# Math 221: Chapter 16 Study Guide

- Find div F and curl F. Look at problems 16.1.13-18
- Find the parametrization for a curve and then evaluate a line integral
along the curve . Look at problems 16.2.21-24.
- 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
- Show that the integral is independent of path and find its value. Look
at problems 16.3.9-14
- Show that the vector field is conservative and find a potential function
for it. Look at problems 16.3.1-6.
- Evaluate the closed line integral using Green's Theorem. Assume
that the curve C is oriented counterclockwise. Look at problems 16.4.3-13
- 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.
- Evaluate the surface integral where the surface is defined parametrically.
Look at problems 16.5.27-30
- Evaluate the surface integral. Look at problems 16.5.1-10
- Evaluate the flux of F across a surface. Look at problems 16.6.7-12
- Use the Divergence Theorem to evaluate the surface integral F dot
n. Look at problems 16.7.5-15
- 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

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
Total |

Pts |
10 |
6 |
14 |
8 |
8 |
8 |
6 |
8 |
8 |
8 |
8 |
8 |
100 |