Math 8201 Real Variables
Spring 2007
Prof. Peckham
Homeworks and Tests
- Set 1 Due Friday Jan. 26, 2007:
- Read Chapter 1, Introduction to Rn
- 2c-g, 10, 18ab, 19, 24, 26, 32c, 34, 36, 40ade, 43, 48, 56
- Set 2 Due Friday Feb. 9, 2007:
- Read Chapter 2, sections A and B: Lebesgue Measure in Rn
- Section A: 2,3,4a,4b, 4c (hard), 5, 9,10,12, 16, 24 for A intersect B only
- Set 3 Due Friday Feb. 23, 2007:
- Read the rest of Chapter 2. Just skim the Appendix.
- Do problems: 25, 26, 28, 29, 31, 34, 43
- Set 4 Due Wednesday March 7, 2007:
- Read Chapter 3.
- Do problems: 3,6,7,8,9,11,19
- Spring Break March 12-16, 2007
- Set 5 Due Monday March. 19, 2007 :
- Read Chapter 4, except for the section on modulus of continuity.
- Do problems: 1,7,10
- Read Chapter 5.
- Do problems 2,6,12,14,16,17,21,22 (for s1 + s2 only)
- Exam 1 Fri. March. 23. Covers Chapters 1 - 5. See review sheet
for list of topics.
Test 1 topic list - PDF file
- Set 6 Due Friday April 6, 2007:
- Read Chapter 6.
- Do problems: 1,2,3,4,7(optional), 9,10,12,16,17,20,24,35
- Set 7. Due Friday April 20, 2007:
- Read Chs. 7 and 8.
- Do problems 1,2,3,4(1st inequality only),6,11,17,22 (Show h is C1 only.)
Note that you must compute h'(0) directly from the definition of derivative.
- Exam 2
Any 90 min time slot after Wed. 5/2/07.
Covers mostly Chapters 6 - 8. See Review Sheet for details.
Exam 2 topic list - PDF file
- Final Problem Set. Due Monday May 7, 2007.
- Do problems 1 - 4 on the Final Problem Set Handout:
Final Problem Set - PDF file
- A bad definition of inner and outer measure.
- An alternative (but equivalent) definition of Lebesgue measure.
- Convolutions
- Showing the Cantor-Lebesgue function is continuous by showing it is the
uniform limit of continuous functions.
- Ch 8 problems: 1, 11 (for n=1 and 2 only), 12.
Hint for 1: For one order of integration, substitute u=xy. Then show that the
integral is the square of the integral from 0 to infinity of
e-t2.
This page (http://www.d.umn.edu/~bpeckham/www) is maintained by
Bruce Peckham (bpeckham@d.umn.edu)
and was last modified on
Friday, 20-Apr-2007 17:49:45 CDT.