course information          


    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.


Question-answering sessions Sat., Jan 29, 1:00 to 2:30 and 3:00 to 4:30 in Bradley 105. 
Here are some practice problems that may help you prepare for the test.
 The first exam on Sunday, Jan 30, in Bradley 101, from 6:00 to 8:00pm, covers up to and including day 10.  No triple integrals involving cylindrical or spherical coordinates will be on Sunday's test.
Solutions to first exam.
   
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

Tutorial on Sunday the 6th is from 1:00 to 3:00, not 7:00-9:00 as usual.
No class Friday the 11th and no tutorial Thursday the 10th.

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

     The second exam on Tuesday,  March 1, in Bradley 101, from 6:00-8:00pm, covers days 11 through 22.  
Question-answering session Monday, 2/28 from 5:30 PM to 8:30 PM in Bradley 102. 
Here are some practice problems that may help you prepare for the test.
Solutions to second exam.

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.

 Final exam: Sat, 3/12, 3:00-6:00, in Moore B03.