**Learning objectives**

- Use differentials to make linear approximations:
- for small and

- Use gradients to make linear approximations:
- for small

- Use the gradient to compute directional derivatives
- Understand the geometry of the gradient

**Before class**

- Read Hughes-Hallett sections 14.3, 14.4, 14.5.
- Ponder Hughes-Hallett problems: 14.3: 7, 17, 18, 24, 26; 14.4: 1, 2, 7, 17, 23, 32-3; 14.5: 33, 49.

**In class**

- Notes on directional derivatives and the gradient
- Work problems
- Differentiation with Mathematica
- Mathematica notebook for guitar string partial derivatives

**On your own**

- More on differentials: approximating equations