Math 553 Partial Differential Equations
Eigenfunction of the Laplacian on an L-shaped region. (The Mathworks.)
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
- 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
- SoftwareIt 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
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.