**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

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

- 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.*