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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.

Course Coordinator
Cihangir Özemir
Course Language
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