Math 8201 Real Variables
Spring 2011
Prof. Peckham
Homeworks and Tests
- Set 1 Due Friday Jan. 28, 2011:
- 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. 11 ):
- Read Chapter 2, sections A and B: Lebesgue Measure in Rn
- Section A: 2,3 (OK to use result of Ch 1, 31),4a,4b, 4c (hard), 5, 9,10,12, 16, 24 for A intersect B only
- Set 3 Due Wednesday Feb. 23, 2011:
- Read the rest of Chapter 2. Just skim the Appendix.
- Do problems: 25, 26, 28, 29, 31, 34, 43
- Set 4 Due Monday March 7, 2011:
- Read Chapter 3 and Chapter 4, Section A.
- Do Ch 3 problems: 3,6,7,8,9,11 (for invertible matrices only), 19
- Do Ch 4 problem: 1
- Exam 1 Fri. March. 11, 2-4pm. Covers Chapters 1 - 3, 4A. See review sheet
for list of topics.
Test 1 topic list - PDF file
- Spring Break March 12-20, 2011
- Set 5 Due Monday March. 28, 2011 :
- Read Chapter 4, except for the section on modulus of continuity.
- Do problems: 7,10 (1 done earlier)
- Read Chapter 5.
- Do problems 2,6,12,14,16,17,21,22 (for s1 + s2 only)
- More Problem Sets ...
- Set 6 Due Friday April 8, 2011 DUE DATE MOVED to Monday, April 11.:
- Read Chapter 6.
- Do problems: 1,2,3,4,7(extra credit), 9,10,12,16,17,20,24,35 (extra credit)
- Set 7. Due Friday April 22, 2011:
- Read Chs. 7 and 8.
- Do Ch. 7 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 . Friday April 29, 2011. 2-4pm.
Covers mostly Chapters 4 - 8. See Review Sheet for details.
Test 2 topic list - PDF file
- Final Problem Set. Due Tuesday May 10, 2011. Problems TBA.
- 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 only), 12. Extra Credit: 4, 11 for n=2.
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.
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and was last modified on
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