# Study Guide - Chapter 15

## Math 221

### In-Class Exam (60 points)

All questions on the exam are directly from the chapter 15 review.

1. Determine whether a function F is conservative, and if it is, find the potential function f. 2 parts. Look at problems 5 - 12.
2. Find the divergence and the curl of a vector field F. Look at problems 13 - 20.
3. Evaluate the line integral over the specified paths. 2 parts. Look at problems 21 - 26.
4. Evaluate the integral of F dot dr over the specified curve. Look at problems 29 - 34.
5. Use the Fundamental Theorem of Line Integrals to evaluate an integral. Look at problems 37 - 38.
6. Use Green's Theorem to evaluate the line integral. Look at problems 39 - 44.
7. Verify the Divergence Theorem by evaluating the double integral of F dot N as a surface integral and a triple integral. Look at problems 49 - 50.

### Take home exam (40 points)

1. 15.1.71 - also find the potential function.
2. 15.2.60
3. 15.3.34
4. 15.4.42
5. 15.5.46
6. 15.6.36
7. 15.7.18
8. 15.8.24