TEXT: Walter Strauss, Partial Differential Equations, An Introduction, 2nd Ed., Wiley, 2007, ISBN 0470054565

COURSE DESCRIPTION:

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations. Examples are the vibrations of solids, the flow of fluids, the diffusion of chemicals, the spread of heat, the structure of molecules, and the radiation of electromagnetic waves. This course is a continuation of the Series and Boundary Value Problems Course (MAT 401), and focuses on the modeling of scientific and engineering problems by partial differential equations, on methods of solution, and representations of solutions of partial differential equations.

PREREQUISITES: Calculus III and Differential Equations.

TOPICS:

1. Review and Introduction (Ch. 1-4)
   • Heat Equation
   • Separation of Variables
   • Fourier Series
   • Wave Equation
   • Laplace's Equation
2. Characteristics (Ch. 5)
3. Distributions and Transforms (Ch. 6)
   • Distributions
   • Fourier Transform
   • Laplace Transform
4. Higher Dimensional PDEs (Ch. 7,8,9)
   • Bessel Functions and Orthogonal Polynomials
   • Sturm-Liouville Theory
   • Problems in Cylindrical and Spherical Coordinates
5. Nonhomogeneous Problems (Ch. 10)
   • Green's Functions
6. Numerical Methods (Ch. 11)

OFFICE HOURS:

M, 3-5 PM T,R, 9-10 AM

GRADES:

Test (Feb. 10) Test (March 17) Test (April 14) Final (cumulative)

30 points 30 points 30 points 40 points

A+ >= 97 points A = 93,...,96 points A- = 90,...,92 points etc.

All tests and the final exam will be closed book. The lowest test score will be dropped.