George B. Arfken, Hans J. Weber
"As to a comparison with other books of the same ilk, well, in all honesty, there are none. No other text on methods of mathematical physics is as comprehensive and as complete...I encourage the students to keep their copies as they will need it and will find it an invaluable reference resource in later studies and research." - Tristan Hubsch, Howard University
More that 90,000 copies sold!
Why Is This Textbook So Widely Used?
I am a graduate physics student with a strong mathematical background. This is the textbook used for our 2 semester course in mathematical methods for physics. The book is massive, both in content and physical weight. The cover is attractive and the printing seems to be fairly high quality. Now comes the difficult part of the review: finding other positive comments. First of all, I have only used a few chapters of the book thus far, so my comments pertain only to those. Some difficulties I have found... There are no answers to any exercises making the book fairly useless for self-study. The material is very uneven, as if each section was written what ever happened to proof reading? The class INSTRUCTOR doesn't like the book, but is forced to use it by the department, and has regularly emailed the authors with corrections and recommendations. None of the students in the class like the book. You may be forced to use this book, but I would recommend other books as supplements (e.g., the book by Mary Boas and several in the Schaum Outline Series).
A physicists handbook for mathematics -- not a textbook
The lecturer of our undergraduate Mathematical Methods for Physics course said that he recommends Arfken's book because it will be useful also later as a reference book. Hearing those words, I could not help but to think "this is one of *those* books". And indeed, although Arfken's and Weber's book covers quite a wide range of mathematics, it does so by being very concise, e.g. there is usually only one example per topic. This is one example of why it is not a good textbook. Not following Arfken's course, I will give another example: there are no answers and no solutions for any of the problems, making it very undesirable from the viewpoint of the person who cannot attend all the lectures. Finally, text itself is quite concise, and often it stops at telling the things rather than explaining them also. I guess I have to admit that I am not one of the excellent students mentioned by a reviewer, for I liked Kreyszig's Advanced Engineering Mathematics much more. As a contrast to Arfken's book, it offered many examples and helped to understand what the thing was all about. Unfortunately, it does not cover nearly all of the topics covered by Mathematical Methods for Physicists. If Mathematical Methods for Physicists is going to be your first introductory text to these topics and if you are not supported by very good lectures I can only say that may God have mercy on your soul.
An undergraduate review
My instructor chose Arfken as the text for our Mathematical Physics class. He has a high opinion of the book, although he did not require it to be read and did not assign any of the exercises. Rather than using Arfken, most of the students in my class used various mathematics and physics books from the university library. My opinion of Arfken is that it is so condensed that it is not understandable to undergraduates. You need to consult other texts extensively to fill in the gaps. For example, Arfken develops tensor analysis on pages 126 thru 130, 5 pages total. My copy of Applications of Tensor Analysis by McConnell does the same on it's first 171 pages. I hesitate to say that Arfken is useless, but you can draw your own conclusion from my last example. Arfken is so abbreviated that it is not useful to the undergraduate as a reference either, in my opinion. Perhaps it is useful to persons who are familiar with the subject matter in advance, I am not sure. Were one or a group of people to flush this book out it might be more useful, but it would no doubt become many volumes.
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