Math 6326    Partial Differential Equations, Fall 2017.

Lectures will be  Tu-Th 2.30-4pm in AH301. Office hours are Tu-Th 1-2pm in PGH696
or by appointment.

Prerequisite for this class is the Introduction to Real Analysis sequence M4331-4332 and a good knowledge of classical multivariable  calculus. A certain amount of material from M6320-6321 will also be used - especially the properties of real Hilbert
spaces as covered in M6360.

The course will start with a quick revision of multidimensional calculus and the definitions of weak derivatives and their properties.
 Hilbert Sobolev spaces will be defined and properties of bilinear forms on these spaces will be introduced.
Variational methods  and weak solutions of boundary value problems will be described and analyzed.
Results about eigenvalue problems for elliptic operators and trace theorems for Sobolev functions will be proved.

Throughout issues related to the Laplace and Poisson equations are used for motivating the general approach. These issues are central to providing a mathematical basis for much of physics and engineering, so problems from applications will also be used as examples.

There is no prescribed text for the course and the instructor will provide  notes on much of the material. The first semester will cover much of the material in the first
three chapters of "Hilbert Space Methods in Partial Differential Equations" by
Ralph E. Showalter. The treatment will be quite different to that of this text. The text is available free on the internet or from Dover Publications.

  Other excellent texts that treat some of the material  that will be covered include
Robert McOwen, "Partial Differential Equations, Methods and Applications", Prentice Hall, chapters 4 - 8.
L.C. Evans, "Partial Differential Equations", AMS, chapters 5 and 6.
Haim Brezis,  "Functional Analysis, Sobolev Spaces and Partial Differential Equations", Springer


At the beginning some homework will be assigned; later in the semester students will be asked to participate in some  (group) projects. There will not be any exams for the course.

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

 

 

Current Address: Department of Mathematics, PGH Building, University of Houston, Houston, Texas 77204-3008
Phone(UH): (713) 743-3500 - Fax(UH): (713) 743-3505