Mathematical Methods of Physics 2nd Edition by Jon Mathews (PDF)

Description

Unmarked book with light wear, might be Asian printing although not stated

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Excelent textbook on mathematics

⭐Excellent

⭐While they cover a decent range of topics, the pedagogy in Matthews and Walker is weak. Less important, but more annoying: when bought new at a price of about $100, the binding on this paperback (a paperback for $100? really?) cracked within weeks. The paper quality is also poor. It’s as if Matthews and/or Walker were printing and binding the books themselves in their basement using elmer’s glue and old newspapers.If you have the choice,

⭐by Mary Boas is a far superior textbook. While there may not be full overlap in topic coverage between the two books, Boas is better in terms of price, quality, and especially pedagogy.

⭐I acquired this book in 1984 when I was at Caltech in the Phd. theoretical physics program (having sold my disliked Arfken book to a mechanical engineering roommate, and using the proceeds to purchase this book). It was recommended for the candidacy (qualifying) exam on mathematical physics at Caltech. The book is not a reference book, it is relatively short for a mathematical methods book at about 500 pages.And it is little dated, so that while it has a couple of excellent final chapters on tensor analysis and differential geometry, and group theory, there is no modern treatments of connections, forms, gauge theory, topology, and string theory applications, that you would find for example in Physical Mathematics by Cahill.What sets this book apart (and what I think accounts for many of the relatively low ratings) is that it essentially teaches by example. And it has many excellent examples along with good problem sets at the end of each chapter, which include many problems of varying difficulty, but all doable and informative. The book has very good beginning chapters on differential equations, covering some topics that usually get lost in DE books and courses, as well as a nice short chapter on evaluation of integrals. I remember using the example of an integral over a solid angle with vector products in the denominator which I needed while verifying a calculation on gravitational radiation from the sun, in Weinbergs famous book on gravitation and cosmology.The book is junior/senior/beginning graduate level and geared at physics majors (students who can usually teach themselves, and don’t get scared with a little jumping around, and introduction of new techniques). This is a practical book not focused on pedantic rigor, but on doing calculations and getting answers.

⭐What I disliked most is that this is a most diffucult book even for the majority of physics graduate students. This explains the paucity of reviews and their very low level.What could possibly be the motivation to write such a book? I could never figure this out. If the idea is that new breakthroughs in physics won’t come from students who can’t pass a course based on this book, this book would then be very discouraging to the otherwise motivated student whose background is otherwise suitable to pursue physics as a career. One assist to comprehend this materi comes from the highly regarded theoretical physicist Lorlla M. Jones University of Illinois at Urbana-Champaign entitled “An introduction to Mathematical Methods of Physics” specifically written to make the contents of this book more tansparent to physics graduate students and upper level under graduates. The chapters on complex variable are particularly well done.The best book that covers essentially all topics that would interest a graduate physics student or any engineering science student is the third edition of “Mathemathical Methods in the Physical Sciences” by Mary L. Boas. Mary Boas is also a celebrated mathematician and physicist with a Doctorate in physics from the Massachusetts Institute of Technology. My recomendation is to pass up Mathews ans Walker and to go with Mary L. Boas.

⭐I have owned this book since I took my first undergraduate mathematical physics course in 1972. Since that time, however, I have not really found Mathews and Walker to be terribly useful. My problem is that it is difficult for me to learn to use mathematical methods if they are presented without proof. For example, the Theory of Residues is used in many parts of this book–but it is presented without first proving Cauchy’s Theorem. Part of my difficulty is that if I do not go through the proof, I feel that I am not aware of the limits of the method in question. Also, the proof allows me to develop an intuitive feel for the method. That said, I can see that this book might be good as a reference to sort of remind you how to use a method that you had learned earlier in a more complete treatment. Or, by perusing M&W you might come upon a method that you can research in more depth though a more complete book.One recent useful piece of information that I have found in this book (p.76), and which I have yet to find anywhere else, is the derivation of the relationship that expresses the beta function in terms gamma functions. Please note that I am attaching this scanned page for the perusal of the reader. This was a particularly important expression for me to understand because of the central role that it plays in renormalization in quantum field theory. See Chapter 9 of

⭐, equation (9.16), p.314, and Appendix A (pp.382-385) for the application of beta/gamma function relationship.

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