MAT 234E - Partial Differential Equations

Course Objectives

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.
To develop a basic understanding of the theory and methods of solutions for these problems.

Course Description

Partial Differential Equations-Introductory Concepts, First-Order Linear Equations, Ideas On Derivations of The Fundamental PDE’s, Types of PDE Problems, Classification of Second-Order Linear Equations. Initial Value Problem for The Wave and The Heat/Diffusion Equations on The Whole Line, Energy Methods and Maximum Principle for Uniqueness. The Homogeneous Heat/Diffusion Equation on The Half-Line, The Homogeneous Wave Equation On The Half-Line and On A Finite Interval By The Method of Reflections. The Inhomogeneous Wave and Heat/Diffusion Equations On The Whole Line. The Wave and Heat/Diffusion Equations Under Initial and Boundary Conditions by The Method Of Separation of Variables. Harmonic Functions, Laplace's Equation, Maximum Principle, Uniqueness, Invariance, Poisson's Formula. Green's Identities and Green's Functions.