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.
Assignment 14 - Do not hand this in to be graded, even though some questions are starred. These questions are just to show you what I would suggest.
Read: Hubbard and Hubbard Sections 6.11 and 6.12.
Exercises:
Section 6.11: 1*, 2, 4, 5*, 6*, 7, 8, 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.
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
Comments: We have already discussed much of what is in Section 6.12. If there remains sufficient time I will discuss Newton's theorem about the gravitational field around a spherically symmetric body (not in the book). There will also be a review sheet for the final exam forthcoming.
This has been a great year and it has been a real pleasure and a privilege to teach you!