Introduction to Partial Differential Equations - Math 825 - Spring 2008

Lecturer:

Irina Mitrea, 225 Kerchof Hall, im3p@virginia.edu, Phone: 928-2787.

General description:

The scope of the course is to present an introduction to the theory of partial differential equations (PDEs). We will cover topics from the theory of linear PDEs: (1) integration on surfaces, (2) integration by parts, (3) Laplace's equation: fundamental solutions, Green functions, mean value formulas, maximum principles, boundary value problems, (4) introduction to the theory of distributions and the Fourier transform, (5) Sobolev spaces: traces and extensions, Sobolev inequalities, embeddings, (6) the basic theory for important linear partial differential equations: the heat equation and the wave equation.

Prerequisite: The course is appropriate for any student who has finished Math 731 - Graduate Real Analysis.

References:

L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, Vol. 19, 1998.

M. E. Taylor, Partial Differential Equations, Basic Theory, Springer-Verlag New York, Inc., 1996.

G.B. Folland, Introduction to Partial Differential Equations, Princeton Academic Press, 1995.

R.A. Adams and J.J.F. Fournier, Sobolev Spaces, Academic Press, 2003.

W. P. Ziemer, Weakly Differentiable Functions, Graduate Texts in Mathematics, Springer Verlag, 1989.

Course web page:

http://www.people.virginia.edu/~im3p/mathpage825_2008.html

Lectures:

MW 14:00- 15:15 p.m., Kerchof 317

Office Hours:

Irina Mitrea, 225 Kerchof Hall, TBA (or by appointment).

Grading:

Two projects (related to the covered material) will be assigned during the semester. Each project counts 30%. The remaining 40% will be given for homework (4 assignments) and class participation.