Partial derivatives

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 $\Delta z \approx (\partial z/\partial x) \Delta z + (\partial z/\partial y)\Delta y$ for $z=f(x, y)$ and small $\Delta x$ and $\Delta y$
• 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