- 1.
- Stewart, Section 14.8, Exercises 1, 2, 10, 19.
- 2.
- Show by direct calculation that the conclusion of Stokes
Theorem does not hold for
.
- 3.
- Let
,
- (a)
- Find the gradient of . Find the curl of .
- (b)
- Show that
, everywhere except on the
non-negative part of the -axis, where
- (c)
- Let
be the curve
oriented in the
anti-clockwise direction when viewed from above. Use Stokes theorem
to show that if
is any oriented surface with oriented boundary , and
does not intersect the non-negative part of the , then

- 4.
- (Optional) Suppose
is a vector field with
, everywhere in -space. Define
in terms of
by