Section |
pages |
I.S. |
Recall the handout with hints to assorted problems from Chapter 7. Surely you will use these solutions wisely: giving a problem a good honest shot before looking at the solution. I expect you to review a solution before asking a question in class. |
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| 7.0 | 7.a | Read the following about paths & curves:
2.6 and 7.a from the Informal Summary,
from the bottom of page 406 through ex 7 on page 408,
from the middle of page 412 through the middle of page 413.
Read the 3 page handout with comments on 1997 Quiz 6, which is the first few pages of the handout containing hints on Ch 7 homework. |
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| 7.1 | 400 | 7.b | 3, 4, 7a, 9, 10, 12, 13 |
| 7.2 | 402 | 7.c | read examples 1-9, 11, 12 from this section |
| 7.2 | 417 | 7.c | 1, 3, 4, 10, 11, 12, 14, 17 |
| 7.2 | 420 | 7.c | Problem 18 is unrealistic. So instead of doing this problem, figure out why it is unrealistic. Hint: look at the speed of the biker. For help, look at the Maple worksheet ch7s2n18.mws. |
| 7.3 | 427 | 7.d | 3, 4, 5, 6(ellipsoid), 7, 10b, 12 (a-7.d.2, b-2.11part 1, c-2.11part2). Hint: helpful on some is 7.f.2. |
| 7.4 | 438 | 7.e | 1, 2, 4(just using formula (3)), 6, 9, 20 (coupler = sphere minus what is bored out). Hint: helpful on some is 7.f.2. |
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| 7.5 | 466 | 7.e | 1 (it's a 4 sided surface with vertices
(1,0,0), (1,1,0), (0,0,1),(0,0,0)),
3(easier way than in SG is to use 7.d.5 and do two ways using 2 different parameterizations of the hemisphere), 4(ans: 0), 5, 7, 8, 9(without loss of generality, (x_0,y_0,z_0) can be any point on the sphere (why?) so pick a point that makes integration do-able), 10, 11, 19. Hint: Helpful on several is 7.f.2 |
| 7.6 | 460 | 7.f&g | 4(enclosed surface, ans: pi),
6(open surface, ans: -16pi), 7(enclosed surface, outward pointing normal, ans: 2pi) 8, 9, 15(open surface, outward pointing normal, hint: use symmetry to cancel some of the integral), 16(open cone, outward pointing normal), 17(open surface, outward pointing normal, ans: (2*pi*a^3bc)/5, hint: PHI(theta, phi) = a*sin(phi)cos(theta) i + b* sin(phi)sin(theta) j + c*cos(phi) k) |
| Ch 7 Review | 462 | 7.a-h | 1, 3, 4(ans: 0), 5,
6(ans: 8a^2, hint: use symmetry), 7b, 9(hint: x^2+(y/2)^2 = z^2), 10, 12a (ans: sqrt(3)/6), 12b, 13, 15, 16, 17(hint: 7.c.6), 18(open surface, ans: 2pi*r^2), 19, 21, 22(open surface, ans: -15pi/2, can also use Gauss' Thm), 23, 24, 26(open surface, ans: 2pi), 27 (open surface) |
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