# Study Guide - Chapter 15

## Math 221

### In-Class Exam (60 points)

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

- Determine whether a function
**F** is conservative, and if it is, find the potential function **f**. 2
parts. Look at problems 5 - 12.
- Find the divergence and the curl of a vector field
**F**. Look at problems 13 - 20.
- Evaluate the line integral over the specified paths. 2 parts. Look at problems 21 - 26.
- Evaluate the integral of
**F** dot d**r** over the specified curve. Look at problems 29 - 34.
- Use the Fundamental Theorem of Line Integrals to evaluate an integral. Look at problems 37 -
38.
- Use Green's Theorem to evaluate the line integral. Look at problems 39 - 44.
- 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)

- 15.1.71 - also find the potential function.
- 15.2.60
- 15.3.34
- 15.4.42
- 15.5.46
- 15.6.36
- 15.7.18
- 15.8.24