Rating: 
Summary: Not a math text
Review: Arfken's book has become a classic in mathematical physics teaching, but I don't think it could be regarded as a good text for such purpose because its is not really a mathematical text. This book is just a collection of formulas, EASY examples, problems, and references, and as such it is quite good, but the indefense undergraduate needs more than that to tackle the subject.As a working mathematician I use the book mostly as a list of formulas. When I was a teacher I also found here a lot of interesting exercises to include in the exams. As a conclusion, I find the text good as a reference, but bad as a course text.
Rating: 
Summary: NOT for (aspiring) theoretical physicists
Review: Arfken's book is not meant for anyone who has his mind set on theoretical physics, be it superstrings or quantum chaos or anything of the sort, simply because of its use of the old methods of vector calculus (and its brother, tensor calculus). Instead of discussing differential forms, lie groups, differentiable manifolds and things of theoretical interest, he spends hundreds of pages on all sorts of odd equations which you'll probably never run into during your lifetime except in a course on mathematical physics. Perhaps engineers might adopt a different view, since they tend to deal more with differential equations - I'm talking from the theoretical perspective. I would recommend Hassani's book instead of Arfken's for these matters. Make sure you check it out before you decide on buying Arfken's book! I will not deny it has its value as a reference, but even as such it also has its faults -many results are not demonstrated or even stated in the text, and are left as exercises for the reader. If this is supposed to be a reference, where are the results??? Another problem this book has is that it lacks any sort of unifying theme, e.g., recasting mathematical physics using exterior calculus, or using vector spaces. Again, this might be a good thing when using it as a reference, but then again, I already mentioned it stinks as a reference as well. There are many books out there that summarize neatly the properties of all of the special functions you'll need in your lifetime.
Rating: 
Summary: what?
Review: being a university student, and not a bad one btw, i found it very unpleasant to have so many question marks run in my head after every other paragraph. the book is unable to really explain things clearly, and to chaotic too be a reference text. take my advice and find a book less condescending and clearer.
Rating: 
Summary: Una buena base de referencia
Review: Este libro es una buena base para referencia en la materia, pero no es lo ideal si se quiere tomar como texto de estudio. el libro es de dificil lectura, pero sirve como guia de estudio, si se tiene algun texto axuilar o se toma alguna clase en que se expliquen los conseptos. Recomendable si se esta familiarizado con la matemática y la física avanzada.
Rating:
Summary: Awful as a text, semi useful as a reference
Review: Go out and buy Hassani to learn all of the material in this book and much more, buy Schaum's outlines of mathematical tables and formulae for the reference. This book is replete with minimal explanations and problems that are not the equal of the level of presentation. This is absolutly horrid as a text. I used it for a graduate math-physics course but always used other sources to learn from. I should point out that I aced the course but would have probably failed had I tried to learn from arfken.
Rating:
Summary: Don't plan on learning anything from this
Review: Great for reference, TERRIBLE to learn from. I am trying to use this required text in a course that is not teaching the student ANYTHING. If you know the material, no problem this is a good summary. If you don't know it, get another text.
Rating:
Summary: An Old Standard
Review: I admit that I have more often used this book as a reference than anything else, but what I like about it is that the sections are so compartmentalized that I find I can pick it up in the middle of something and start reading on a subject without alot of difficulty. Some books have much overhead notational and stylistic information which needs to be understood before a particular section can be profitably read. This puppy I find I can just open to a random page and start reading. This book does not give lots of explicit examples, but there are lots and lots of problems and they vary greatly in difficulty and often apply to multiple physical situations where the machinery in question finds application. I really like the problem sets and also the fact that there are explicit answers given after the problem as well as answers given explicitly in the statement of the problem. For those who crave explicit examples I think I would suggest several of the schaum's outline series as being a nice complement. There is not an explicit Schaum's on math methods but there are several on subsets of Arfken's book. I'd specifically mention those by Murray Spiegel.
Rating: 
Summary: A succint guide to the mathematical methods
Review: I am a student who really enjoy physics.
To guide through the major math methods in physics, I choose
this books.
I can use one words to describe this book:succint.
It really help me alot when I really eager to grasp some math concepts such as tensor,group,fourier series,trasform...ect.
Within the short time,I can understand the math language that
many undergraduate or graduate text books are using.
On the other hand,this book provide many example and
interesting exercise that remind us when the math tool is used in the field of physics.
I highly recommend this to whom has completely suffcient in caculus and need to grasp the main concepts of mathematical
physics.
Rating:
Summary: Great for self-teaching. Arfken uses the Socratic method.
Review: I am an M.S. in physics and use the book for reference and filling in the gaps in my knowledge. In each section, Arfken teaches the bare essentials and then asks the student to work out the rest of the body of knowledge in the exercises. Each new theorem or principle is clearly developed in small learnable steps, and the student has the feeling of Developing Physics, instead of just learning about it. Most exercises are of the type "Prove that statement (or equation) X to be true", so the student doesn't have to worry too much about numerical answers. Each exercise or topic is carefully built on the foundation of what went before. When finished, I *really understand* the deeper issues of the topic. Dr. Arfken's perspectives on the subject matter also open up entire new worlds to explore. Many times, at the end of an exercise, I realized I had just proven a statement of which I had always wanted to see the proof. There is a strong Aha! content to the entire book.
Rating:
Summary: Needs elaboration: Add 5 pages per page.
Review: I am convinced that the author of this book has made the assumption that the reader has had pretty significant exposure to most of this already. Therefore, this is nothing more than a "all in once place" reference on math methods for physicists. The reason for the diverse range of opinions on this book is due to the various backgrounds of students. For most physic undergrads now taking a grad level math methods course, our exposure to differential eqns, complex functions, tensors, group theory, etc. is superficial. Here is a good entrepreneurial idea for an accomplished physicist that can relate to us mere mortals. For each page that Arfken has provided on a topic, ELABORATE (add 5 pages per page to it and now you have a useful textbook that every graduate student in physics should have). It would save us a fortune in buying the many additional supplemental texts required if you are stuck with Arfken.
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