Customer Reviews

Mathematical Methods for Physicists, Fourth Edition

5 star:		(15)
4 star:		(6)
3 star:		(9)
2 star:		(18)
1 star:		(14)

 

 

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 by a different author (graduate student?). The explanations and examples are mediocre at best (contrast with the Mary Boas book). There are MANY typos - 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).

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.

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.

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.

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.

The best thing that can be said about this book is that it reads like some kind of encyclopedia of physics math ( and not a complete one at that). There is a lot here but the author is another one of those who believes the student is best served by working it out for himself. That may be true but it is also the easy way out for textbook writers and teachers. Also, the course should at least be set up so that the student can find out the correct answer. My experience is that the mathematical physics courses that use this book are not. At the time this book first came out there was no other suitable book. That, unfortunately, is how so many of the physics texts become classics, not by being useful or good. Also, the treatment is mostly of very classical mathematical physics. I pity the student who attempts to get a good background in group theory from this book for use in GR or particle theory. Better books exist nowadays partly as a reaction to this book. Find one you like and use it.

I have been a physics professor now for nearly 18 years and this is one of the worst TEXTbooks I have seen. It is essentially a large reference book for those that already have mastery of the topics and is of very little use as a textbook.

Basic pedagogical problems abound such as: 1) Topics in many chapter sections are dependent upon other sections perhaps many chapters ahead of the current topic... and those referenced sections are in turn dependent upon other chapter sections elsewhere in the text. This leaves one to wonder if the Authors had meaningful structure of the text in mind when they wrote it. 2) There are few useful examples for students. Most of the useful information is left to the student to work out as exercises without textbook guidance. 3) Section problems are unclear as to what the Authors are asking and since students are largely left to their own devices to discover crucial concepts, the text becomes largely irrelevant.

This book is a reference NOT a textbook. Students will need to have other well written Textbooks on hand such as Mary Boas's "Mathematical Methods in the Physical Sciences to make sense of the material THEN go back to this book once they have mastered a topic to see if they can glean what the authors intend.

In physics, there are "status symbol" textbooks that, unfortunately, departments adopt to try to impress others of their rigor, high level and expertise. These books do little, if anything, to help students learn and therefore are poor textbooks. This is one of those books.

Most physicists I know say that while this is not the best of textbooks, it's a great reference. I sometimes ask them to refer me to a useful section. They usually can't.

This book is the standard in graduate math courses for physicists. It's a shame. We buy this book for the course and then either seek out other texts (or the internet) for elaboration, or more often, we trudge through all the math that Arfken leaves out. I've rarely used any math not found in this book, but also rarely has this book been useful enough to show me how to use the math. It's sort of like a dictionary. Everything is mentioned, but if you want to learn about something, you need to know a lot more than just a definition.

Boaz's undergraduate math book is a good text for this subject. Unfortunately, it doesn't go in depth enough for all of a graduate course. For the same price as Arfken, I own about a dozen Dover editions, one for each of the important sections covered in a year long course.

A topic that we thoroughly exhausted but is not taught too often these days is complex analysis and the calculus of residues. Residues were much more important for solving complicated integrals before computers became so commonplace. For this, I recommend "Complex Analysis" by Tristan Needham. It's a tome of all things complex, but if you have the time, or are just curious, it's a great book.

If possible, get a list of alternative sources from you professor before you take the class requiring this book. Then buy them, do not buy this awful monstrosity.

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.

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.