Math 240B Homework (Winter 02)

Click on the highlighted link to retrieve the homework assignment. You should look try all of the problems assigned but only hand in those problems with a "*" on them.

1. Homework #1 is due Monday January 14.  Do the following exercises from and Chapter 7b of the notes.

Chapter 7b: 7.5*, 7.6, 7.7*, 7.11, 7.15*

2. Homework #2 is due Wed January 23.  Do the following exercises from Chapter3c and Chapter 8b of the notes.

Chapter3c: 3.7
Chapter 8b: 8.1--8.3, 8.4*, 8.5*, 8.8, 8.9*, 8.10*, 8.11*

3. Homework #3 is due  Friday February 1.  Do the following exercises from Chapter 8 and Chapter 9 of the notes.

Chapter 8b: 8.11*, 8.12*, 8.13, 8.14*  (Note 8.12 -- 8.14 are new exercises. Click here to get the problems.)
Chapter 9:  9.1, 9.4*, 9.5*, 9.6

4. Homework #4 is due  Friday February 8.

Chapter 9:  9.2, 9.3*.
The following problems are taken from the file hm4.pdf. (The last two pages of this file are some added notes about essential supports that I covered in class.)
hm4.pdf:    9.4, 9.5*, 9.9*, 9.10*, 9.11*, 9.12*

5. Homework #5 is due  Friday February 15. Do the following problems.

From  hm5sup: 9.12*, 9.13.
From lecture notes, Chapter 10:  10.1, 10.2, 10.3*, 10.4*, 10.5*, 10.6*, 10.10* (Postponed)

The midterm will be on Wednesday, February 20.

6. Homework #6 is due  Monday February 25. Do the following problems:

From lecture notes, Chapter 10:   10.6*, 10.10*, 10.11*, 10.12*, 10.14, 10.15*, 10.22*

7. Homework #7 is due  Wednesday March 6. Do the following problems:

From lecture notes, Chapter 10 Addendum:   10.22, 10.23*, 10.24*, 10.25*, 10.26*, 10.27*, 10.28*, 10.29*, 10.31, 10.32*, 10.33*

Corrections:

In 10.23, the sum should be over k in Z^d not Z.
In 10.24, assume that f is 2m -- continuously differentiable and |\alpha|<= 2m.
In 10.26, assume that F^ is in l^1(Z^d) not  l^1(N^d)  as stated in the problem.

8. Homework #8 is due  Wednesday March 13. Do the following problems:

From Lecture notes Chapters 11-12  do 11.6*, 11.7*, 11.8, 11.9*, 11.10*, 11.11.

Corrections to Problems 11.10 and 11.11 are in the following file: Chapter 11  fix. ### Remarks on Homework

The homework is an important part of this class. The homework is your best chance to learn the material in this course. You may consult others on the problems, but in the end you are responsible for understanding the material. I suggest that you try all the problems on your own before consulting others. Even false starts on problems will help you learn.

Dan Curtis is the grader for this course. Here is what he will be looking for in your solutions.

1. The solutions must be written clearly. This includes good handwriting and good English. If I have to struggle to read what you have written, I will not grade the problem!
2. The solutions should be complete and clear. A good rule of thumb is: if you have some doubt about your solution it is probably wrong or at best incomplete.
3. Results that you use in your proof from undergraduate analysis or from the text book or the notes should be stated clearly. Here is an example of what I am looking for:

… So we have shown that fn converges to f uniformly. Since each fn is continuous and the uniform limit of continuous functions is continuous, we know that f is continuous.

The reference to a theorem from undergraduate analysis is in Italics. Jump to Bruce Driver's Homepage.                       Go to list of mathematics course pages.