Customer Reviews

Introduction to Partial Differential Equations with Applications (Dover Books on Mathematics)

5 star:		(3)
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3 star:		(1)
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Thoe & Zachmanoglou have written an easy-to-follow introductory book on PDEs with heavy emphasis on physical interpretations. The book begins with a brief study of quasi-linear PDEs and their geometrical properties followed by a series of chapters concentrating on elliptic, hyperbolic, and parabolic linear PDEs. The discussion of each type of PDE includes well-posedness, uniqueness, and basic solution methods. Proofs are generally simplified to keep the reader focused on the PDEs.

I recommend this book for those wishing to gain a more complete knowledge of PDEs without technical proofs. For those wanting a more rigorous discussion, Thoe & Zachmanoglou provides an excellent starting point.

This book is a good book from the mathematical point of view and a good overview of the overall mathematical framework. For example, looking at a PDE, what can one say about the solution? Does it exist? Is it unique? What properties does the solution have? The book's emphasis is on presenting the various types of PDE's and then using physics to illustrate its usefulness. For example, the section of the book on quasi-linear and linear equations of the first order first looks at all of the mathematical underpinnings of this kind of equation. Only afterwards does the book look at the applications of such PDEs for solving problems in traffic flow and gas dynamics. In contrast "Partial Differential Equations for Scientists and Engineers" by Farlow assumes you have a specific physics problem you are attempting to solve and then goes about showing you how PDE can help.
Thus, my advice for someone who wants to study PDE and learn the practical applications is that they should first read and study this book for the theory and some of the applications. Then, buy and read Farlow's book. See if you can determine how to solve each physics problem presented in that book with PDEs. If you can, you are on your way to saying you know Partial Differential Equations from both a theoretical and practical standpoint.

From just basic usage of the book, and with almost no introduction to PDEs, I found the book to be very helpful. This book starts out the way any PDE book should, a review of ODEs and then a careful, systematic approach to PDEs with very helpful illustrations. After the PDE is introduced, many different examples of PDE application are shown (such as the heat equation, Laplace's equation, and the wave equation), and with very careful demonstration of the use of the PDEs. I would have to say that any math or physics (especially in mechanics) person would benefit greatly to have either read or own this book.

I use it as a reference for a Boundary Value Problems course at the college level. Not a beginner level text, you need a background in DEs and linear algebra.

Inexpensive and a classic.

This is an awesome book. It's an introduction, but you'll want a background in differential equations and probably multivariable calculus before jumping in to this book. Topics are treated rigorously and there is minimal "hand waving."

I am a sophomore student in computer engineering, and my professor used this book as a supplement to his notes (http://www.aei.mpg.de/~horst/math4999-2pdf.pdf) while doing a course on introductory differential equations, and it came in quite handy

poorly organized complicated explanation where it can be written in easier way. I would look for something else to learn PDEs