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.
Rating: 
Summary: A useful book for physics students
Review: I find the book by Arfken and Weber very usefull as a reference book in everyday work. I study experimental physics on university level. It is very good as an experimentalist to have had all the courses in higher mathematics but 2-3 years later, when you have have a concrete problem in physics, you do not want to spend a whole day looking through all your fancy textbooks.
The book is written for physicist only and they do it well. When they give an example, and they do that a lot, they choose from the problems you find in physics textbooks. E.g. the Angular Momentum operator is used to show how ladder operators works, giving Clebsch-Gordan coefficients (they remember Wigner 3j-symbols) and the Wigner-Eckart theorem at the same time. Young-tableau, Calculus of Variations (Lagrangians pop in naturaly here), Rayleigh-Ritz variational method, Greens Functions, Dirac-equation (how to handle it and use the Pauli and Dirac matrices ...), Commutators, Bra-ket notation, all the complex integration stuff (residues, ...). The functions of the trade (Legendre, Bessel, Hermite, Laguerre, ...) what they are, how to use them, their properties (exact and asymptotic behaviour), how to do the numerical evaluation, ...
The most helpfull property of the book are the examples. From classical to quantum mechanics, chemistry (e.g. reflection symmetries of crystals) to coulomb exitation of nuclei. They are well choosen, e.g. the mathematics used for describing coulomb exitation in nuclei is very close to what is used to describe gravity fields, both are essentially particle motion in a potential field. Just because a problem is stated in one field of physics this does not play a major role in the example.
The book can be used as a first textbook on mathematics, but not (in my opinion) for self study! It is too compact in its explanations for that. I do not think that it can replace a "real" textbook on mathematics i.e. with formal proofs to give understanding etc.
But for a student in physics when you have to learn to APPLY the mathematics and as a reference book when you have a given problem it is VERY useful.
There are a lot of problems WITH answers AND hints, again problems that are often found in physics textbooks.
There are references at the end of each chapter to books about mathematics and physics, e.g. where to find a book that deals with the more detailed mathematical treatment of a given problem in physics or a more advanced study of the mathematics itself.
There are drawbacks: nonlinear dynamics and fractal behaviour is all but absent. Wavelets are completely missing, a very sad thing since they are so useful in signal analysis. Statistics and how to calculate errors given a data sample is missing. How to handle those errors in further calculations is also missing.
You have to limit the scope of the book somewhere but nonlinear dynamics is something you often find in articles and experiments and statistics is vital in understanding experimental results to say nothing of the expanding field of Random Matrix Theory.
The index is sufficient but can be improved a lot to make the value as a reference work greater. It is the index and the lack of a section on statistics that makes me rate the book 8 and not 9.
Rating: 
Summary: A poorly organized collection of formulas.
Review: I found this book quite superficial despite its length. Little more than a compendium of formulas. Poorly organized and typeset. Reasonable price per page, which pushes my rating from 0 to 2. The oldie but goodie (and inexpensive) Abramowitz and Stegun is better for reference and quick lookup. Morse-Feshbach, Courant-Hilbert and even Whittaker-Watson make more sense for in depth study although they are outdated on several topics. Poor in numerical methods and modeling. Unsuitable as textbook.
Rating: 
Summary: Clear, concise, comprehensive and stimulating.
Review: I had used Arfken as my source text for the mathematical physics option of the first year undergraduate physics course at Oxford back in 1990. For this purpose at least, the text had seemed perfect. It covered all of the required mathematical techniques (only the chapters on Group Theory, Integral Equations, and Nonlinear Methods were unnecessary) at just the right (i.e. rather fast) pace and with just the right amount of detail. The exercises were chosen well to ensure that underlying concepts became vividly engraved into ones mind and provided fine preparation for the examinations ahead. I should confess to having thoroughly enjoyed working through the algebraic-manipulation-filled exercises in Chapters 9 (Sturm-Louiville Theory) through 13 (Special Functions) - which perhaps says something about the kind of people who might enjoy this book. The conciseness of the text (which is the reason it has been possible to cover so much ground) is probably most useful only to students of well-above-average mathematical ability, and may provide insufficient support to those who find themselves struggling with the concepts introduced. Nevertheless, more able students can expect rapidly to become proficient in tackling the kinds of problems which arise in mathematical physics and engineering in later life. I give the book five stars as I still have great fondness for it from my undergraduate days, and continue to refer to it (and indeed to refer my students to it) today for the vast array of useful mathematical techniques which it covers. While it may not be the best book for those who find mathematics a chore, it should be a delight for those with a natural flair for the subject and with a mathematical physics bent.
Rating:
Summary: A salad of typos
Review: I have had the misfortune to teach from several editions of this pathetic textbook. The later printings of the 3d edition, by Arfken alone, were quite free of mistakes and of typos. But the early printings of the 5th edition by Arfken and Weber are loaded with typos and have some errors. Most of these typos are in equations that were correct in the 3d edition. My students have had a hard time learning from this book. Also, the binding of this $99 book is cheap cardboard -- the hardcover edition does not really have a hard cover. All in all,
this is a typical Elsevier product: inferior and expensive.
Rating:
Summary: A salad of typos
Review: I have had the misfortune to teach from several editions of this pathetic textbook. The later printings of the 3d edition, by Arfken alone, were quite free of mistakes and of typos. But the early printings of the 5th edition by Arfken and Weber are loaded with typos and have some errors. Most of these typos are in equations that were correct in the 3d edition. My students have had a hard time learning from this book. Also, the binding of this $99 book is cheap cardboard -- the hardcover edition does not really have a hard cover. All in all,
this is a typical Elsevier product: inferior and expensive.
Rating:
Summary: Praise from an industry physicist
Review: I invite the students on this page to take, or at least appreciate, a long-term view. Arfken pays off in the working world, with its comprehensive coverage of topics, short self-contained discussions which don't require a lot of flipping back and forth to other chapters, a clear writing style, and few proofs to get in the way. When I need to tackle a new problem which results in a coordinate system, function or technique that I'm rusty on, Arfken is usually the first book I pull off the shelf. Properties of Chebyshev polynomials for filter theory, or elliptic functions for the current density on a microstrip transmission line? Integral transforms? A comparison of Green's functions in 1, 2 and 3 dimensions for different electromagnetic diff eq's, all in one table? Group theory for certain phased-array antenna analyses? (really!) Tensors for analyzing flexure in superconducting magnet structures? Error functions for communications theory? It's all here in a quickly digestible form, with enough depth to solve a problem or at least prepare you to turn to a specialty text and quickly extract what's needed. I always learn something from the examples, which typically apply the same mathematical tool for my problem to some completely different area of physics. Arfken may not be an optimal text for a one-year course, but it's been my reliable working companion for 24 years. When my 2nd edition finally falls apart, I'll probably replace it with a new one.
Rating:
Summary: Great text for reference and learning
Review: I noticed that most student reviews seemed to disparage this book as a textbook, so I am writing this to provide an alternative veiwpoint. My intermediate Math Methods class used this book and I have not yet enountered a math problem in any of my grad classes that I couldn't use this book as an aide to solve. The book is clear yet concise, which allows for a large breadth of material to be covered in one semester effectively. Yes, some material is not covered with great depth, but I think that Mathematical Methods Books by design are not meant to be thourough, mathematically rigourous books but rather books that will present the method of solving, if not the exact solution, of most problems one might encounter in the physical sciences. I reccomend this book. Like all other Math Methods books I have seen it will require other texts as supplements if one wants a reference for every problem one could encounter.
Rating:
Summary: Great text for reference and learning
Review: I noticed that most student reviews seemed to disparage this book as a textbook, so I am writing this to provide an alternative veiwpoint. My intermediate Math Methods class used this book and I have not yet enountered a math problem in any of my grad classes that I couldn't use this book as an aide to solve. The book is clear yet concise, which allows for a large breadth of material to be covered in one semester effectively. Yes, some material is not covered with great depth, but I think that Mathematical Methods Books by design are not meant to be thourough, mathematically rigourous books but rather books that will present the method of solving, if not the exact solution, of most problems one might encounter in the physical sciences. I reccomend this book. Like all other Math Methods books I have seen it will require other texts as supplements if one wants a reference for every problem one could encounter.
Rating: 
Summary: Not good to learn from
Review: I used this book in a Math Methods 1st year Graduate Physics course, and I dont think I really learned anything from it.
It doesnt do well at TEACHING you anything, you'll have to buy another book with examples or find them somewhere, and that itself can be difficult. I found myself referring to Mary Boas' book for a few examples if I wanted to learn anything, but when you get to Group Theory you'll end up lost because the professor will run right over the material and textbooks on that subject arent that great. If i'm looking for an equation or a mathematical rule, this book is great. Ive used it for Quantum and Jackson E&M quite a bit.
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