1. | (due 9/4) as many as needed from 15.3 # 13-38, including at least # 17-24, 30-34, 37, 38 |
2. | (9/4) 15.3 # 68(d)-(f), 69, 70(a), 70(c) |
3. | (9/4) 15.1 # 6, 21-22, 24-27, 29-30, 32, 34, 63, 64 |
4. | (9/4) 15.3 # 41-44, 77 |
5. | (9/4) 15.4 # 4, 5, 12, 15 (for 12 and 15, just find L(x,y), no need to explain why the function is differentiable), 19, 25, 27, 28, 31, 32, 34 |
6. | (9/20) 15.5 # 4, 5, 9, 12-14, 22, 23, 26, 39, 43-44 |
7. | (9/20) 15.6 # 6, 8, 10, 12, 15, 16, 18, 20, 22, 27-29, 37(a)(b), 41, 42, 48, 51 |
8. | (9/20) 15.7 # 27, 29, 32, 39, 41 |
9. | (9/20) 15.8 # 3-5, 29, 30 |
10. | (10/4) 16.2 # 4, 5, 9, 10, 15, 26, 28 |
11. | (10/4) 16.1 # 2, 3, 11-14 |
12. | (10/4) 16.3 as many as needed of 1-28, including at least 5, 6, 10, 15, 16, 21, 24, 27, as many as needed of 37-48 including at least 37, 39, 45, 47 |
13. | (10/4) 16.4 # 7-12, 17, 19-23, 25, 29-30 |
14. | (10/18) 16.5 as many as needed of 3-14, including at least 5, 10, 12-14 |
15. | (10/18) 16.6 # 3-5, 7, 9, 10, 21 |
16. | (10/18) 16.7 # 7, 11, 16, 19, 27, 39(a)(b) |
17. | (10/18) 16.8 # 11, 12, 17, 20, 21, 25, 35, 36 |
18. | (10/18) 16.9 # 2, 3, 4 |
19. | (11/8) 17.1 # 1, 2, 5, 6, 9, 29-32 |
20. | (11/8) 17.2 # 2-6, 13, 14, 17-20, 31, 32 |
21. | (11/8) 17.3 # 1, 2, 5, 6, 8, 12, 14, 18, 19, 27, 33 |
22. | (11/8) 17.4 # 9, 11, 12, 14, 15, 19 |
23. | (11/27) 17.5 # 12 |
24. | (11/27) 17.5 # 3, 5, 9, 13, 16, 18-20, 28, 35 |
25. | (11/27) 17.6 # 2, 3, 17, 21, 22, 35, 36, 45 |
26. | 17.7 # 5, 7, 9, 13 (follow the model of example 2 of section 17.7), 15 (parameterize the cylinder as x = 3 cos(u), y = 3 sin(u), z = v for 0\leq u \leq 2\pi, 0 \leq v \leq 2), 16 |
27. | 17.7 # 19 (use formula 8 of section 17.7), 21 (since the downward orientation is used, one must negate the expression in formula 8), 22 |
27. | 17.7 # 23 (use the parameterization x=2 sin(\phi)cos(\theta), x=2 sin(\phi)sin(\theta), z=2 cos(\phi), dS = 4 sin(\phi) dR, 24 (same hint), 26 (done in class), 35 (M_{xy} is the surface integral of the function z) |
28. | 17.8 # 3, 5, 8, 14, 15 |
29. | 17.9 # 3, 5, 6, 9, 23, 24, 25 |