# Math 221: Chapter 16 Study Guide

- Find div
**F** and curl **F**. Look at problems 16.1.13-18.
- Find a parametrization for the given curve and use it to evaluate the line integral. Look at problems 16.2.21-24.
- Evaluate the line integrals. Two parts. Look at problems 16.2.7-10 and 16.2.11-18.
- Show that the integral is independent of path and find its value. Look at problems 16.3.9-14.
- Show that
**F** is conservative and find a potential function for it. Look at problems 16.3.1-6.
- Use Green's theorem to evaluate the line integral. Look at problems 16.4.3-13.
- Evaluate the surface integral over the surface represented by a vector valued function
**r**. Look at problems 16.5.27-30.
- Evaluate the surface integral. Look at problems 16.5.1-10.
- Find the flux of the vector field
**F** across the surface. Look at problems 16.6.7-12.
- Use the Divergence Theorem to find the flux of
**F** across the surface σ with outward orientation. Look at problems 16.7.5-15.
- Use Stoke’s Theorem to evaluate the integral. Look at problems 16.8.7-14.

## Notes

- Most of the the problems are directly from the text.
- Show work, but you may use Derive to evaluate the integrals.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
Total |

Pts |
12 |
8 |
16 |
8 |
8 |
8 |
8 |
8 |
8 |
8 |
8 |
100 |