Prerequisites: Math 5210 or consent of instructor.
Text: Partial Differential
Equations,
by Lawrence C. Evans. ISBN 0-8218-0772-2
Course Description: 3 credits. PDEs of classical
physics, Hilbert space methods, variational methods, distributions,
regularity.
Homework: Problems will be assigned regularly. A random subset
of
problems from each assignment will be graded. Late homework
cannot be accepted. Students may consult one another and freely
discuss
homework problems, however the assignments you turn in must represent your own work.
| Due date |
Assignment |
| 1/25/2006 |
Section 1.5: 1, 2, 3, Section 2.5: 1, supplementary exercises 1. |
| 2/13/2006 |
Complete the details for
(14) and (12), page 24, Section 2.5: 2, 4, 8. |
| 2/27/2006 |
Section 2.5: 6, Produce a reasonably accurate picture of a "heat ball" in 1+1 dimensions, Complete the details of obtaining (16) from (15) on page 71, Section 2.5: 13, 15, 17, 18. |
| 3/29/2006 |
Section 3.5: 2, 3(a),(b),
5. |
| 4/17/2006 |
Section 3.5: 8, 13
(note errata), 14, Find the dispersion relation for the equation u_{tt} - u_{xx} + au = 0, a > 0, Prove that R(A) is closed in the proof of the Lax-Milgram Theorem, Prove the Poincare inequality in the case p = n = 2. |
| 5/03/2006 |
Section 4.7: 2. Section 6.6: 1, 2, 7(a), 8. Section 5.10: 7. |
Interesting Links:
Errata for Partial Differential Equations,
third printing.
Russell Richins' Notes on Functional Analysis.
Grades: Your grade will be determined by your homework scores.
Students with disabilities may contact the instructor at the beginning of the semester to discuss special accomodations for the course.
Copyright notice: All printed and electronic materials provided
to you in this course are protected by copyright laws.