Introduction to Partial Differential Equations with MATLAB (Applied and Numerical Harmonic Analysis) - Softcover

Cooper, Jeffery M.

Softcover

ISBN 10: 1461272661 ISBN 13: 9781461272663

Publisher: Birkhäuser, 2012

Synopsis

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.

About this title

Review

"Cooper's book stands out among a host of PDE works. It not only adequately treats traditional core partial differential equation methods but also integrates analytic solutions with numerical schemes through the implementation of MATLAB routines. As an application-oriented book that provides the basic definitions, theorems, and analyses of the solutions, it contains the core topics needed for a sound background in partial differential equations.... One of the book's excellent features is the availability of illustrative and challenging problems, some of which have been cast in the form of MATLAB projects. Such features undoubtedly make this a suitable work for a laboratory component of an introductory PDEs course. Recommended. Undergraduates through faculty."   ―Choice

From the Author

Goals of the text and information about errata.
The field of partial differential equations has evolved greatly over the last 50 years. Many types of nonlinear problems are better understood, and the advent of convenient, powerful, computational tools has increased the importance of numerical methods. However, the usual first course in partial differential equations treats only linear boundary value problems with the technique of separation of variables.

The goal of this text is to provide a wider, more varied, first view of the subject, and to take advantage of the ease in programming of MATLAB and its excellent graphics.

In addition to the standard core material, I have introduced some nonlinear problems and numerical techniques. As each equation is discussed, an appropriate finite difference scheme is proposed. These schemes are implemented in MATLAB mfiles available on my web-page at the mathematics department of the University of Maryland, and on the publisher's web page.

On my web-page you will find an abbreviated table of contents and a sample of some of the MATLAB graphics.

I hope that the misprints will not cause great inconvenience. A list of errata is currently available in pdf and postscript formats on my web-page and on the publisher's web-page under "Additional Resources." It will be updated frequently.

I would appreciate receiving word of misprints by e-mail or regular mail. I welcome suggestions for improvements to the text or to the MATLAB codes.

Edition details

• Publisher: Birkhäuser
• Publication date: 2012
• ISBN 10: 1461272661
• ISBN 13: 9781461272663
• Binding: Paperback
• Language: English
• Number of pages: 556