Math 2573H Honors Calculus III Fall Semester 2002

Assignment 4 - Due Thursday 10/3/2002

Read: Williamson and Trotter, Chapter 5 Section 2 and Chapter 5 Section 3 as far as we get in class. I think it is probable that we will not get to the end of Section 3 this week, so I only set questions on the beginning of that section.

Exercises:
Chap 5 Sec 2 (pages 156-159): 1, 2, 2d*, 4, 10 (use the definition of linear given on page 150), 11, 11c*, 13, 14b*, 17, 18*, 19,
Chap 5 Sec 3 (pages 167-170): 1, 1i*, 3e*

We are studying sophisticated material in these sections. There are difficult and substantial concepts, whose subtleties are sometimes not obvious, and often the treatment is deliberately brief and sketchy. This is because the authors know very well that there is much more that can be said about the topics they write about, but they consider that in this text it is better not to get stuck on the details but rather to make some progress towards the applications. The trouble is that from time to time you have to take things on trust, and you only get a restricted view of what is being presented. So, what's new?, you ask! Not much. Sometimes this business is annoying, and sometimes it doesn't matter. For example, it is a pleasant surprise to discover that an open interval of the real line is called open because it is an open set, but not knowing this last year was no disadvantage.