Customer Reviews

Applied Partial Differential Equations (4th Edition)

5 star:		(5)
4 star:		(6)
3 star:		(3)
2 star:		(0)
1 star:		(5)

 

 

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.

I have taught a graduate level "mathematical methods for engineers" course (or any of the similar name permutations) for many years. My course is essentially a two-semester course in PDEs with associated topics thrown in: it is truly a combination of PDEs with engineering physics problems. I have struggled to find a satisfactory text and have tried many different ones in the process. I find Haberman is ultimately the best choice. Perusing the reviews, I am not surprised to see the criticisms there. This subject matter is sometimes to obscure for engineering/physics students but too superficial (e.g. lacking in proofs and formalism) for purists in mathematics. It's a tough line to walk and nothing is perfect out there. My opinion is that Haberman does a very nice job balancing the physics with an appropriate amount of mathematical detail. Are there topics I'd like to see that aren't? Sure, but that's always going to be true. The all-inclusive text would be multiple volumes and a thousand pages and probably still some would complain important topics are left out.

The closest other text is the PDE text by Nakhle Asmar (I've used that too for a couple of years). It spends more time on special functions and is nice in that regard. However, it definitely falls short in important categories, most notable the whole topic of Greens functions is not introduced.



For my opinion

While the presentation of the book was very understandable (especially compared to some other partial differential equation textbooks), there are few worked examples in the book. For those who want worked examples, just type in the google key words "haberman site:.edu". If this book could include some of those worked examples, it would be much better.

The book also uses slightly different notation from that of many other books.

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.

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.

I used a very very large part of this book in my first year of graduate school and I haven't meet such a CLEARLY written book on the topic of applied partial differential equations (PDEs). The author develops various methods of solving problems of PDEs in a highly pedagogical and reasonable manner. Sometimes there may be a few (only!)"dark points" in the development of the subject, but with some effort on the side of the reader every step seems ultimately reasonable (especially if the reader goes through those special points more than once). The background of an undergraduate physics student is more or less enough for a thorough study of Haberman's book (besides that, things that may seem unfamiliar to the reader are touched in separate supplements dispersed all over the book). There are also plenteous unsolved exercises throughout the book, some of them accompanied by an answer. The reader may notice that there are not many examples given by the author, but this is highly mitigated by the smoothness and clearness of the presentation of the related theory or method - in other words, even if sometimes there is not any solved example ... I can safely re-assure that you will be able to implement the stuff you learned and go directly to the unsolved problems (this is something that happens only with very few books out there!). Concluding I need to say that this book will probably not satisfy mathematicians since it lacks what is usually defined as "mathematical rigor" - the main purpose of the book is to teach a whole array of methods for tackling PDEs as well as present the underlying idea behind each and every method, starting with simple ideas/methods in the beginning and going towards more and more sophisticated methods at a later stage. Highly recommended for those who want to learn the technical part of PDEs!

Decent textbook. Explains when mathematical constraints are imposed for the sake of physical phenomena, and generally makes no tricky leaps when explaining things. Conveys relatively clearly and isn't afraid to resort to less-than-rigorous language at all times.

I found this book much more explanatory than another book I had purchased for a different partial differential equations class. This book does just what it says, it is more applied, and I found that much more useful as I am a scientist. They do a fairly good job of explaining why they are doing things, and have appendixes to show more of the gory detail of a derivation than they show in the regular text if you want it.

I bought this book hoping that it will be useful for my Engg Analysis course. I dropped the course to take something else, but anyway:
The book is easy to follow only if you have an instructor to guide you. My professor said something about this book being more readable. According to him, the other books in the subject were so cryptic, they might as well have been written in Arabic! The book begins with the heat equation, which is of interest to mechanical engineers. There are plenty of unsolved examples, so you will be busy. Brushing up on your undergrad-level calculus/linear algebra will save you much of the pain. Overall, a good book.

Took two semesters of PDE's and this was used for the 2nd semester course. Very good for learning and for reference.