**Math 3593H Honors Mathematics II Spring Semester 2006**

**Assignment 6** - Due Thursday 3/2/2006

**Read:** Hubbard and Hubbard Sections 4.9 and 4.10.

Exercises:

Section 4.9 (pages 491-492): 1, 3*, 4, 5, 6*.

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

**Comments**

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 change of variables, and we will need it starting in Section 5, in Proposition 5.3.2.