Math 2573H Honors Calculus III Fall Semester 2002

Assignment 7 - Due Thursday 10/24/2002

Read: Williamson and Trotter, Chapter 6 Section 4 (omitting 4F).

Some comments about what we are doing and what we are missing out: I set no homework questions from the exercises on pages 210-211 because they are all of the type 'Show that ...' and I am unlikely ever to ask you questions like this. On the other hand these questions are good practice in working with the chain rule, and you might do very well to work through some of them. The chain rule is a lot to take on board, and I think that the way to deal with this is to do a lot of computations with it. So if you feel insecure about the chain rule, or are puzzled by what it says, do try some more questions. It will help.

On page 209 is an important theorem, the Inverse Function Theorem. It will probably seem plausible here, but it will be hard to appreciate its true importance. Mathematicians emphasize this theorem because it is important in a more advanced setting, which we cannot go into here.

We are completely missing out Chapter 6 Section 3, which contains another theorem, the Implicit Function Theorem. This is closely related to the Inverse Function Theorem. However this material is unnecessary for us.

Chapter 6 Section 4 contains a lot of material which should be familiar from last year. The new thing is the method of Lagrange Multipliers. This is also described in the book by Simmons which we used last year, and you might prefer to look there.

Exercises:
Chap 6 Sec 4 pages 230-232: 5*, 15, 16, 17*
Chap 6 Sec 4 pages 236-237: 3, 4*, 5, 6, 7*, 11*

You should probably look at more exercises than these, but it is late at night as I write this, and I have not time to choose more. Please choose them yourselves!