Mathematics 13
Winter 2004
tentative
Syllabus
Day 
Date 
Topic

Sections in text 
Homework

1 
15 
Review vectors,
dot and cross products, lines, planes, determinants. Matrix
multiplication 
1.11.6 
webwork and Section
1.3: 11; Section 1.6: 11 
2 
17 
Polar, cyclindrical
and spherical coordinates. (Standard bases will not
be covered.) 
1.7 
webwork and 1.7:
19, 23, 25, 31, 33 
3 
19 
Review functions
of several variables 
2.12.3 
webwork 
4 
112 
Derivative of vectorvalued
functions 
2.3 
webwork and 2.3:
21, 23, 25, 35(a) 
5 
114 
Chain rule 
2.4, 2.5 
webwork and 2.5:
15, 17, 19 
6 
116 
Directional derivatives
and the gradient, start curves 
2.6, start 3.1 
webwork 
No class Monday the 19th. Class
meets Tuesday the 20th during Xhour.
7 
120 
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 
121 
Vector fields 
3.3 
webwork 
9 
123 
Divergence, Curl,
Gradient and the Del operator 
3.4 
webwork and 3.4: 13, 14. 
10 
126 
Intro to Volumes, Cavalieri's
principle 
5.1 
webwork and 5.1: 7,
13

11 
128 
Double integrals 
5.2 
webwork 
12 
130 
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 
22 
Changing the order of integration 
5.3 
webwork and 5.3: 9, 13 
14 
24 
Triple integrals 
5.4 
webwork and 5.4: 11, 13,
21 
15 
26 
Change of variables 
5.5 
webwork and 5.5: 9, 11,
15, 17, 21 
16 
29 
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 
210 
Applications of multiple integrals 
5.6 
webwork and 5.6: 9, 17 
18 
211 
Scaler and vector line integrals 
6.1 
webwork and 6.1: 20 (answer:
25 (pi  2) ) 
19 
216 
More Scaler and vector line integrals 
6.1 
webwork and 6.1: 15 
20 
218 
Green's theorem 
6.2 
webwork and 6.2: 13, 15 
21 
220 
Conservative vector fields 
6.3 
webwork and 6.3: 13 
22 
223 
Parametrized surfaces 
7.1 
webwork 
23 
225 
Areas of surfaces 
7.1 
webwork 
24 
227 
Surface integrals 
7.2 
webwork and 7.2: 1, 5, 7, 11 
25 
31 
Stokes's theorem 
7.3 
webwork and 7.3: 3, 5 
26 
33 
Stoke's and Gauss's theorems 
7.3 
webwork 
27 
35 
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.)