Partial Differential Equations : An Introduction

Rating:
Summary: A darn good book
Review: I honestly don't understand several of the reviews here. At the one extreme, we have people who complain that there are not enough examples, and there are too many gaps in the proofs.
Well, that is partly the point. At some point in math, you have to move beyond the spoon fed approach of a typical lower division calculus textbook and fill in the gaps and figure out the examples for yourself.
At the other extreme, one person complained that the exercises were uninspired and did not lead away from the text. The only response I have to that is "are you reading the same text that I am?"
The title is not misleading. The book is a concise introduction to PDEs. One should have had some upper divison analysis, and some lower divison ODEs but that's about it.
I have had a graduate course in PDEs, which I basically failed to understand. I was able to get through the course, but without ever getting any "big picture". This is probably because I had never taken an undergraduate PDE course. I now have got to the point where I need to know undergraduate level PDEs and this textbook has been perfect. It is hard, but readable. The questions cover a lot of material and have a wide range of difficulty. As I've worked my way through the book, I feel that I am finally getting to grips with the subject, and beginning to see a big picture.
One of the better textbooks in my collection

Rating:
Summary: Very poor introduction!
Review: I used this book in a tough applied math course, and the quality of this book did not help matters much. There are a couple of good things about this book. The material chosen is appropriate and reasonably comprehensive for an intro PDE text. In other words, the table of contents is a nice read. The notation is very clean and concise throughout, as is the typesetting. The bibliography was also useful, pointing me to some great supplementary texts.

Now for the bad parts. An intro PDE book should explain clearly the basic concepts behind PDEs, including how certain famous equations (wave, heat, Laplace, etc.) arise in physical modeling. It should explain in detail the various computational techniques for finding analytical solutions to these equations. It should explain relevant elementary theorems needed for these computational techniques. This book attempts to do all of these things, but does so poorly. The basic problem is that the book's explanations and examples are too terse and incomplete for an introductory text. Analytically solving a PDE is a relatively difficult task, involving several computational steps and techniques. Examples of these techniques should be worked in detail, but in this book, they frequently omit steps or fail to explain where or how a particular technique is being applied. Theorems are often not stated, or if they are, proofs are either omitted or partially sketched. This makes the book difficult for beginners, but it is not a terrible reference if you have already been exposed to the material.

My advice: given the price of this book and its mediocre quality, you would do better by looking elsewhere for an intro PDE text.

Rating:
Summary: The best I've encountered so far
Review: I'm writing my first review just to improve this books ratings, since in my opinion, this book doesn't deserves anything below 4 stars.

This book contains the most comprehensive exposition of PDEs at undergraduate level I've seen so far, all the problems that I've came across are discussed here, the author does all the important intermediate steps and presents all the subjects very easily. Moreover, all the subtleties (namely, why we dropped that solution or why the eigenvalues are like that.) are discussed. The author also offers depth understanding of the physical model that every PDE is modelling.

All the necesary mathematical background is an ODE and Multivariable Calculus courses.

Rating:
Summary: A Truism: This is a terrible book on a fascinating subject
Review: May I begin by stating that my critique is based on having read and used the first 7 chapters, with some familiarity with chapters 9, 11, and 13. With that said, just about every NEGATIVE comment and review posted prior to this review, I believe, is for the most part quite accurate and nightmarishly true. In particular, Strauss states the obvious, while omitting key and crucial steps (this isn't limited just to his proofs). One might notice that the last comment is similar to the Rudin style. Let me assure you that unlike Rudin, Strauss' presentation is not elegant, it does not inspire, and simply cannot be compared to Rudin. Some other major flaws include: hasty organization, lack of depth and breath in theory, and the problem sets consist mostly of trivial proofs and unimaginative applications. I would not recommend this book under any circumstances. If you want to learn PDEs, take the graduate course.

(Continue reading only if you have to use this book for a class)

If you are unfortunate enough to be forced to read this book, here is some advice:

::Prerequisites::
It is explicitly stated in the preface that this book is intended
for undergraduates at the junior/senior level. I believe that in order to learn anything meaningful from Strauss, it requires that you have already had the following courses: calculus, multivariate calc (vector calc), linear algebra, analysis, and ordinary differential eqns. (Complex analysis, is not necessary, but does illuminate specific areas. Fourier analysis, is not necessary. Since half the books tries to establish main theorems of Fourier analysis--may I add, not at a rigorous level.)

Part of the reason why this book is abhorred so much, is that it assumes the reader is somewhat 'mathematically mature'. To many this process begins after multivariable calc (unless you took the rigorous honors) with an *upper* division linear algebra or analysis course (lower division lin. alg. doesn't count). This is where the student is first asked to write his/her own proofs. After such courses, expressions such as "it is easy to show..." and "the reader can verify for him/herself..." imply that the student is encouraged, if not expected, to actually do it for themselves.

The student who has taken the aforementioned courses, should be adequately prepared to read Strauss. However, students with this much (actually its not much at all) preparation will probably find Stauss' book a joke and lacking in rigor. Ch 5 on Fourier Series attempted to develop L_2 theory and tried to set Fourier series on a rigorous base, but I feel it failed miserably.

::Conclusion::
Only mathematics majors will probably get something meaningful out of this book, but only if they are sufficiently prepared. Other like engineers or physicists, could learn PDEs from this book, but it is highly unlikely.

::Recommendations::
If you really want to learn PDEs, you should skip taking an undergraduate PDE course that uses this book and take a Graduate PDE course. You will heavily on analysis, thus try to take an Analysis Honors course at your school.

Rating:
Summary: A Poor Text
Review: My biggest problem with this book is that the author states what is blindingly obvious but fails to examine some of the more subtle areas. It seems that by stating that a double integral is for two dimension and a triple for three one is just filling up space. Most of the remarks are of this kind. The exercises, furthermore, are not inspired. They are mostly just complete the proof, or redo the proof for a different dimension type of problems. While such questions are required, there are no questions which explore the finer details of the subject.

Moreover, there seems to be no feeling of continuity. It's a very staggered flow and does not make for enjoyable reading. The lack of discussion, rigorous proofs, precise definitions for such a rich subject makes this text almost worthless. Perhaps covering less but in greater detail would serve better as an introduction to PDEs.

Rating:
Summary: A Poor Text
Review: My biggest problem with this book is that the author states what is blindingly obvious but fails to examine some of the more subtle areas. It seems that by stating that a double integral is for two dimension and a triple for three one is just filling up space. Most of the remarks are of this kind. The exercises, furthermore, are not inspired. They are mostly just complete the proof, or redo the proof for a different dimension type of problems. While such questions are required, there are no questions which explore the finer details of the subject.

Moreover, there seems to be no feeling of continuity. It's a very staggered flow and does not make for enjoyable reading. The lack of discussion, rigorous proofs, precise definitions for such a rich subject makes this text almost worthless. Perhaps covering less but in greater detail would serve better as an introduction to PDEs.

Rating:
Summary: A good book, but a bit tough for newbies to the subject
Review: This text was incorporated into a third year applied math class in PDES I took some n > 3 years ago.

I can't say it was the best introduction to the subject for me at that time, but it helped (although not immensely), and it was practically self contained.

Rigour is not even an issue here, so it won't even appeal all that much to purists seeking a first exposure (like I was).

Rating:
Summary: Explanations are weak!
Review: This book is written from the following point of view: You have alredy been exposed to PDEs in the past, used a different and better book, and are now refreshing your knowledge. Strauss "concisely" and quickly moves through topics and simply highlights the obvious stuff you should have learned. Strauss is a good reference book for quick review, but not especially good for those adverse to equation reading rather than words.

Rating:
Summary: Don't waste your money on this crap!!!
Review: This book isn't worth the paper it is printed on! I would give it ZERO stars if Amazon gave me the option.

This is the required textbook for my class in PDEs, and I cannot imagine why any instructor or math department would choose this book, unless it was the author himself or a stockholder in the publishing company. Is worthless as an undergraduate textbook on partial differential equations, even for a mathematics major.

It is incredibly lacking in detail and description for such a complex subject. There is a dearth of examples and the explanations insufficient for the student. There are numerous times in the book where the author says: "Some of these problems are worked out in the exercises" or "it can easily be shown" or "This case is left as an exercise." There is one example where the author even says: "That was stupid: We could have guessed it! (see p. 58). Simple for who? Maybe for a mathematics professor or graduate student, but not for a person learning about the material for the first time!! One reviewer, who liked this text and who thought other reviews were unfair, remarked: "At some point in math, you have to move beyond the spoon fed approach of a typical lower division calculus textbook and fill in the gaps and figure out the examples for yourself." Perhaps you can do this if you are learning PDEs on your leisure time, but if you are at a university on the quarter system and are taking several other demanding classes at the same time, you just don't have the time to "fill in the gaps" yourself! Additionally, filling in the gaps requires a certain level of insight and intuition that not all of us have. After all, not everyone who uses partial differential equations is a mathematician. Some of us are engineers and scientists in other fields, who need practical and thorough approach to learning PDEs. If this describes you, then DO NOT buy this book!

I am tempted to rip out the pages of this book and use them for toilet paper! Unfortunately, this textbook is used as the required text for a 3 quarter PDE series at UC-Davis, so I am stuck with it for another 2 quarters!