**Learning objectives**

- Learn what a fourier series is
- Work with some examples, using Mathematica to calculate coefficients
- Evaluate approximations with a finite number of terms using the Energy norm ()
- Derive the heat equation and use fourier series to solve it for temperature distribution in finite length metal rod (if time allows)

**Before class**

- Read Hughes-Hallett section 10.5
- Ponder Hughes-Hallet questions 10.5:1-5.

**In class**

- Work with the square wave
- Here’s some Mathematica for the square wave