# Math 221: Chapter 16 Study Guide

1. Find div F and curl F. Look at problems 16.1.13-18
2. Find the parametrization for a curve and then evaluate a line integral along the curve . Look at problems 16.2.21-24.
3. Evaluate the line integral. Two parts, one is with respect to the arclength parameter, the other is with respect to x and y. Look at problems 16.2.7-18
4. Show that the integral is independent of path and find its value. Look at problems 16.3.9-14
5. Show that the vector field is conservative and find a potential function for it. Look at problems 16.3.1-6.
6. Evaluate the closed line integral using Green's Theorem. Assume that the curve C is oriented counterclockwise. Look at problems 16.4.3-13
7. Determine if the vector field is free from sources and sinks. If it is not, then find the sources and the sinks. Look at problems 16.7.27-30.
8. Evaluate the surface integral where the surface is defined parametrically. Look at problems 16.5.27-30
9. Evaluate the surface integral. Look at problems 16.5.1-10
10. Evaluate the flux of F across a surface. Look at problems 16.6.7-12
11. Use the Divergence Theorem to evaluate the surface integral F dot n. Look at problems 16.7.5-15
12. Use Stoke's Theorem to evaluate the integral. Look at problems 16.8.7-14

## Notes:

• Some of the problems are either directly from the text or very similar to problems from the text.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 Total 10 6 14 8 8 8 6 8 8 8 8 8 100