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

E. C. Zachmanoglou (Author), Dale W. Thoe (Author), Mathematics (Author)

Book Description

Publication Date: February 1, 1987 | ISBN-10: 0486652513 | ISBN-13: 978-0486652511

This introductory text explores the essentials of partial differential equations applied to common problems in engineering and the physical sciences. It reviews calculus and ordinary differential equations, explores integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory and more. Includes problems and answers.

Product Details

• Paperback: 432 pages
• Publisher: Dover Publications (February 1, 1987)
• Language: English
• ISBN-10: 0486652513
• ISBN-13: 978-0486652511
• Product Dimensions: 8.5 x 5.4 x 0.8 inches
• Shipping Weight: 15.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #232,917 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

55 of 57 people found the following review helpful:

4.0 out of 5 stars Excellent introduction to PDEs, January 25, 2000

By 

Daniel J. Bodony - See all my reviews

This review is from: Introduction to Partial Differential Equations with Applications (Dover Books on Mathematics) (Paperback)

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.

29 of 29 people found the following review helpful:

5.0 out of 5 stars Shows mathematic viewpoint and then applications, April 20, 2006

By 

calvinnme - See all my reviews
(HALL OF FAME REVIEWER)    (VINE VOICE)    (TOP 50 REVIEWER)   

Amazon Verified Purchase

This review is from: Introduction to Partial Differential Equations with Applications (Dover Books on Mathematics) (Paperback)

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.

18 of 19 people found the following review helpful:

5.0 out of 5 stars Understandable, Excellent Reference, September 30, 2005

By 

Euler, Jr (Duke University) - See all my reviews

This review is from: Introduction to Partial Differential Equations with Applications (Dover Books on Mathematics) (Paperback)

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.