Course Description

Class times: MWF 11, in Room TBA of the Skiles Building.
Instructor: Evans Harrell, Skiles 134, tel. 894-4312, e-mail harrell@math.gatech.edu
Instructor's office periods: M 3:30-4:30, W 12:00-1:00, F 12:00-12:30, Skiles 134

Texts: L.C. Evans, Partial Differential Equations. For review of the elementary theory, you may refer to the on-line text by Evans Harrell and James Herod.

Prerequisites: Students must be familiar with analysis, as represented by Math 4318 at Georgia Tech. Also highly advisable are undergraduate courses on partial differential equations and their applications in science and engineering. Helpful subjects to know about include Hilbert space and complex function theory.

Grading and requirements: There will be exams on Friday, 22 September, and Friday, 10 November; and there may be pop quizzes on other Fridays. Homework problems will be posed in the lectures or on the Web, and will be collected and discussed on Fridays, but not systematically graded. They might, however, appear on the exams. You will have an opportunity to review your class standing after each test from the Web page.

Missed tests, special accommodation, etc. There will be never be an opportunity to retake a missed exam after the event. Any special accommodations must be requested in writing or by electronic mail two weeks in advance of any scheduled event, and it is the student's responsibility to take the initiative for any such accommodations.

Description: Partial differential equations arise whenever something changes continuously and the rates of change are related by a law. Some subjects in which fundamental laws are expressed as PDEs are: acoustics, astrophysics, ecology, electromagnetism, epidemiology, finance, fluid mechanics, quantum mechanics, rational mechanics, thermodynamics, and transport theory. (The list could go on and on.)

In this class we will begin by deriving some representative PDEs, to show the interplay between physical and mathematical ideas. We then discuss some essential mathematical questions, of well- posedness and classification of differential equations. After this we take a closer look at the properties of different types of PDEs and the methods available for solving them, whether exactly or approximately.

A tentative outline of topics is available at the Official School of Mathematics Course Description. We may, however, deviate from this depending on the interests of the students.