# Introduction to Partial Differential Equations with MATLAB

• Jeffery Cooper
Textbook

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

1. Front Matter
Pages i-xv
2. Jeffery Cooper
Pages 1-18
3. Jeffery Cooper
Pages 19-72
4. Jeffery Cooper
Pages 73-110
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Pages 111-155
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12. Jeffery Cooper
Pages 455-458
13. Back Matter
Pages 459-541

### Introduction

Overview The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. The core consists of solution methods, mainly separation of variables, for boundary value problems with constant coeffi­ cients in geometrically simple domains. Too often an introductory course focuses exclusively on these core problems and techniques and leaves the student with the impression that there is no more to the subject. Questions of existence, uniqueness, and well-posedness are ignored. In particular there is a lack of connection between the analytical side of the subject and the numerical side. Furthermore nonlinear problems are omitted because they are too hard to deal with analytically. Now, however, the availability of convenient, powerful computational software has made it possible to enlarge the scope of the introductory course. My goal in this text is to give the student a broader picture of the subject. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods. I feel that it is important for the student to see nonlinear problems and numerical methods at the beginning of the course, and not at the end when we run usually run out of time. Furthermore, numerical methods should be introduced for each equation as it is studied, not lumped together in a final chapter.

### Keywords

Boundary value problem Fourier transform MATLAB Maxwell equation discrete Fourier transform fast Fourier transform fast Fourier transform (FFT) numerical methods operator wave equation

#### Authors and affiliations

• Jeffery Cooper
• 1
1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-1754-1
• Copyright Information Birkhäuser Boston 1998
• Publisher Name Birkhäuser, Boston, MA
• eBook Packages
• Print ISBN 978-1-4612-7266-3
• Online ISBN 978-1-4612-1754-1
• Buy this book on publisher's site
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