- 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
.
Math 13 Winter 1999
1999-03-02