Math 231 (PDE) Web Site


231 Hmwk
PDE Lecture Notes

Math 231A-C: (Partial Differential Equations) 2002-03


Instructor: Bruce Driver, APM 7414, 534-2648.

Meeting times: MWF 12:30 -- 1:45 PM in APM 6218.

Course Description: Math 231A is the first quarter of an introductory graduate course on partial differential equations..  The course should be of interest to mathematicians, engineers, physicists, or anyone who is interested in using partial differential equations in their studies. 

Textbook: Lawrence C. Evans, "Partial Differential Equations," American Mathematical Society, Graduate Studies in Mathematics, Volume 19, 1998.

Prerequisites: Ideally it would be good to have had a course in advanced calculus which included an introduction to Lebesgue integration theory, metric spaces and normed spaces.  In practice, it should be enough to have good calculus skills provided you are willing to take a few basic convergence theorems on faith.  I will go over these convergence theorems as necessary.

Office Hours: MWF from 3:00 -- 4:00 PM.


Tentative Course Plans

231A Course Plan

bulletThe basic theory of ordinary differential equations in Banach spaces
bulletImplicit and Inverse functions theorems with a couple of applications to ODE and PDE
bullet First order nonlinear partial differential equations.
bullet Cauchy-Darboux-Kovalevskaya theorem.
bulletElliptic ODE boundary valued problems
bulletHeat and Wave Equation in one space variable.

231B Course Plan

bulletSpectral Theorem for self-adoint operators, including compact and unbounded operators related to PDE.
bullet Fourier Transform (an example of the spectral theorem) with applications to Laplace's, heat and wave equations.
bulletProperties of solutions to Laplace, heat and wave equations.

231C Course Plan

bulletSobolev spaces and other functions spaces and some of their properties.
bulletNon-constant coefficient elliptic, heat and wave equations.
bulletNon-Linear PDE's and Techniques as time permits




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Last modified on April 03, 2003 at 09:25 AM.