
1-24 |
Changing the order of integration |
5.2, 5.3 (320-323) |
p. 355: 18, 19, 20, 21; p. 323: 5,
6, 12, 14 |
| 10 |
1-26 |
Triple integrals |
5.4 (324-332) |
pp. 333-334: 1, 2, 6, 9, 12, 15, 19. p. 356:
23, 25, 27 and problem 3 This assignment is due Monday, Jan. 31. |
| 11 |
1-28 |
Questions, problems, catch-up |
No homework, but day 10's assignment is long. |
| 12 |
1-31 |
Change of variables |
5.5 (334-353) |
p. 354: 2(a), 8, 11, 15, 16; p. 373: 10, 13(Hint:
u=x^2-y^2, v=x^2/4+y^2) |
| 13 |
2-2 |
More change of variables |
5.5 |
p. 356: 24, 26; p. 373: 9, 11, 12 and
problem 4 |
| 14 |
2-4 |
Applications of multiple integrals |
5.6 (356-366) |
pp. 369-370: 4, 9, 17, 18; p. 372: 6
and problem 5 |
| 15 |
2-7 |
Review
parametric curves, arc length; start line integrals |
3.2
(197-199); 6.1 (377-389) |
p.
214: 3, 5, 8; pp 389 -390: 1a, 2, 3, 20 |
| 16 |
2-9 |
Line
integrals |
6.1 |
pp.
389-390: 7, 10, 12, 13, 17, 21 |
| 17 |
2-14 |
Green's
theorem |
6.2 (391-398) |
pp. 398-399:
4, 5, 6(Just evaluate the integral using any method.), 7, 8 and problem 6 |
| 18 |
2-16 |
Green's
theorem |
6.2 |
p. 399:
10, 11(b), 15, 19 and problems 7,8 |
| 19 |
2-18 |
Conservative
vector fields |
6.3 (400-407) |
pp. 409-410:
1, 2(Do part (c) first, and then parts (a) and (b) are easy.), 4, 8,
10, 13*(Don't hand in, answer in back of book), 16(Just evaluate the
integral using any method.) and problem
9 |
| 20 |
2-21 |
Parametrized
surfaces |
7.1 (415-427) |
pp. 428 - 429:
3, 4, 8, 17, 19, 20 |
| 21 |
2-23 |
Scalar surface
integrals |
7.2 (430-445) |
p. 448: 5,
7, 10; p. 485: 7b, 8 and problem
10 |
| 22 |
2-25 |
Vector surface
integrals |
7.2 |
pp. 448 - 449:
3, 4, 15, 18, 21, 22 and problem
11 |
| 23 |
2-28 |
Questions, problems,
catch-up |
||
| 24 |
3-2 |
Stoke's and Gauss's
theorems |
7.3 (449-464) |
pp. 464-465: 4(Just
compute the integral of curl F over S using any method.), 5, 11
and problems 12, 13, 14 |
| 25 |
3-4 |
Stoke's and Gauss's
theorems |
7.3 |
p. 465: 6,
7(For problems 6 and 7, just compute the outward flux of F across
the boundary of D using any method.), 9, 14 and problems 15, 16 |
| 26 |
3-7 |
Stoke's and Gauss's
theorems |
7.3 |
p. 484: 1a, 2 (just
set up the iterated integral with limits of integration); p. 486:
10; p. 465: 12 and problems 17, 18 |
| 27 |
3-9 |
Questions, problems,
catch-up |
Last turorial / Question-answering session
Thursday 7:00-9:00 in Bradley 105.
Here are some practice problems that may help
you prepare for the final.