Applied Partial Differential Equations (4th Edition) (Hardcover)

by Richard Haberman (Author)

Editorial Reviews

Product Description
Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations. Topics addressed include heat equation, method of separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, finite difference numerical methods for partial differential equations, nonhomogeneous problems, Green's functions for time-independent problems, infinite domain problems, Green's functions for wave and heat equations, the method of characteristics for linear and quasi-linear wave equations and a brief introduction to Laplace transform solution of partial differential equations. For scientists and engineers.

From the Back Cover
Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations. Topics addressed include heat equation, method of separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, finite difference numerical methods for partial differential equations, nonhomogeneous problems, Green's functions for time-independent problems, infinite domain problems, Green's functions for wave and heat equations, the method of characteristics for linear and quasi-linear wave equations and a brief introduction to Laplace transform solution of partial differential equations. For scientists and engineers.

See all Editorial Reviews

Product Details

• Hardcover: 769 pages
• Publisher: Prentice Hall; 4 edition (April 5, 2003)
• Language: English
• ISBN-10: 0130652431
• ISBN-13: 978-0130652430
• Product Dimensions: 9.2 x 7.1 x 1.3 inches
• Shipping Weight: 2.7 pounds (View shipping rates and policies)
• Average Customer Review: 3.2 out of 5 stars See all reviews (12 customer reviews)
• Amazon.com Sales Rank: #49,976 in Books (See Bestsellers in Books)

  Popular in these categories: (What's this?)

  #9 in	Books > Professional & Technical > Professional Science > Mathematics > Applied > Differential Equations
  #11 in	Books > Professional & Technical > Professional Science > Mathematics > Mathematical Analysis
  #12 in	Books > Science > Mathematics > Applied > Differential Equations

Customer Reviews

Most Helpful Customer Reviews

18 of 20 people found the following review helpful:

5.0 out of 5 stars Smooth transition to advanced topics!, August 22, 2005

By	A reader (WY USA) - See all my reviews

Most books on PDEs either address very basic, introductory concepts or tackle advanced topics requiring Measure theory. In addition, they focus mainly on theoretical concepts and do not provide adequate worked examples. Haberman's text is immensely useful both in bridging the gap between elementary and advanced books as well as in providing many, many completely worked problems. Indeed once you have had a basic course in PDEs you could use this text to teach yourself graduate-level topics such as Green's functions.

I do not try to convey the impression that this is a mere cookbook - "here's a problem, let's look up the solution". To the contrary. Haberman provides the motivation for each kind of mathematical treatment and interprets his results, pointing out their important consequences. His presentation of Gibbs' phenomenon is the most clear and comprehensive I have yet come across.

I heartily recommend this book especially to Math and Physics seniors who hope to continue on to graduate school in either of these subjects. In either case, it is expected of you to be adept at Green's functions and Haberman's book lays the groundwork for this topic.

7 of 8 people found the following review helpful:

3.0 out of 5 stars Somewhat tedious for those who love math, July 20, 2008

By	Deucalion - See all my reviews

This book succeeds at making PDEs accessible to a wide audience. As the title applies, it is extremely applied in flavour. Mathematics and mathematical physics students, given the choice, should look elsewhere.

An overarching feature of the book is its mathematical simplicity - very much in the vein of modern introductory calculus texts. This book neglects to introduce any tools of mathematical analyis. As a result, it is accessible to students unfamiliar with analysis. Consequently, most theorems can only be stated, not proven. Now, the theory of Fourier series is advanced and its neglect is understandable. However, this text neglects to define even basic types of convergence (uniform, mean). As a result, Chapter 3, on Fourier series, is basically the presentation of a cookbook set of rules regarding operating on Fourier series. Chapter 5, on Sturm-Liouville theory, becomes a set of statements of the various theorems, with practical applications such as proving the positivity of eigenvalues of the heat equation and "showing" completeness of the eigenfunctions (though this isn't proved, just stated).

Although the authors note their intent to show the connection of PDEs to physics, this book doesn't make a very good "mathematical physics" textbook, for several reasons. Among these is the above-mentioned neglect of discussions of convergence. The book is also neglects discussion of orthogonal polynomials or functions (Bessel and Legendre functions appear in Ch. 7, on higher-dimensional PDEs, but the treatment is cursory and not unified in a general discussion of orthogonal functions). Also, in many cases the book limits itself to real-valued functions, and uses awkward notation for complex conjugation, Hermitian conjugate, etc., in the rare cases these appear. There is negligible discussion of the use of contour integration or conformal mapping in the solution of PDEs - contour integrals are briefly introduced in Chapter 13 in the context of inverting the Laplace transform.

Serious math and physics students will also be irritated by the exposition in this text. A chapter typically begins by considering a PDE, then introducing tools (solution of boundary value problems, Fourier series, orthogonality relationships) in an ad hoc manner. Personally, I found this somewhat irritating: it lacks brevity, elegance, and good organization. However, it does explain how to solve a given problem.

On the other hand, the book does cover an interesting variety of topics, including Green's functions, Laplace transforms, and dispersive waves and nonlinear PDEs. These are of course introductory glances at these subjects.

There is a brief chapter on numerical methods. I didn't look at this carefully, but it seems like a very sketch of how to solve PDEs numerically which would need to be supplemented. A brief section is devoted to the finite element method. The Crank-Nicholson scheme, so important in physics, receives a paragraph.

Ultimately, I would recommend this book for those who need to learn about basic applied PDEs. Those with some background in analysis, or who need a deeper understanding of the subject, should seek a more rigorous and detailed exposition.

11 of 14 people found the following review helpful:

4.0 out of 5 stars Class text for Intro to PDE course, July 21, 2005

By	Digital Kamerad (New Jersey, USA) - See all my reviews

A good text to begin learning PDE with- I looked at two other books and preferred learning from this one over the others. The notation is clear, the worked examples are enough to get you started without baby-stepping through everything. Challenging hw problems, and the lessons are well laid out.