Introduction to Partial Differential Equations - Math 825 - Spring 2008
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.
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.