Math 3593H Honors Mathematics II Spring Semester 2004
Assignment 5 - Due Thursday 2/26/2004
Read: Hubbard and Hubbard Sections 4.1, 4.3, 4.5.
Section 4.1 (pages 411-415): 3, 5, 6, 9*, 10*, 11, 14a*, 15, 16.
Section 4.3 (pages 434-435: 1*, 2, 5*.
Section 4.5 (pages 452-455): 6, 7, 8, 11*, 12, 13, 14*, 15, 16, 18*, 19.
We are going to make very rapid progress now, by missing out several sections from Chapter 4. I am trying to concentrate on the things I think you really need to know. Next week we will continue in this fashion and miss out Sections 4.6 and 4.7 as well.
Sections 4.1 and 4.3 are theoretical in nature, concentrating on the foundations of what can and cannot be done, and you will probably feel that you could guess the highlights anyway (e.g. Theorem 4.3.7: continuous functions can be integrated). In Section 4.6 the heavy-duty result is Fubini's theorem, but they relegate the proof to an appendix. For your purposes the more important thing is to be able to do calculations where you change the order of integrations, and I think you probably have already an idea of how to do this. In fact, I think you could probably do the exercises to Section 4.5 right now.
Why does a chicken coop have only two doors?
Because if it had four doors, it would be a chicken sedan.