Math 509: Advanced Analysis (Spring 2007)
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Faculty: Jerry L. Kazdan
Telephone: (215) 898-5109 email: kazdan AT math upenn edu Office Hours: Wed. 10:30-11:30 (and by appointment) in DRL 4E15 |
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TA: Ricky Der , Office DRL 4N27,
email: rickyder AT math upenn edu |
Final Exam, Tues. May 1, 9-11, Room: DRL 4C8 (our classroom)
Text: Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill, 1976.
Some References: books, articles, web pages
Example: An open set whose area is not defined (in the sense of the Riemann Integral).
Lecture notes: Weierstrass Approx Thm
Homework Assignments:
- Set 1 (pdf) (Due: Tues., Jan. 16; late papers accepted until 1PM Wednesday.)
- Set 2 (pdf) (Due: Tues., Jan. 23; late papers accepted until 1PM Wednesday.)
- Set 3 (pdf) (Due: Tues., Jan. 30; late papers accepted until 1PM Wednesday.)
- Set 4 (pdf) (Due: Thurs., Feb. 8; late papers accepted until 1PM Friday.)
- Set 5 (pdf) (Due: Tues., Feb. 20; late
papers accepted until 1PM Wednesday.)
You may find the following lecture notes interesting: "The Magic of Iteration" by Richard S. Palais - Set 6 (pdf) (Due: Tues., March 13; late
papers accepted until 1PM Wednesday.)
The folllowing notes give a useful application of implicit function theorem Matrices: A(t) to the dependence of the eigenvalues and eigenvectors of a matrix A(t) on a parameter t..
If one perturbs the polynomial p(x)=(x-1)(x-2)...(x-20), how much do the roots move? This and many fascinatinq questions are discussed in Forsythe: Pitfalls in Computation See section 8 for this example. - Set 7 (pdf) (Due: Thurs., March 16; late papers accepted until 1PM Friday.)
- Set 8 (pdf) (Due: Thurs., March 30; late papers accepted until 1PM Friday.)
- Set 9 (pdf) (Due: Thurs., April 5; late papers accepted until 1PM Friday.)
- Set 10 (pdf) (Due: Thurs., April 12; late
papers accepted until 1PM Friday.)
Notes on the Dirichlet problem for the disk: large type, printable size
Exams: (One 3 × 5 card with notes allowed)
Some old Exams from this course (Spring 2005) Exam 1; Final Exam [ Solutions]
Spring 2007: Exam 1 [Solutions ]; Final Exam [Solutions ]