Math 321 Assignment 1
This assignment is due in class on Friday January 17.
1. (20 pts) Let f : [0, 1] R be dened by
cfw_
1/q if x is rational, x = p , p, q Z, q > 0, p and q have no common divisors ,
q
f (x) =
0
if x is not rational.
Is f integrable? Pro
Math 321
Review
December 2011
Note: This le might contain typos and/or errors. Use it at your own risk.
Answers
2. 2
3. 0
1
4.(a) B = , dened for = 0, i.e. away from z-axis,
(b) B = 0, (c) i. 2, ii. 0, iii. 2
5. 4/3
6. 3L3
7.(a) dened for r = 0, (b) v = 0
Math 321
Review
December 2011
Vector calculus
1. Prove the identity
2. Calculate
C
(v w) = w (
v) v (
w).
x + 3y dx + 2x y 2 dy, where C is the ellipse x2 + 2y 2 = 2.
3. Let C be a closed curve not passing through the origin and let be a
constant. Comp