MATH-6500 Partial Differential Equations

 

Instructor: Victor Roytburd (Amos Eaton 405, Ph. 276-6889, roytbv)
Office hours: TBA (or by appointment)
Course web-page: www.rpi.edu/~roytbv/pde/pde07.html

Course meets: Mo, Th 2–4. Starting September 6, we will meet in CA 113

Course Description

The course is a first graduate course in partial differential equations. Here is a description from the catalog:

A course dealing with the basic theory of partial differential equations. It includes such topics as properties of solutions of hyperbolic, parabolic, and elliptic equations in two or more independent variables; linear and nonlinear first order equations; existence and uniqueness theory for general higher order equations; potential theory and integral equations.

 

Textbooks:

L. C. Evans, Partial Differential Equations, AMS,  ISBN: 0-8218-0772-2

R. B. Guenther and J. W. Lee, Partial Differential Equations of Mathematical Physics, Dover Pub.

 

Tentative Course Outline

  • Laplace’s equation: fundamental solutions. (Evans pp. 18-25, 613-620, and 627-528)
  • Digression on distributions and mollifiers. (Guenther & Lee pp. 413-416, see also this; Evans pp. 629-631)
  • Laplace’s equation: local regularity, Green’s functions, the maximum principle. (Evans pp. 25-28, 33-43; Guenther & Lee pp. 301-320)
  • Variational methods for Laplace’s equation. (Evans pp. 25-28, 33-43, and 629-631; Guenther & Lee sections 11-3–11-4, pp. 448-462 )
  • The heat equation: the fundamental solution; maximum principle; energy methods
  • Primer of Fourier series and integrals.   
  • The wave equation. Spherical means. 
  • PDEs of the first order.
  • Introduction to conservation laws.
  • Separation of variables; hyperbolic systems.
  • Hilbert space methods and weak solutions of boundary value problems for Laplace’s and other elliptic equations.
  • Elliptic potential theory.

Grading policy (tentative):

Homework 50% of course grade

Midterm(s) and a final 50% of course grade

 

Homework Assignments

Here is a master list of homework problems from previous years. Not all of them will be assigned, and some new problems will be added.

Assignment 1, due September 13th.

Assignment 2, (updated) due September 27th.

Assignment 3, (updated) due October 11th

Assignment 4, due October 25th

Assignment 5, due November 12th

Assignment 6, due December 6th

 

Instructor's Web Page: Roytburd, Victor

Email: roytbv at rpi dot edu

Last updated November 26, 2007

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