MAT 462

Fall 2006

Syllabus

Text: Applied Partial Differential Equations, 2nd edition (by David Logan)

Instructor: Hank. Kuiper

Office: PSA 625 phone: 965-5004

messages: 965-3951 email:kuiper@asu.edu

URL: http://math.la.asu.edu/~kuiper

This is not a rigid syllabus. Homework assignments can be found at my homepage at the MAT 462 link.

There are other books you may want to consult. One that you might even want to order (e.g. from amazon.com) is “Partial Differential Equations, an introduction” by David Colton (Dover Press, $19.95)

We will do chapters 1-4 of the text. But that is not all. On the one hand we will spend some time reviewing basic, pre-requisite mathematics: complex numbers, linear algebraic equations, some very basic concepts from ordinary differential equations, and concepts from multi-variable calculus. On the other hand, we will at times go just a bit beyond what the text supplies. Here is the order in which we will cover the material (not exactly like the book

1. Review: Complex numbers, complex-valued functions, power series, Euler’s formula.

2. Review: Concepts from multivariable calculus: Green’s Theorem, integration by parts, divergence theorem, Green’s identities.

3. Models: diffusion, vibrating string and vibrating membrane, boundary conditions, steady states.

4. Review: Ordinary differential equations (first order linear, second order linear).

5. First order linear and quasilinear partial differential equations.

6. The Fourier ring, Fourier series, some simple second order PDEs.

7. The Fourier transform. Diffusion in R^N, N=1,2,3.

8. General solution of the wave equation and d’Alembert’s solution.

9. The essentials of Sturm-Liouville theory.

10. Homogeneous second order linear PDEs.

11. Non-homogeneous second order linear PDEs.

12. Topics (e.g. problems on the disk, Fourier-Bessel series, problems in a sphere).