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)