' MATH 509, Spring 2007

## Math 509: Advanced Analysis (Spring 2007)

 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 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 ]