 
Summary: 18.024ESG Problem Set 8
Pramod N. Achar
Spring 2000
Tuesday
1. Exercises 1 and 2 in Section 10.5 of Apostol, Volume II.
2. Exercise 8 in Section 10.9 of Apostol, Volume II.
Thursday and Friday
3. (a) Show that the vector field f : R2
R2
given by
f(x, y) = (x + y)i + (x  y)j
is conservative, i.e., is the gradient of some scalar field.
(b) Suppose r : [a, b] R2
is a differentiable curve, say
r(t) = f(t)i + g(t)j.
Compute
b
a f · dr in terms of f(a), f(b), g(a), and g(b).
4. Determine whether the following vector fields f : R2
R2
