MAT 331E - Partial Differential Equations

Course Objectives

1. To have a fundamental knowledge of how partial differential equations and initisl and boundary value problem associated with them arise and of how they are classified.
2. To have a fundamental understanding of how such problems can be solved.

Course Description

The single first order equations; general solutions of linear and quasi-linear equations and Cauchy problem, nonlinear equations. Second order linear equations in two independent variables; Cauchy problem and classification, canonical forms. One dimensional wave equation; Cauchy problem, D’Alembert’s solution, Inhomogeneous wave equation. Elliptic equations; Laplace equation, max-min principle, boundary value problems and Green’s functions. Parabolic equations; initial and boundary value problems, fundamental solutions and Green's functions. Analytical methods of solution; separation of variables and integral transform techniques.