Mathematics 13
Winter 2004
tentative
Syllabus
| Day |
Date |
Topic
|
Sections in text |
Homework
|
| 1 |
1-5 |
Review vectors,
dot and cross products, lines, planes, determinants. Matrix
multiplication |
1.1-1.6 |
webwork and Section
1.3: 11; Section 1.6: 11 |
| 2 |
1-7 |
Polar, cyclindrical
and spherical coordinates. (Standard bases will not
be covered.) |
1.7 |
webwork and 1.7:
19, 23, 25, 31, 33 |
| 3 |
1-9 |
Review functions
of several variables |
2.1-2.3 |
webwork |
| 4 |
1-12 |
Derivative of vector-valued
functions |
2.3 |
webwork and 2.3:
21, 23, 25, 35(a) |
| 5 |
1-14 |
Chain rule |
2.4, 2.5 |
webwork and 2.5:
15, 17, 19 |
| 6 |
1-16 |
Directional derivatives
and the gradient, start curves |
2.6, start 3.1 |
webwork |
No class Monday the 19th. Class
meets Tuesday the 20th during X-hour.
| 7 |
1-20 |
More curves, arc length
parametrizations |
3.1, 3.2 |
webwork and 3.2: 3. Also,
find the arc length or unit speed parametrization of the curve
in this problem. Answer: x(s) = the expression
for x(t) given in the problem, but replace t with (s/2
+ 1)^(2/3) - 1. |
| 8 |
1-21 |
Vector fields |
3.3 |
webwork |
| 9 |
1-23 |
Divergence, Curl,
Gradient and the Del operator |
3.4 |
webwork and 3.4: 13, 14. |
| 10 |
1-26 |
Intro to Volumes, Cavalieri's
principle |
5.1 |
webwork and 5.1: 7,
13
|
| 11 |
1-28 |
Double integrals |
5.2 |
webwork |
| 12 |
1-30 |
More double integrals |
5.2 |
webwork and 5.2: 5,
7, 11, 13 |
Last quarter's first math 13 test is here.
Here are some suggested review problems
from the book: 1.8: 13, 15, 17; 2.5: 13;
3.2: 12; 3.3: 17, 23; 3.4: 5,
7, 11(Can the vector in this problem be the curl of some vector field?)
5.1: 3, 7; 5.2: 3.
| 13 |
2-2 |
Changing the order of integration |
5.3 |
webwork and 5.3: 9, 13 |
| 14 |
2-4 |
Triple integrals |
5.4 |
webwork and 5.4: 11, 13,
21 |
| 15 |
2-6 |
Change of variables |
5.5 |
webwork and 5.5: 9, 11,
15, 17, 21 |
| 16 |
2-9 |
More change of variables |
5.5 |
webwork. Optional problem: Find
the volume of the solid {(x,y,z): (x/(1+z^3))^2 + (y/(1 - z^3))^2 < or = 1, -1 < z < 1} by changing variables, and check your work by using Cavalieri's principle. |
| 17 |
2-10 |
Applications of multiple integrals |
5.6 |
webwork and 5.6: 9, 17 |
| 18 |
2-11 |
Scaler and vector line integrals |
6.1 |
webwork and 6.1: 20 (answer:
25 (pi - 2) ) |
| 19 |
2-16 |
More Scaler and vector line integrals |
6.1 |
webwork and 6.1: 15 |
| 20 |
2-18 |
Green's theorem |
6.2 |
webwork and 6.2: 13, 15 |
| 21 |
2-20 |
Conservative vector fields |
6.3 |
webwork and 6.3: 13 |
| 22 |
2-23 |
Parametrized surfaces |
7.1 |
webwork |
| 23 |
2-25 |
Areas of surfaces |
7.1 |
webwork |
| 24 |
2-27 |
Surface integrals |
7.2 |
webwork and 7.2: 1, 5, 7, 11 |
| 25 |
3-1 |
Stokes's theorem |
7.3 |
webwork and 7.3: 3, 5 |
| 26 |
3-3 |
Stoke's and Gauss's theorems |
7.3 |
webwork |
| 27 |
3-5 |
Stoke's and Gauss's theorems |
7.3 |
webwork |
Some review problems from the book covering material
from the latter part of the course that might help you prepare for the final:
5.6: 3, 11; 5.7: 5, 13; 6.2: 1; 6.4: 11; 7.2:
3; 7.3: 1, 7; 7.5: 1a, 2(Just set up the integral. answer: Integral
of theta from 0 to 2 pi , integral of z from -a to a of (1 + 2z^2)^.5 ) ),
8(answer: (4 pi/3)(2^1.5 - 1))
Most of an old math 13 final
is here. (There were two more questions on this
final involving material we did not cover.)