Math 553 Partial Differential Equations

Professor Richard S. Laugesen, Fall 2007

The course begins with the method of characteristics for first-order equations and then proceeds to examine the famous second-order partial differential equations of mathematical physics, namely the heat (or diffusion), wave and Laplace equations. The focus is initially on finding formulas for solutions, but then moves to the qualitative theory: how do solutions change as the initial and/or boundary data changes, what is the speed of propagation of the solutions, how does the energy behave as time passes, and so on. Also, how do these features differ between the three classical equations?

• Course Announcement
  
• Course Information
  Grading procedures, contact information, practice test, etc.
• Math 553 Syllabus
  Lecture by lecture description of materials to be covered
• Reading Sources
  Texts that provide alternate perspectives on course topics.
• Homework, Notes and Comments, and Handouts
  Homework, discussions of the materials, test information and other handouts
• Software
  It is a good idea to learn the basics of the free software package Iode, which (among other things) handles the wave and heat equations in one space dimension. The package runs under Matlab. I can help you get Iode installed and running.
  Just for fun, on the math department unix network you can also try out the PDE Toolbox: start Matlab, then type "pdetool" at the Matlab prompt. This toolbox handles the wave, heat and Laplace equations in two space dimensions, even with variable coefficients and a variety of boundary conditions.