MATH 550

Professor Girardi

Chapter 8 Homework

Section

pages

I.S.

 Recall the handout with hints to assorted problems from Chapter 8 Review. 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.
8.1 476 8.ab.1 1, 2, 3b, 5(see ex 4 p 126), 13, 15
8.2 490 8.ab.2 1 (try doing without Stokes' Thm just far enough to convince yourself that it is a computational nightmare),
4(see ex 5 p 490),
5(think of dividing S into 2 or 3 elementary Stokes' Surfaces),
9 (there is a mistake in key - can you find it? BTW: there is an easier way to do this problem),
10(ans: 0; hint, an ellipsoid is the union of its top&bottom parts),
12(see 7.g.4),
17(hint: see S 8.2 # 10).
8.3 501 8.c 2, 3, 4, 7, 9, 13b, 15b,
23(on 23b: you are not expected to be able to solve such a differential equation ... just read the Study Guide to see the solution.)
8.4 515 8.ab.3 1(hint: 4.3), 3, 5b, 6b
Ch 8 Review 552 8.ab 1, 3, 9, 14, 15, 17, 18, 19
Ch 8 Review 552 8.c 5, 7, 11, 13, 20, 21

Chapter 8 Review - vF denotes the VECTOR F and o denotes dot product and iint denotes double integral

Problem

Do several ways

1
  1. find iint_S (curl vF) o d(vS) by parameterizing S
  2. use iint_S (curl vF) o d(vS) = iint_S [(curl vF) o vn ] dS
  3. use Stokes' Thm
3 & 9
  1. use iint_S vF o d(vS) = iint_S [ vF o vn ] dS = sum_{six sides} iint_{one side} iint_S [ vF o vn ] dS
  2. use Gauss' Thm
14
  1. directly by parameterizing the curve C
  2. use Green's Thm
15
  1. find iint_S vF o d(vS) by parameterizing S
  2. use iint_S vF o d(vS) = iint_S [ vF o vn ] dS
  3. use Gauss' Thm
18 & 19
  1. find int_C vF o d(vs) by parameterizing the curve C
  2. use Stokes' Thm

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