Math 6327, Partial Differential Equations, Spring 2012.

            Classes are Tu-Th 4.00-5.15pm PGH 348

             My office is PGH 696 and Office hours are Tu - Th 2.30-3.30pm or by appointment.
            Office telephone is 713-743-3475 or you can send email to Auchmuty at uh.edu.

        The prerequisites for the class include metric space topology and Math 6320-2. I will also assume that students are knowledgeable about Lebesgue and Sobolev spaces, weak calculus and the N-dimensional Fourier transform as was covered in Math 6326 in Fall 2011.

          The first topics to be covered will be the initial value problem for the heat equation on R^N. The fundamental solution will be derived and studied and the representation of solutions will be developed. The representation of the solution of the Black-Scholes equations will also be derived.

            Thereafter attention will be focussed on initial boundary value problems for evolution equations on nice bounded regions in R^N. Existence, uniqueness and continuous dependence results will be studied. Also the approximation and representation of solutions using Galerkin-type methods and energy estimates.    We will concentrate on linear equations of parabolic type

          The course grades will be based on solutions of a number of Homework sets. There will not be a midterm or final exam.

          The recommended texts for the course are
Haim Brezis, Functional Analysis, Sobolev spaces and Partial Differential Equations, Springer, 2011 and
Lawrence C. Evans, Partial Differential Equations, American Math Society.
Both these books are highly recommended for anyone interested in PDEs   - and provide quite different treatments of the modern theory of PDEs.
          Other books that have related material are
Robert McOwen, Partial Differential equations, 2nd ed, Prentice Hall
Eberhard Zeidler, Nonlinear Functional Analysis and its Applications, Vol 2A, Springer.

        Some notes on optimization that have a careful treatment of classical multivariable calculus are available
here. Optimization Notes

       If you have any questions, please call  713-743-3475 or send e-mail to auchmuty@uh.edu.