**Learning objectives**

- Understand multiple integrals as sums
- Interpret multiple integrals of densities
- Evaluate multiple integrals numerically and algebraically
- Describe regions algebraically using inequalities
- Cartesian coordinates in 2 and 3-space
- Polar coordinates in the plane
- Cylindrical and spherical coordinates in 3-space

**Before class**

- Read Hughes-Hallett sections 16.1, 16.2
- Ponder Hughes-Hallett problems: 16.1: 3, 5, 9, 11, 13, 15, 25; 16.2: 1, 3, 5, 11, 15, 17, 19, 43.

**In class**

- Intro to integration: what kinds of problems lead to integrals?
- Find a population from a contour map of population density
- Exercises on double integrals
- More exercises