## Math 221 - Chapter 18 Study Guide

1. 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*
2. Find div F and curl F. Look at problems 18.1.5-10*
3. Evaluate the line integral. Two parts. Look at problems 18.2.3-6*, 9-19*
4. Show that the integral is independent of path and find its value. Look at problems 18.3.9-14*
5. Show that the vector field is conservative and find a potential function for it. Look at problems 18.3.29-34*
6. Evaluate the closed line integral. Assume that the curve C is oriented counterclockwise. Look at problems 18.4.3-13*
7. Evaluate the closed line integral using Green's Theorem. Assume that the curve C is oriented counterclockwise. Look at problems 18.4.3-13*
8. Evaluate the surface integral. Look at problems 18.5.25-28*
9. Evaluate the surface integral. Look at problems 18.5.1-6*
10. Evaluate the flux of F across a surface. Look at problems 18.6.5-15*
11. Use the Divergence Theorem to evaluate the surface integral F dot n. Look at problems 18.7.1-13*
12. 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