Partial Differential Equations: An Introduction | 
| Author: Walter A. Strauss
Publisher: Wiley
Category: Book
Buy Used: $10.00
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Avg. Customer Rating:  24 reviews
Sales Rank: 162705
Media: Hardcover
Number Of Items: 1
Pages: 440
Shipping Weight (lbs): 1.6
Dimensions (in): 9.3 x 6.2 x 1
ISBN: 0471548685
Dewey Decimal Number: 515.353
EAN: 9780471548683
ASIN: 0471548685
Publication Date: March 17, 1992
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Product Description
Covers the fundamental properties of partial differential equations (PDEs) and proven techniques useful in analyzing them. Uses a broad approach to illustrate the rich diversity of phenomena such as vibrations of solids, fluid flow, molecular structure, photon and electron interactions, radiation of electromagnetic waves encompassed by this subject as well as the role PDEs play in modern mathematics, especially geometry and analysis.
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| Customer Reviews: Read 19 more reviews...
 A graduate understanding of undergraduate material May 9, 2008
you should first read about the Green functions in some other books to appreciate Strauss's way of explaining things. He is clear, and easy to follow. The way he presented the material is not so advanced, Nevertheless the concepts are beyond undergraduate. This book is one of the best books in PDE's I've seen, specially chapters 7-11 and most specifically he did an awesome job for the Green functions.
GOOD FOR WHAT IT DOES--NO ONE BOOK DOES IT ALL March 9, 2008
2 out of 2 found this review helpful
I've spent the past seven years or so working on analytical and numerical solutions to the various PDEs that price financial derivatives. My focus has been very much on getting and extending useable answers. When it comes to PDEs specifically, I'm mostly self-taught, but my background in real variables and functional analysis is solid.
In some ares of mathematics, a single, classic text whose exposition is top-notch, or that inspires despite its exposition, manages to cover the field well. For example, I'm thinking of books like Halmos (Measure Theory), Rudin (Real and Complex Analysis), or Segal and Kunze in real variables and integration; Lax or Reed and Simon I (Functional Analysis) in functional analysis; Lang (Algebra) in algebra; and Kelley (General Topology) or Milnor (Topology from the Differentiable Viewpoint) in topology.
I've yet to find a single reference for PDEs that addresses all of my questions, but several books taken together manage nicely. I jumped around in these books when I was learning the subject, and I'm convinced that such cherry-picking is the best approach for PDEs, since the field is so broad in theory and applications. The downsides, of course, are expense and potential confusion from conflicting notation and approach.
Ignoring just for the moment the vast area of approximate solutions by discretization and perturbation techniques, here's who seems to be best for what, when the problem involves linear PDEs:
:: Need quick intuition: Farlow, Myint-U and Debnath, Brown and Churchill;
:: Need more theory: Stakgold (Green's Functions), Evans, Folland;
:: Need help on modeling: Strang (CSE), Stakgold (BVPs), Haberman (Applied PDEs), Farlow;
:: Don't understand how concepts relate: John, Garabedian, Strauss, Carrier and Pearson (PDEs);
:: Can't find tough enough exercises: Carrier and Pearson (PDEs), Kevorkian;
:: Need inspiration or deep intuition: Courant and Hilbert (both volumes), Zeidler (Nonlinear Functional Analysis 2A [Linear Monotone Operators], Applied Functional Analysis [especially AMS 108]).
I've ranked books very subjectively within each category on a composite of things like relevance, completeness, clarity, and ease-of-use. And I should stress that I'm no doubt ignoring many fine favorites purely through unfamiliarity.
WHERE DOES STRAUSS FIT? I repeat, all of these books address each of the needs in some measure, but no one is adequate for them all. The terse treatment and broad coverage in Strauss are great for tying concepts together and revealing their logical relationships. This is especially evident in the superb Chaps. 1 and 2-3, as well as in Chaps. 9 and 10, which treat the Cauchy Problem and BVPs in space, respectively.
Chapter 11's discussion of eigenvalue problems, and particularly their asymptotics, is remarkable at the book's level but nowhere near that in Garabedian or especially that in Courant and Hilbert, which is the original synthesis of work beginning with Weyl to which Courant and Hilbert each contributed in important ways. (The notes to Sec. XIII.15 of Reed and Simon IV [Analysis of Operators] have the history of Dirichlet-Neumann bracketing, the main methodological advance.) Both of Stakgold's works also discuss this problem but not as well as Strauss.
I've done very little teaching (and I wasn't very good at it!), so my views should be taken with a grain of salt perhaps larger than usual, but if I chose Strauss as a text, I'd have to believe either that my lectures would fill in the gaps that Strauss so clearly has or that other books on my syllabus could take up the slack. If you're having trouble learning "from Strauss," the problem may lie not with the book, but with an incomplete course, since Strauss is, in many ways, only a good set of summary notes. Again, it's good as far as it goes, but it doesn't go the whole way; that's why you need the other books.
CHOOSING A SINGLE REFERENCE. If I were packing for a desert island, I'd take Courant and Hilbert and Garabedian despite their age, since everything I need can be backed out of their presentations with some effort. (An alternative to C&H is either of Zeidler's state-of-the-art books, if you're theoretically inclined, and your computational skills are strong.) The treatment in C&H is profound and downright majestic. Many have spent a productive professional lifetime in these books, and C&H-2 comes close to being the sort of reference I describe in the second paragraph. In addition. since basic approaches to the three classic, second-order, linear equations and their variants--the gist of a first course--have changed so little in the past 50 years, publication date may not be as much a factor in selecting a single reference as it would be in some other areas. Indeed, it's well worth reading Fourier's original memoir on heat conduction, possibly modulated by a modern treatment like Carslaw and Jaeger (Conduction of Heat in Solids). (Levine [Partial Differential Equations, Chap. 13] contains a technical precis of Fourier's original approach.) Note that I am selecting a reference, however, since neither of these works is an introduction. For example, Garabedian assumes the reader is comfortable with separation-of-variables and Fourier series.
TRANSITIONING TO DISCRETE APPROXIMATIONS. If I also took Gil Strang's new book to ease the transition to discrete approximations and eventually building and evaluating numerical code, I'd forget the rest of the list without worries. Indeed, as Courant mentions in the preface of C&H-2, there was to have been a brief third volume dealing with discrete approximations for existence and construction of solutions. Strang would stand nicely in its stead, if not for existence, then certainly for construction.
Actually doing numerical work is another matter entirely, of course, and I've given some idea of the books I've found useful for these problems in my brief review of Chung's book on computational fluid dynamics.
HOW ABOUT PERTURBATION SOLUTIONS? Finally, if I closed my eyes and pretended that I'd always separate variables, so I only needed to worry about perturbation solutions of hairy ODEs, I'd toss in Bender and Orszag and feel pretty good about analytical approaches.
If I just couldn't bring myself to make that assumption, I'd take Kevorkian and Cole (Multiple Scale and Singular Perturbation Methods), which deals in part with perturbation solutions of PDEs directly, and Verhulst, which is a bit longer on intuition.
The brave might also consider Van Dyke (Perturbation Methods in Fluid Mechanics), which deals specifically with singular perturbations of the Navier-Stokes equations and their many variants. To go this route you'd have to believe that you could adapt Van Dyke's results to whatever problems you ran into, which can be real work.
ONCE MORE...WITH FEELING! If I were learning things from scratch again, I'd sleep with Farlow under the pillow and Garabedian under the bed, regardless of what textbook my instructor had chosen. For the careful Farlow raises at least as many questions as it answers--purists have my guarantee that they'll hate it. You need to supplement Farlow with greater depth in your areas of interest, and in most instances Garabedian cleans things up nicely.
An added plus is that since the books are reprints, published by Dover and AMS Chelsea, respectively, their cost is quite reasonable, even though Garabedian is beautifully printed and library-bound (would you believe sewn-in signatures?).
This review is a lot longer than I'd first intended, and its recommendations are in many ways idiosyncratic but certainly worth their cost. Partly, I think that's a function of the field itself. There seem to be as many approaches to learning PDEs as there are backgrounds and interests. The diversity of sources is likewise broad, and their quality is quite high. The beauty and power of the subject have lured many first-class mathematicians, like a striking number of the authors mentioned above, into writing basic texts. In the end someone's treatment will answer your questions, pretty much no matter what they are, if you just have the patience to look around. After enough looking, of course, you'll find you can answer many of your own questions.
One of the things that makes real-world PDEs in whatever field such fun is that getting an answer is all that's important. It doesn't matter what books you use, what willing help you receive from whom, or how you reformulate a problem to make it more tractable, as long as a useable result eventually emerges from your efforts. There's much to be said for learning the field in the same no-holds-barred way, and I hope my remarks can get you started in this direction.
 stay away from this book November 9, 2007
0 out of 2 found this review helpful
As an intro to PDE book, it's simply put, terrible. The author must have forgotten that he was writing a book aimed at undergraduates. No simply examples, not a single one. The book jumps straight into theory right from the first chapter and beyond. The exercises involve very intricate proofs and there are no simple computational exercises, none. If you've taken math analysis or some kind of easier PDE course, then maybe you'll like the book, but if you're like me and you go from ODE's to PDE's than the transition is way too rough.
Strauss PDEs June 17, 2007
3 out of 3 found this review helpful
I have only read bits of this book, but every time I read it I come to the same conclusion. I think the previous reviewers have highlighted the key problem with this book. A previous reviewer wrote: 'If you are a Scientist or Engineer and just want to learn PDE's to solve problems in science find another book, because this book is not the book for you.' There is some truth in this. However, in the preface Strauss wrote: 'This is an undergraduate textbook. It is designed for juniors and seniors who are science, engineering or mathematics majors.' It would appear that the book is simply not very suitable for the wider audience it was intended for - in particular it is too advanced for less experienced undergraduates. Also, despite containing numerous applied examples, these examples are dealt with so briefly that they would make little sense to a scientist or engineer who has not already studied the applied material in depth on other courses. This is somewhat inevitable as the book attempts to include a wide multitude of examples, and so its strength is also its weakness. This book is not a 'one size fits all' but was clearly advertised as one and ends up simply belittling itself in trying to be one thing whilst actually being another. It is a very good reference, however, and is very valuable to scientists and engineers who have already studied much of the material in an applied context, but the text is somewhat disjointed as it reads more like a catalogue of PDEs rather than as a 'how-to-do-it from first principles' manual. The book looks attractive, but every time in the past that I started reading it I soon put it down again! However, I have begun to read the book seriously from cover to cover. Maybe a taught course that is constructed around the book would work, indeed it is a valuable source of examples, but this is not a good book for self-taught study, except perhaps to those with more maths than a typical junior undergraduate. I would however recommend it as a must in the library of anyone who deals with PDEs on a frequent basis, or who wishes to teach the subject. In short - great for the right audience but the right audience is not exactly the one advertised in the preface! (This is a common failing of many textbooks). Since I began to seriously read this book from cover to cover and I am finding it fairly straight-forward, but then I have studied PDEs before. However, those who do not like the book should be comforted, because at first I never liked it either - but give it a chance and read it carefully and remember that many of the examples will not make complete sense until you have studied the science behind them in other courses. In this sense, the text is a valuable reference to senior science and engineering graduates. I think for someone new to the topic the text probably skips the odd crucial sentence of explanation. However, for an advanced mathematics, science or engineering undergraduate the strength of this book is that it puts everything together and so is a valuable reference and valuable to consolidate what you have studied on other courses. However, because it is so all-inclusive, it would need to be several hundred pages longer if it were to describe everything clearly from first principles (even assuming competence with ODEs). So, if you still don't like it, then come back to it in a year or so. I shall update this review if, as I continue with the text, my view changes.
What are you guys talking about? This book is AMAZING! October 5, 2006
10 out of 12 found this review helpful
I have never commented on a book, up until now... and I do so only because I don't think that this book gets enough credit.
People have complained Strauss may not have explained some proofs in as much detail as he could have, people complained that he didnt give enough examples, I think this is more of a problem with the readers than the writers. If you need someone to hold your hand through every step and detail, I think you should reconsider why you are studying what you study.-
I am an undergraduate at NYU, one of the best research institutes for PDE's. I thoroughly enjoyed reading this book, it gives an amazing description of what PDE's are, how to solve them, and how they are used in science. One thing I REALLY enjoyed about this book was it did not do what many other books do: first dive into seperation of variables and focused only on that. Instead Strauss shows how to solve first and second order equations without boundary conditions, giving a very elegant prose doing so!
However, I think much of the problem that people are having with this book is that it's not a "one-size fits all." (Which I don't think any book can be!) If you are a Scienctist or Engineer and just want to learn PDE's to solve problems in science.. find another book, because this book is not the book for you.
That being said, if you are Mathematics student or interested in a more deep study of PDEs this is really a good book for you. You definitely should have taken Calc. 1-3, Linear Alegbra, ODE, and I recommend one semester of Analysis (for function spaces) before tackling this book, that is what I had, and I loved this course.
PDE is a difficult subject/course and Strauss does an amazing job at explaining it, if someone like me can get PDEs so well from this course, than I seriously believe that complaints about this book is due to fault in the readers and not the writer.
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