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Mathematics for Physics: A Guided Tour for Graduate Students Hardcover – 9 Jul 2009

4 out of 5 stars 1 customer review

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Product details

  • Hardcover: 820 pages
  • Publisher: Cambridge University Press; 1 edition (9 July 2009)
  • Language: English
  • ISBN-10: 0521854032
  • ISBN-13: 978-0521854030
  • Product Dimensions: 18.9 x 4.5 x 24.6 cm
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 731,553 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description

Review

'The amount of material in Mathematics for Physics is definitely more than enough for two single-term courses; that provides a potential lecturer considerable flexibility. … The many features that make the book valuable to students and teachers also represent a substantial step toward making modern mathematics a part of the working arsenal of practising physicists. I strongly recommend it to those who feel the need to upgrade their mathematics repertoire.' Physics Today

Book Description

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. Topics are illustrated through carefully chosen examples, exercises and problems drawn from realistic physics settings. Solutions to the exercises are available at www.cambridge.org/9780521854030.

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Top Customer Reviews

Format: Hardcover
I was very happy with the practical examples in this thorough treatment of the essential mathematical tools of physics. The book is well-organised and relatively easy to follow, considering the level of the material presented. I would expect it to be useful not just at post-graduate but also undergraduate level, and as a suitable reference for practicing physicists.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: HASH(0x8ed2c57c) out of 5 stars 11 reviews
46 of 48 people found the following review helpful
HASH(0x8ed69708) out of 5 stars Great book! 14 April 2010
By James - Published on Amazon.com
Format: Hardcover Verified Purchase
Warning: review based on first half of book.
I used this book for a graduate level Mathematical Physics class where We worked through Chapters 1 through 9. I've skimmed a little through the rest which also looks good. So let me tell you it's strengths and weakness. The book is definitely intended for graduate physics students. Most of the examples are actual physics uses of the math you learned (and there a lot), because of this you probably need a solid undergrad background in physics at least classical mechanics, E&M and Quantum, as well as Calculus, Linear Algebra, Differential Equations (and more math exposure the better!).

Strengths:
1. It goes through a lot of math! In fact because of this it is useful as a reference book as well, the book is 800 pages. Covering a broad range of traditional mathematical physics and more modern methods(e.g. Differential Geometry, Groups, ect.)

2. Lots of real world examples. This I think is probably it's biggest strength, and makes it worth the purchase, at least for me. The starts by explaining the mathematical concept, and then gives you worked out examples from physics. A lot of modern mathematics is extremely abstract, these examples help to get a feel for what the math actually says.

3. The explanations are thorough. For the most part, the book does not gloss over topics. The rigor is what one would expect for a theoretical physics, not as rigorous a pure math course, but more rigorous then what is presented in physics courses.

Weakness:
1. Because the book covers a lot of material and gives so many worked out examples 'simple' steps in derivation are omitted. For the most part this is not a problem. It just means you have to spend more time on each page, perhaps with pencil and paper, but it does make it hard to casually read. (This probably better then the other option where every step is included, the book would have probably been 2000 pages)

2. This is probably a statement about the material in general then about the book. The math is hard. It takes a lot of time and work on the part of the reader to really understand a lot of these concepts.

Overall:
As an aspiring theorist, I have a lot of math and physics books on the shelf(more like shelves). Its hard to say for sure but I see this as a book I can and will return to throughout my graduate school experience for help on understanding the math used in my courses. If your a senior in undergrad physics or somewhere in your graduate program this is a book that will return the investment. If you want a mathematical reference that is relevant to physicist this book is also for you. If you haven't taken that many math courses or don't have a solid physics background you might want to explore other books before diving into this one.
19 of 20 people found the following review helpful
HASH(0x8ed69954) out of 5 stars Not a useful reference 9 Nov. 2010
By Scelesti - Published on Amazon.com
Format: Hardcover Verified Purchase
This was the required text for a graduate course I took in Mathematical Methods for Physicists. We covered material from chapters 1-6, 8, and 17-19 which deal with calculus of variations, function spaces, linear differential operators, ordinary and partial differential equations, Green's functions, special function theory, and topics from complex analysis. The book deals with many other topics, namely group theory and differential topology & calculus on manifolds, but these were not covered in the course I took.

What are the strengths of this book? I suppose it would be useful if you have a *very strong* background in many of these topics already and just want another perspective. The topics covered are broad, and the applications that the authors have chosen to covered may be useful, depending on your area of interest.

What are its weaknesses? Every time I had to reference this book to supplement my notes from class or to help with homework problems, I became frustrated very quickly. Too many steps are omitted in derivations to follow the logic of the authors, and on many occasions they give a partially worked example rather than the mathematical details required to make the concepts clear. I want a book for my reference library that I can pick up, page to the section that deals with the topic I'm interested in (like the book by Kreyzig: Advanced Engineering Mathematics, Textbook and Student Solutions Manual) and read a clear exposition of the mathematics, rather than having to slog through a vague, partially worked example from another area of physics and try to guess what the authors mean. After spending several hours trying to connect one line of a derivation with the next and ultimately failing on several occasions, I started looking elsewhere for textbooks. Let me mention as well that I am a fluid dynamicist by training; I'm certainly no stranger to long and messy derivations.

In short, this book could be useful *supplement* to other applied mathematics texts in your library, but do not expect to be able to pick it up as a reference and obtain useful information in a timely manner.
11 of 15 people found the following review helpful
HASH(0x8ed69918) out of 5 stars Confusing, obscure, and poorly organized. Avoid this one. 5 Dec. 2010
By Oliver D. Hanson - Published on Amazon.com
Format: Hardcover Verified Purchase
I used this text in a graduate math physics class. We covered the first 9 chapters (approximately), with some skipping around. The authors play fast and loose with notation, are excessively sparse, and seem to emphasize overly 'mathematical' excersizes -- often losing sight of this book's purpose: to teach physicists. By the end, I found the only time I was even referencing this book at all was to copy down homework problems. For actual content (and to assemble sufficient supporting material in order to answer those homework questions), I sought out other textbooks which presented topics more straight-forwardly and clearly.
3 of 4 people found the following review helpful
HASH(0x8ed69c0c) out of 5 stars Wide, in depth coverage of modern math for physics 6 Oct. 2012
By a-brperr - Published on Amazon.com
Format: Hardcover Verified Purchase
This book is well written, and contains an excellent, wide array of important topics in math for physics. This book is unlike many others in that it achieves a much deeper understanding of modern math concepts like distributions (generalized functions), and other functional analysis concepts, as well as covering high level differential geometry, algebra and complex analysis. The treatment is, admittedly at a slightly higher level than most first-year graduate texts for physics students, but I think it is very reachable for students with a great interest in the deeper math behind today's physics research, and with a good background in mathematics (Linear Algebra, Calculus, Differential Equations, and some proof based course). There is no treatment of general (point-set) topology, but rather it treats higher level differential topology topics in a very nice way without the need for it.
HASH(0x8ed69c6c) out of 5 stars Covering a broad range of topics and very confusing 4 Oct. 2013
By wdg - Published on Amazon.com
Format: Kindle Edition
This book covers a broad range of topics and its organization is quite fresh (starting with calculus of variation) compared to other similar books in the market. The book offers numerous insights, provided you can get through the derivation. However, as other reviewers suggested, many of the examples in the book were partially worked out and many important steps in the derivations were omitted outright. This is very disrupting unless you are taking a course on this subject, having a excellent instructor and using this title as the textbook. For this reason, I can only recommend this title to experienced person who needs an advanced reference book. In some way, this book is more like a review than a textbook.

Some notations in the book does not make sense. For example, in the first chapter, the author sometimes used dot notation (like \dot{x}) to represent partial derivative against the convention, sometimes total derivative. And the meaning of such notation is not at all clear in the context.

P.S. Michael Stone's website has two lecture notes on which this book was based on. I couldn't find much difference between the book and the lecture notes. So unless Prof. Stone vastly revise this book, his lectures notes is good enough for me. No need for this book.
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