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)