- Stewart, Section 14.8, Exercises 1, 2, 10, 19.
- Show by direct calculation that the conclusion of Stokes
Theorem does not hold for
- Find the gradient of
. Find the curl of
- Show that
, everywhere except on the
non-negative part of the -axis, where
are strictly positive constants.
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
- (Optional) Suppose
is a vector field with
, everywhere in -space. Define
in terms of
are arbitrary constants. Show by direct calculation that
everywhere in -space.
Math 13 Winter 1999