MATH 477: Partial Differential Equations

Prerequisites & Bulletin Description

Course Objectives

The principal aim of Partial Differential Equations is for students to learn the fundamental techniques for solving boundary value problems for certain classes of first and second order linear partial differential equations. Students who successfully complete Partial Differential Equations should

• Be able to solve first order linear partial differential equations with constant coefficients using characteristic coordinate transformations.
• Be able to use partial differential equation to model one-dimensional heat flow and one-dimensional wave motion and reduce these problems to ordinary differential equations using separation of variables. Using the solutions to these ordinary differential equations students will be able to solve the original problems by using Fourier series.
• Be able to understand the general theory of Sturm-Liouville problems and demonstrate how this theory is used to solve Dirichlet, Neumann and Robin boundary value problems for the heat equation, the wave equation and Laplace's equation.

Evaluation of Students

Students will be graded on their ability to devise, organize and present in correct mathematical English solutions to problems. While instructors may design their own methods of evaluation student performance, these methods must include in-class examinations, graded homework assignments and a final exam.

Course Outline

Textbooks & Software

Richard Habeman, Applied Partial Differential Equations, 4th edition

Nakhle Asmar, Partial Differential Equations and Boundary Value Problems

Wolfram Research, Mathematica

Submitted by: David Ellis 
Date: May 29, 2003