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Math 201 (section 3)
October 18, 2004
Read:
Section 15.5 (chain rule, EXCEPT "implicit functions," p. 972-973)
Section 15.6 (gradients and directional derivatives)
(for next week) Section 15.7 (maxima and minima)
Prepare for Quiz Monday, Oct. 25:
Given a function of the form z=f(x,y), be able to compute its gradient vector (either generally as a vector-valued function of x and y, or for a particular point (x0,y0)). Also, given a function f(x,y) and a unit vector u, compute the directional derivative of f(x,y) in the direction u.
Problems to turn in:
Section 15.5: 1, 2, 7, 8, 13, 16, 23, 35
Section 15.6: 1, 2, 4, 8, 12, 21, 24, 32, 34
(We'll do 36, 47, 56 later, in class or as homework)
Planning ahead:
| week 7 | Oct. 18 | 15.5, Chain rule |
| Oct. 20 | 15.6, Gradients and partial derivatives Homework 7 due | |
| Oct. 22 | More gradients, vector fields (17.1), quadratic surfaces (13.6) | |
| week 8 | Oct. 25 | 15.7, Maxima and minima; kinds of critical points Quiz? Introduce projects Homework 8 due |
| Oct. 27 Oct. 29 | More critical points; quadratic approximation; gradient search | |
| week 9 | Double Integrals!! (Chapter 16) Arc length (14.3) Quiz? Homework 9 due Monday | |
| week 10 | More double integrals. Quiz? Homework? Exam Wednesday Nov. 10? | |
| week 11 | Still more integrals | |
| wks 12-14 | Chapter 17, vector calculus (div, grad, curl, Green, Stokes) |