**Math 3593H Honors Mathematics II Spring Semester 2006
**

Exercises:

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

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.