MAT 331 - 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.