## Math 221 - Chapter 18 Study Guide

- Sketch the vector field by drawing some typical non-intersecting vectors. The vectors need
not be drawn to the same scale as the coordinate axes, but they should in the correct
proportion to each other. Look at problems 18.1.1-4*
- Find div
**F** and curl **F**. Look at problems 18.1.5-10*
- Evaluate the line integral. Two parts. Look at problems 18.2.3-6*, 9-19*
- Show that the integral is independent of path and find its value. Look at problems 18.3.9-14*
- Show that the vector field is conservative and find a potential function for it. Look at
problems 18.3.29-34*
- Evaluate the closed line integral. Assume that the curve C is oriented counterclockwise.
Look at problems 18.4.3-13*
- Evaluate the closed line integral using Green's Theorem. Assume that the curve C is oriented
counterclockwise. Look at problems 18.4.3-13*
- Evaluate the surface integral. Look at problems 18.5.25-28*
- Evaluate the surface integral. Look at problems 18.5.1-6*
- Evaluate the flux of
**F** across a surface. Look at problems 18.6.5-15*
- Use the Divergence Theorem to evaluate the surface integral
**F** dot **n**. Look at problems
18.7.1-13*
- Use Stoke's Theorem to evaluate the integral. Look at problems 18.8.1-8*

### Notes:

- *'d problems are directly from the text.

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

Pts |
4 |
8 |
16 |
8 |
8 |
8 |
8 |
8 |
8 |
8 |
8 |
8 |
100 |