MATH 293, Homework 15, "due" 12/11/96 
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
(nothing to hand in)

Sergei will write up solutions to some representative problems.
Copies of these will be available in Thurston 102 by 5 PM
on Monday December 9, 1996.

*) Review chapter 12.1,3,4,5,7,9 on partial derivatives and 
   gradients of scalar functions of 2 and 3 variables
   (if you have not done so already).  For the material
   in chapter 14 you need to know at least the following:
     > partial derivative,
     > gradient,
     > directional derivative (using gradient),
     > normal to a surface (using gradient).

*) Chapter 14.7: "STOKES THM".
   You need to know how to calculate curl of a vector
   field.  Given the curl you need to be able to do surface
   integrals based on the result (nothing new in doing
   these, just a new integrand).  You are not expected 
   to remember Stoke's Theorem.  However, the homework 
   problems in chapter 14 are good practice for surface 
   and path integrals.  Also, Stokes Theorem reduces to 
   Green's Theorem in the plane, and you are expected to 
   know that.
    
*) Chapter 14.8: DIVERGENCE THEOREM
   You should be able to do most of the problems in
   this section.

*) Pgs 1134-1139 (Chapter 14)  give additional problems 
   that might be helpful for study.  Some of the "additional 
   exercises-theory,  examples, applications" are good 
   test-like problems. (Similarly, problems on 
   pgs 1056-1060 provide a review for Chapter 13)