## Exercise 9a

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