### Handouts and Extras

Chapter 2:

- Chapter 2: Steps to Determine Type of DE
- Chapter 2: Name that DE!

Chapter 4:

- Section 4.4: Gilles' handout on the Method of Undetermined Coefficients
- Section 4.7: Gilles' handout on the Constant coefficients and Cauchy-Euler equations

#### Chapter 5:

- Section 5.1: Gilles' handout on Linear combination of Sine and Cosine
- Section 5.1: A student asked me what it would look like if you had damped oscillation plus an external force which is sinusoidal but with a slightly different frequency. As we've seen, damped oscillation looks like this. Undamped oscillation plus an external sinusoidal force can give a beat frequency. Damped oscillation with beats can look something like this (depends on the constants), but as you can see there is an initial "beat" state, which decays away until only the steady state solution (from the external force) is left.

Chapter 7:

- Gilles' table of Laplace transforms
- Gilles' problem book on Laplace transforms

Chapter 8:

- Summary of solutions for homogeneous linear systems of DEs.
- Gilles' exercises on systems of DEs (do only the 2x2 cases!).

### Review Materials

Completing the Square – if you need a reminder on how to complete the square, then this is the worksheet for you!