AM 223 SYLLABUS, Fall 2005-06

MWF 10:00-10:50 am (C Hour), B&H 161

AM 223-224 (MA 237-238) is the core graduate sequence on partial differential equations. In the first semester, the focus is on the basic theory of linear equations and quasilinear equations. This forms a basis for the study of nonlinear equations in the second semester. The topics for the first semester will include:
  1. The classical theory of Laplace's equation, the heat equation and the wave equation.
  2. The theory of distributions and weak solutions.
  3. First order equations.
The treatment is for the most part rigorous and self-contained. We will begin with explicit solution formulas and work towards a general theory.

Prerequisites: Real analysis (AM 211, MA 221 or equivalent). A good rigorous introduction to advanced calculus will suffice for the most part, if you are willing to take some things on faith. Strictly speaking, no prior exposure to PDE is necessary, but of course it would help.

Textbooks: There are several excellent texts on partial differential equations, each with a different perspective. John's book includes a lot of the material for the first semester, but not all. If you plan to take both semesters, you should invest in Evans' book. The subject is vast, and browsing is strongly encouraged.
  1. F. John, Partial differential equations , Springer 1981.
  2. L. C. Evans, Partial differential equations , AMS 1998.
  3. J. Rauch, Partial differential equations , Springer, 1991.
  4. D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order , Springer 2001.

Lecture notes

I typed up lecture notes for this class until I ran out of steam. Here is the current version of lectures on Laplace's equation and the heat equation.

The remainder of the course is available online thanks to Andreas Kloeckner's real-time(!) TeX transcription of lectures. However, this has not been proofread, and I am not sure I will clean it up until I teach the class again.

Homework and exams

HW 1 , Solutions.
HW 2 , Solutions.
HW 3 , Solutions.
HW 4 , Solutions.
HW 5 , Solutions.
HW 6 , Solutions.
Exam , suggested simplifications, and Solutions.

File translated from TEX by TTH, version 3.66.
On 21 Aug 2006, 11:01.