18.02 Problem Set 11
Due Thursday 11/20/08, 12:45 pm in 2106.
Part A
(10 points)
Hand in the underlined
problems only; the others are for more practice.
Lecture 30. Thu Nov. 13
Vector fields in 3D; surface integrals and flux.
Read: Notes V8, V9.
Work: 6A/ 1, 2, 3
, 4; 6B/ 1
, 2
, 3
, 4, 6
, 8
.
Lecture 31. Fri Nov. 14
Divergence theorem.
Read: Notes V10; 15.6.
Work: 6C/ 1a, 2, 3
, 5
, 6, 7a
, 8
.
Lecture 32. Tue Nov. 18
Divergence theorem continued: applications and proof.
Read: Notes V10; 15.6, and pp. 1054–1055 about heat flow.
Part B
(31 points)
Directions:
Attempt to solve
each part
of each problem yourself. If you collaborate,
solutions must be written up independently. It is illegal to consult materials from previous
semesters. With each problem is the day it can be done.
Write
the names of all the people you consulted or with whom you collaborated and
the resources you used.
Problem 1.
(Thursday, 4 points: 2+2)
Surface area on the sphere.
a) What percentage, rounded to the nearest percent, of the Earth’s surface is north of
Boston? The latitude here is 42
◦
. See (8) p. 842 to convert
φ
to latitude.
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 Fall '08
 Auroux
 Integrals, Vector Calculus, Southern Hemisphere, Vector field, one degree

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