MAT 331E - Partial Differential Equations

Course Objectives

1. To develop a basic understanding of occurrence of the partial differential equations and related problems; such as, initial value, boundary value and initial-boundary value problems in the real world.
2. To develop a basic understanding of the theory and methods of solutions for these problems.

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.