787.03 Summer 2003 Week 7

Week 7 (week of August 4). Topic for the week: Differentiation (Chapter 1.4 in Berkeley Problems, chapter 2 in Kaczor and Nowak V.2).

Next mock qualifying exam: Tuesday, August 12, 6:15 pm. I'll try to reserve MA10.

On Monday, August 4, I reminded us of the homework assignment for Friday (do the Spring 2002 qualifying exam, and Berekely problem 2.4.27). Again try to do the old qualifying exam in a 3 hour block as if it was a real one. Then you can go back and solve whatever you didn't get. For other homework (not to hand in) I suggested we do problems in Berkeley, chapter 1.4, and Kaczor and Nowak V.2, chapters 2.1 and 2.2. In class we solved the following problems: Berkeley 1.4.26, 1.4.17, 1.4.18, and Kaczor and Nowak V.2, problem 2.1.12.

On Tuesday, August 5, we solved the following problems form old qualifying exams related to differentiation: Autumn 95 #2, Spring 95 #5, Autumn 00 #4, and Autumn 99 #5 (we stopped before verifying an elementary but important detail-make sure you check it!).

Here are solutions to problem set 4.

On Wednesday, August 6, we did problems 2.2.17, 2.2.20, 2.2.22 from Kaczor and Nowak, V2, and Spring 92 #2.

On Friday, August 8, we solved problems 2.2.28 (in two ways!) and 2.3.32 from Kaczor and Nowak V.2, and August 95 #3. Erica Whittaker points out that I left out an important detail in the solution to August 95 #3: to show that G(x) \leq 0 so that 0 \geq G(x) \geq -log 2. This follows from the fact that for fixed s, log(s) is less than log(s+t), for t in (0, \infty). I also wanted to solve problems 2.3.40 and Spring 99 #3 but ran out of time.


Matthew Stenzel
Last modified: Mon Aug 11 11:29:13 EDT 2003