Math 3593H Honors Mathematics II Spring Semester 2006

Assignment 13 - Due Thursday 4/27/2006.

Read: Hubbard and Hubbard Section 6.10.

Section 6.10 (pages 656-658): 1*, 2, 4, 5*, 6*, 9, 10, 11, 12(use the hint), 13, 14.
For question 1, locate from somewhere a formula for the volume of a torus.
The way I see to do question 3 it is a standard result to do with centers of mass, which we have not done; thus I omit this question.
Extra Question1: Something seems to be wrong with questions 7 and 8 from Section 6.10. Determine which question is correct, or whether both are correct.
Extra Question 2*: Let B be the half of the unit ball in 3-dimensional space specified by . Let S be the surface which is the boundary of B, so S is the union of a unit disc D in the xy-plane and the upper half T of the surface of a sphere. Let S, T and D be oriented by the normal pointing outward from B. By calculating integrals over D and B, compute the flux of F through T, where F is the vector field

On April 27 the third mid-term exam will be on sections 6.1 - 6.9. On this exam you may use a calculator, but no books or notes. You may have the suspicion that I only let you use a calculator when I think it will be of no use at all to you. This suspicion is probably justified!

Apart from the final section 6.11, in the remaining time I will discuss Newton's theorem about the gravitational field around a spherically symmetric body (not in the book) and perhaps also do one of the topics we missed out earlier on in the semester, such as Section 3.8 on curvature.