**Math 3593H Honors Mathematics II Spring Semester 2004**

**Assignment 7** - Due Thursday 3/11/2004

**Read:** Hubbard and Hubbard Sections 4.10, 5.1.

Exercises:

Section 4.10 (pages 503-505): 1, 2, 4, 5*, 7, 8*, 9, 11, 12*, 13, 14, 17, 18, 19*.

Section 5.1 (page 531): 1, 2*, 3*.

**Peter's Paragraphs**

Perhaps the most important single technique you will have learned in evaluating integrals of a single variable is to make a substitution. The extension of this result to several variables is correspondingly important, not just because it provides a way to evaluate some integrals (e.g. change to polar coordinates), but because it underlies the definition of an integral over a manifold. Section 4.10 is about this, and is something we need to know. On the other hand I cannot see why we need to know Section 5.1, but it is short and not difficult. I give two sections only this week in the feeble hope that I might get through them in reasonable time before the next homework is due, but my expectations in this direction always seem to be proved wrong.

You will see that in general terms we are making tremendous progress at the moment, by missing out huge sections of the book, and I am optimistic that we may be able to take Chapter 6 at a more comfortable pace when we get to it.

**Julian's Joke**

Why did the tiger lose the running race?

Because the other guy was a terrible cheetah.