Math 508: Advanced Analysis I |
Fall 2010 |
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Faculty: Jerry L. KazdanTelephone: (215) 898-5109

email:kazdan AT math.upenn.eduOffice Hours: Wed. 10:30-11:30 (and by appointment) in DRL 4E15TA: Sneha Subramanian, DRL 4C9

email:ssneha AT math.upenn.edu

Text:Kenneth Hoffman,Analysis in Euclidean space, Dover paperback (reprinted from the 1975 Prentice Hall edition); ISBN-10: 0486458040.

In both Fall 2006 and 2008 I taught a similar course. See the web pages Math 508: Fall 2006 and Math 508: Fall 2008Prerequisites & Review Material

Exams:There will be two in-class exams, from 9:00-10:20 on

- Thurs. Oct 14 (just after Fall Break)
- Thurs, Dec. 9 (the last day of class). Because of the structure of the course, this will be cumulative, not just since Exam. 1.
- No Final Exam
You may always use one 3"x5" card with notes on both sides

Some References:books, articles, web pages

Notes:

Some Basic definitions

Relative Topology

Some Basic Inequalities

Completeness of l_{_1}

Two inequalities for integrals of vector valued functions

Notes on Contracting Maps

Note on Convolution

Course Outline (incomplete)

Homework Assignments:

- Set 0 Due: Thurs., Sept. 9 (Rust Remover. This will not be collected.)
- Set 1 Due: Thurs., Sept. 16. [Late papers: accepted until 1:00 PM Friday.]
- Set 2 Due: Thurs., Sept. 23. [Late papers: accepted until 1:00 PM Friday.]
- Set 3 Due: Thurs., Sept. 30. [Late papers: accepted until 1:00 PM Friday.]
- Set 4 Due: Thurs., Oct. 7. [Late papers: accepted until 1:00 PM Friday.]

Solution of Bonus Problem- Set 5 Due: Thurs., Oct. 21. [Late papers: accepted until 1:00 PM Friday.]
- Set 6 Due: Thurs., Oct. 28. [Late papers: accepted until 1:00 PM Friday.]
- Set 7 Due: Thurs., Nov. 4. [Late papers: accepted until 1:00 PM Friday.]
- Set 8 Due: Thurs., Nov. 11. [Late papers: accepted until 1:00 PM Friday.]
- Set 9 Due: Thurs., Nov. 18. [Late papers: accepted until 1:00 PM Friday.]
- Set 10 Due: Tues., Nov. 30. [Late papers: accepted until 1:00 PM Wednesday.]
- Set 11 Due: Never.

You may find the following lecture notes onContracting Mappingsuseful: "The Magic of Iteration" by Richard S. Palais

Old Exams:(you may always use one 3"x5" card with notes on both sides)

Fall 2010 Exam 1 Fall 2010 Exam 2 (Exam 2 solutions)

Fall 2008 Exam 1 Fall 2008 Exam 2 [solutions]

Fall 2006 Exam 1 [solutions]. Fall 2006 Exam 2 [solutions].