**Math 3593H Honors Mathematics II Spring Semester 2009
**

The final exam is on Monday May 11, 1:30-4:30pm in a room to be announced. It might not be the usual classroom. I am getting information about the classroom from

http://www.math.umn.edu/undergrad/

and at the moment it says the information will be available late in the semester.

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.

Section 6.12: We have already done questions like 1, 2, 5 and I am going to steer clear of things like question 3 which go into physics.

Extra Question*: 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

This has been a great year and it has been a real pleasure and a privilege to teach you!