**Learning objectives**

- Interpret and use partial derivatives as multipliers with units
- Make numerical approximations of partial derivatives using formulas, tables of values, and contour plots
- Compute partial derivatives algebraically and with Mathematica
- Use the master equation for and small and
- Use a partial derivative in applied contexts
- Work with the differential of a multivariable function to produce linear approximations and equations of tangent planes
- Use the chain rule to compute partial derivatives of compositions of functions (via variable dependency diagrams )
- Compute and interpret second order partial derivatives

**Resources**

- Textbook: 14.1-14.3, 14.6, 14.7 through Example 3 p 808.
- Suggested problems: 14.1#1, 5, 9; 14.2#1, 49; 14.3#5,13,17; 14.6#1,11; 14.7#3,23,31,51.

**In Class**

- Day 1 Problems on partial derivatives
- Day 2 Derivatives with Mathematica, continue working on partial derivative problems
- Day 3 Using differentials to make linear approximations
- Day 4 Chain rule problems and Textbook problems on the chain rule
- Day 5 Second derivatives for a vibrating guitar string, Textbook problems on second derivatives and notes on Relations among derivatives (PDEs)

**On your own**