## Math 509: Advanced Analysis (Spring 2007)

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: 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 pagesExample: 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 ]