Introduction to Partial Differential Equations with MATLAB [Hardcover]

Jeffery M. Cooper (Author)

Book Description

ISBN-10: 0817639675 | ISBN-13: 978-0817639679 | Publication Date: December 18, 1998 | Edition: Corrected

The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. Introduction to Partial Differential Equations with MATLAB is a careful integration of traditional core topics with modern topics, taking full advantage of the computational power of MATLAB to enhance the learning experience. This advanced text/reference is an introduction to partial differential equations covering the traditional topics within a modern context. To provide an up-to-date treatment, techniques of numerical computation have been included with carefully selected nonlinear topics, including nonlinear first order equations. Each equation studied is placed in the appropriate physical context. The analytical aspects of solutions are discussed in an integrated fashion with extensive examples and exercises, both analytical and computational. The book is excellent for classroom use and can be used for self-study purposes. Topic and Features: • Nonlinear equations including nonlinear conservation laws; • Dispersive wave equations and the Schrodinger equation; • Numerical methods for each core equation including finite difference methods, finite element methods, and the fast Fourier transform; • Extensive use of MATLAB programs in exercise sets. MATLAB m files for numerical and graphics programs available by ftp from this web site. This text/reference is an excellent resources designed to introduce advanced students in mathematics, engineering and sciences to partial differential equations. It is also suitable as a self-study resource for professionals and practitioners.

Editorial Reviews

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 Inside Flap

"Cooper's book stands out among a host of PDE works One of the book's excellent features is the availability of illustrative and challenging problems, some of which have been cast in form of Matlab projects. Such features undoubtedly make this a suitable work for a laboratory component of an introductory PDEs course." --Choice

Product Details

• Hardcover: 560 pages
• Publisher: Birkhäuser Boston; Corrected edition (December 18, 1998)
• Language: English
• ISBN-10: 0817639675
• ISBN-13: 978-0817639679
• Product Dimensions: 9.5 x 6.1 x 1.5 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 2.2 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #62,440 in Books (See Top 100 in Books)
  • #87 in Books > Computers & Technology > Computer Science > Artificial Intelligence

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Customer Reviews

Most Helpful Customer Reviews

38 of 38 people found the following review helpful:

2.0 out of 5 stars An excellent rough draft of a textbook., December 21, 1998

By A Customer

This review is from: Introduction to Partial Differential Equations with MATLAB (Hardcover)

Cooper's book does some things quite well. While most courses on PDE's are reduced to repetitive applications of separation of variables and Fourier series, Cooper offers a new approach. He goes by equation rather than by technique, and introduces nonlinear equations and numerical methods very early. Separation of variables and Fourier series do not come up until Chapter 4. The first chapter, which reviews elements of analysis, is a very good reference. MATLAB is well incorporated throughout the text.

The reason I do not rate this book more highly is that the writing is unbelievably sloppy. There are at least five typos per chapter, usually more. Crucial things, like Green's first identity, are misprinted. There are dozens of typos in the answers in the back, which makes it very hard to check your work.

Judging just by the content, this is a very good book. However, the misprints in the math (to say nothing of those in the text) are so severe that I would not recommend buying it until a better-proofread edition comes out.

11 of 12 people found the following review helpful:

3.0 out of 5 stars Not bad, but the 2nd edition will hopefully be better, February 2, 2002

By 

Kyle Maxwell (Irving, TX) - See all my reviews
(REAL NAME)   

This review is from: Introduction to Partial Differential Equations with MATLAB (Hardcover)

This is a fairly challenging text. It's currently being used in my undergrad PDE course, and the flow of material is a bit out of the ordinary. The book starts off with the method of characteristics and weak solutions, which are slightly more sophisticated and unusual topics than some of the later material, making it difficult to get started. The focus on using Matlab is nice, and most things are fairly well-explained. Typographical errors are rampant, however, making it very poor for self-study (you need someone to point out the errors to you).

All in all, not bad -- the second edition will hopefully be much better, and if you have a decent grounding in multivariate calc and ODE's, you'll be OK.

2.0 out of 5 stars This book is hit or miss, August 19, 2009

By 

MrDNA (Spokane, WA) - See all my reviews

This review is from: Introduction to Partial Differential Equations with MATLAB (Hardcover)

This book does some things very well and some things not so well, depending on your perspective. Perhaps one of its problems is that it attempts to straddle the line between being a book for scientists and being a book for math students.

That said, it could stand a fairly hefty reorganization. For example, the relationship between Green's functions, weak solutions, and fundamental solutions could be brought together in an early chapter instead of spread throughout the book. Same goes for material on eigenfunction expansion.
The material on a given PDE for one dimension should probably be at least near the chapter on the same PDE in multiple dimensions, rather than being separated by 6-7 chapters.

On top of this, the material is sometimes hard to follow in terms of motivation and justification. This is not uniform, however, and some parts of the book are quite clear. And, all things considered, it does a fairly good job of presenting things rigorously without alienating its potential audience of scientists and engineers who are not as versed in proof-based books.

Aesthetically, there are a lot of somewhat serious typos and the typography is atrocious. For example, parentheses are not sized properly, bars written over letters do not cover the letters as they should. These are basic and easy to fix LaTeX errors, and it gives the book an appearance of having been rushed or at least not given the attention to detail it should have been.