Lectures 13/14, Friday, 9/26/08, Monday, 9/29/08:
Section 12.6: Directional derivatives and gradient
Topics
- Directional derivative Duf(x,y):
formal definition (as a limit)
- Computational formula for directional derivative
- Geometric interpretation of directional derivative
- Partial derivatives as special directional derivatives
- The gradient of a function of several variables
- Directional derivative: formula in terms of gradient
- Geometric interpretation of the gradient
- Relation between the gradient and level curves/surfaces
- Tangent planes and normal lines via gradients
Read
Section 12.6. This is a key section in Chapter 12, and I will spend two
lecture hours on it. The section introduces two important concepts
(directional derivatives and gradients) and ties these together with
many of the concepts that have come up earlier in this chapter and in
Chapters 10 and 11.
Homework
Section 12.6: 3, 7, 11, 13, 17, 27, 29, 41, 43, 55.
Solutions.
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Last modified Mon 29 Sep 2008 01:16:06 PM CDT