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MAT 546: Differential Equations

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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.