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