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