MATH 312: PARTIAL DIFFERENTIAL EQUATIONS

General Description

The behavior of many physical systems can be mathematically modeled by partial differential equations (PDEs). Examples appear in the description of flows in porous media, behavior of living tissues, combustion problems, deformation of composite materials, earthquake motions, ...etc. We will study different analytical methods for solving various PDEs, such as the heat equation, the wave equation, and Laplace's equation. If time allows, we will study the properties of some special functions like Bessel and Legendre functions.

Syllabus

Textbook

Richard Haberman, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 5th edition, Pearson, 2013 (Required)

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Course Material

Please note: the posted lecture notes were originally intended for the instructor's purposes only and may not be complete. By no means are the posted lecture notes meant to serve as a substitute for attendance in class and the reading of the text. It is not guaranteed that they are without error either. Should there be any errors, notify and inform the instructor of the error immediately or as soon as possible.

Chapter 1. Heat Equation Lecture Notes

Chapter 2. Separation of Variables Lecture Notes

Chapter 3. Fourier Series Lecture Notes

Chapters 4 & 12. Wave Equation, Method of Characteristics

Chapter 7. Higher-Dimensional PDEs Lecture Notes

Chapter 8. Nonhomogeneous Problems Lecture Notes

Special Functions. Bessel and Legendre Functions (if time permits)

Homework