# MAT 546: Differential Equations

### Department of Mathematics SUNY at Stony Brook

We'll be covering the following topics: Basic PDE, distributions and the Fourier transform, compact operators, Fredholm theory, pseudodifferential operators, Sobolev spaces, regularity theorems for elliptic operators, the Hodge theorem. This is material that all students in geometry, operator theory, representation theory, mathematical physics and PDE need to know.

Textbook: A First Graduate Course in Real Analysis, Part Three, by Daryl Geller, available at the University Bookstore.

Course Lecturer: Prof. Daryl  Geller, Math Tower 4-100B
Phone: 632-8327 email: daryl@math.sunysb.edu
Office Hours: TuTh 2:30-4, in 4-100B or P-143 Math.

Grading: There will be no tests or exams. A number of problems will be given as suggested assignments, during the semester. Students who want to get an A in the course should do a reasonable subset of these problems.

Suggested Problems:

Chapter 11: 11.2.2 and 11.2.3; 11.2.4; 11.2.7; 11.2.9; 11.2.10; 11.2.12; 11.3.1; 11.3.6; 11.4.2; 11.4.3.

Chapter 14: 14.2.1; 14.2.2; 14.2.3; 14.3.1; 14.3.2; 14.3.3; 14.4.1; 14.4.5; 14.4.6; 14.4.8; 14.4.9; 14.6.1; 14.7.2; 14.7.3; 14.9.1.

Chapter 15: 15.1.2; 15.2.1; 15.2.2*; 15.2.3; 15.2.4; 15.2.5; 15.3.1; 15.3.5; 15.3.6**; 15.3.7; 15.3.8; 15.4.1; 15.4.2.

Chapter 16: 16.1.1; 16.1.2; 16.3.1; 16.3.2; 16.3.3; 16.3.6; 16.4.1; 16.4.3; 16.4.4; 16.8.1; 16.9.1; 16.10.1; 16.10.2; 16.11.1; 16.13.1; 16.14.2.

Chapter 17: 17.2.1; 17.2.2; 17.2.4; 17.2.7; 17.2.8; 17.5.1.

Chapter 18: 18.1.1; 18.1.4; 18.1.5; more to come.

*: In part (c), assume supp u is contained in (-N,N), not [-N,N].
**: Replace the hypothesis that the conic sets are disjoint by the hypothesis that they intersect only at the origin.
Final Class: Tuesday, May 18, 5-7:30 p.m., in P-143 (the Undergraduate Office).

DSS advisory. If you have a physical, psychiatric, medical, or learning disability that may affect your ability to carry out the assigned course work, please contact the office of Disabled Student Services (DSS), Humanities Building, room 133, telephone  632-6748/TDD. DSS will review your concerns and determine what accommodations may be necessary and appropriate. All information and documentation of disability is confidential.