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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.
- Sales Rank: #1459267 in eBooks
- Published on: 1998-12-18
- Released on: 1997-12-31
- Format: Kindle eBook
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
Most helpful customer reviews
1 of 1 people found the following review helpful.
Too Many Errors
By mpiaria
I purchased the Kindle version. The typos are simply intolerable. Learning partial differential equations is difficult. This book makes it unbearable.
0 of 6 people found the following review helpful.
did not sue
By mlp
Got this for a class that I was sitting in on until I became to busy between work and school. Therefore, I really can not get a good review on this book.
0 of 0 people found the following review helpful.
This book is hit or miss
By MrDNA
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.
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