# Math 515

## Partial Differential Equations, Spring 2014

### Basic Information

Instructor: Ari Stern

Email: astern@math.wustl.edu

Office: Cupples I, 211B

Office Hours: TuTh 10:30am-12pm

### Lectures

Lectures will be held MWF 10-11am in Rudolph Hall 102. The
first class will be on Monday, January 13, and the last will be on
Friday, April 25. Class will be canceled for Martin Luther King,
Jr. Day (Monday, January 20) and Spring Break (week of March
9-15).

### Homework Assignments

Problem sets will be posted here approximately weekly, and will
be collected at the beginning of class on the due date. You are
encouraged to discuss the homework with your fellow students, and
to collaborate on problems, but your final write-up must be your
own. Please make sure that your solutions are written clearly and
legibly. (Typing up solutions in LaTeX is encouraged, and is
valuable practice for mathematical writing later in your
career.)

- HW1: Evans, Problems 1.5.1, 2.5.1, 2.5.2. Due Wednesday,
January 22.
- HW2: Evans, Section 2.5, Problems 3, 4, 5, 6. Due Wednesday,
January 29.
- HW3: Evans, Section 2.5, Problems 7, 8, 9, 10. Due
Wednesday, February 12.
- HW4: Evans, Section 5.10, Problems 3, 4. Due Wednesday,
February 19.
- HW5: Evans, Section 5.10, Problems 7, 8, 9. Due Wednesday,
February 26.
- HW6: Evans, Section 6.6, Problems 1, 2, 3, 4. Due Wednesday,
March 5.

*Hint:* For Problem 4, you may find it helpful to use
the Poincaré inequality on p. 290.
- HW7: Evans, Section 7.5, Problems 1, 6, 7. Due
Wednesday, April 2.
- HW8: Evans, Section 7.5, Problems 12, 14, 15, 16. Due
Wednesday, April 16.

### Final Project

In lieu of exams, each student will give a final presentation
on a topic in nonlinear PDEs. A short summary (1-2 pages) of the
proposed topic is due Wednesday, March 26. Final presentations
will be given in class during the final week of the term.

### Grading

Grades will be based on a weighted average of homework (50%,
lowest score dropped), final project proposal (10%), and final
presentation (40%).

### Required and Supplemental Texts

The required textbook for this course is *Partial
Differential Equations*, by Lawrence C. Evans (second edition,
AMS, 2010). Evans maintains a
list
of errata [pdf] for this text.