- 1.
- Stewart, Section 14.9, Exercises 3, 12, 17, 18, 21, 22, 23.
- 2.
- Let
, where
,
, and
are positive constants. Find the surface integral of
over
the surface shown, with the given unit normal.

[Drawing: omitted. The drawing depicts a surface that encloses the origin, and has a ``tail'' that curves back over towards the origin, intersects the surface and then encloses the origin again for a second time.]

- 3.
- Let
be the same as in Exercise 2, and let
be the curve
oriented in the anti-clockwise direction when viewed from
above.
- (a)
- Calculate directly the flux of through the bottom half of the unit sphere, with unit normal pointing towards the origin.
- (b)
- Use the divergence theorem to show that if if is any oriented surface with oriented boundary , and does not intersect the non-negative part of the -axis, then the flux of through is .