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The Geometry of Physics: An Introduction Paperback – April 13, 1999

ISBN-13: 978-0521387538 ISBN-10: 0521387531 Edition: Revised

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Product Details

  • Paperback: 678 pages
  • Publisher: Cambridge University Press; Revised edition (April 13, 1999)
  • Language: English
  • ISBN-10: 0521387531
  • ISBN-13: 978-0521387538
  • Product Dimensions: 7 x 1.3 x 10 inches
  • Shipping Weight: 2.5 pounds
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (13 customer reviews)
  • Amazon Best Sellers Rank: #1,787,499 in Books (See Top 100 in Books)

Editorial Reviews

Review

' ... extremely helpful for students in physics and engineering ... recommended to a wide audience ...' European Mathematical Society

'The layout, the typography and the illustrations of this advanced textbook on modern mathematical methods are all very impressive and so are the topics covered in the text.' Zentralblatt für Mathematik und ihre Grenzgebiete

Book Description

This book is intended to provide a working knowledge of those parts of geometry that are essential for a deeper understanding of both classical and modern physics and engineering. This book will be useful to graduate and advanced undergraduate students of physics, engineering and mathematics.

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Customer Reviews

3.9 out of 5 stars

Most Helpful Customer Reviews

93 of 103 people found the following review helpful By Bay Area Educator and Tech Worker on February 21, 2000
Format: Paperback
This book introduces the methods of modern differential geometry and its uses in theoretical physics. The only prerequisites are a good working knowledge of multivariable calculus and linear algebra. The book is very much written for a physics audience(i.e. the book is actually READABLE unlike so many graduate texts in mathematics, and there is an emphasis in actually learning how to CALCULATE things, rather than just staring weary eyed at mathematicians beloved polished proofs that only they can understand) There is an emphasis on physical understanding of the mathematical structures and not too many proofs. Proving things is not a bad thing, but Dr. Frankel seems to know when its most appropriate to do this, and doesn't get too bogged down in the proofs. There is a lot of material in this book (22 chapters) The book is broken into 3 main sections. The first section is on "Manifolds, Tensors, Exterior Forms" Differential forms are not that familiar to physicsts and this is a great place to learn about them. There is very nice section on how to relate Forms to vector Analysis in 3 space that physicists love dearly (see page 94). The second section is on "Geometry and Topology"-mainly Riemannian Geometry and Some Algebraic Topology like DeRham Cohomology, and the third is "Lie Groups, bundles, and Chern Forms". In this third section there is a Chapter on the Dirac equation, and its relation to Spin geometry. The only thing that the book is lacking is that there is no complex algebraic geometry (for aspiring string theorists). It would be nice if some day Dr. Frankel could write a book on this subject, since at this time none exist. I think that even mathematicians could learn a thing or two from this book. Most of differential geometry originated in Physics, not the reverse.
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39 of 41 people found the following review helpful By A Customer on January 8, 2001
Format: Paperback
I picked this book for self-study in order to understand differential topology in physics. It is an excellent book for the breath of ideas applicable to many areas of physics and the author has examples from stat mech, thermo, e & m, classical dynamics as well as relativity. I agree with the previous review that it lacks a sense of direction. Occasionally, Frankel uses a concept without explanation only to define it a hundred pages or so later (e.g. the star operator on em fields). For me these problems made the text tough going. I was frequently derailed by complicated notation (without glossary), lack of direction, and deus ex machina concepts dropped without adequate explanation. Some of the confusion derives from use of coordinates which Frankel finds necessary in order to motivate development of coordinate free forms. It seems that the author could have avoided this as did Darling or introduced Clifford algebra early on. I do not recommend this book for independent study without other texts like Flanders, Darling, Misner Thorne Wheeler, etc. to refer. It would be best to have a tutor guide one through it or re-read it after getting sufficient grounding with other texts. This being said it is valuable addition to my library and I still think highly of Frankel's effort.
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27 of 28 people found the following review helpful By E. M. Stoudenmire on March 3, 2006
Format: Paperback
The other reviews on this page give this book anywhere from 1 to 5 stars, and they are all correct in their own way. The book is inspired, deep and full of physics applications and insights. On the other hand, it skims over mathematical rigor to a large degree and focuses more on defining things, getting a feel for them and moving on to application.

My advice: buy the book for its strengths, and read other books in parallel if you need more rigor. But still, buy it.

Also, things can be confusing on the first two or three reads, but keep at it and you will be glad you did.
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20 of 22 people found the following review helpful By Kevin Roberge on July 25, 2003
Format: Paperback
Having taken a course out of Frankel (over the first 7 chapters) and now having used it in my senior project (topology of circuit analysis) I have to say that I love this book more by the day.
Beforewarned it is not an easy text and you may have to read a section or a chapter over a hundred times. I have found that the material is dense and deep but in a way that welcomes effort. It is weak as far as rigor goes, but rigor can sometimes get in the way of understanding. Use this book alongside mathematics texts in topology, differential geometry and linear algebra and there is much to gain.
For an undergraduate in mathematical physics (which I am) I have come to love this book I highly recommend it to a serious student.
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23 of 27 people found the following review helpful By A physicist on June 14, 2002
Format: Paperback
This book is definitely a must for the mathematically minded physicist. Self-contained, logically structured throughout, absolutely consistent mathematical notation (which nevertheless does not slide into over-sophistication). It is as if Frankel somehow knew about the anger of readers who are never satisfied with the mathematical presentation within similar textbooks. The covered material is the right collection of things that are 'needed' nowadays and missing topics can easily be added by reading sections in Nakahara (which is the best supplementary text). In comparison to Nakahara, Frankel is much more rigorous and precise. For instance the notion of 'tensor product' and its relation to the wedge-product of p-forms is not properly handled in Nakahara, also, Nakahara usually does not motivate the mathematical need of a new construction. Probably only a pure mathematician may find inconsitencies or unsatisfactory conclusions in Frankel's book.
I do not agree to the previous review that Frankel is not suited for self study. On the contrary, Frankel is THE book for self study, it's a pleasure to go through it page by page. Only real requirement: you must like the field. So if you have a sort of a 'feeling' for the strange beauty of topology and manifolds, then this is the book for you. The nice thing about it is that it nevertheless provides 'practical' knowledge, ie. the reader really learns how to use the mathematical concepts 'practically' with paper and pencil. Frankel is right when he claims in his preface that this volume provides a 'working knowledge' of the mathematical tools. Proofs are given almost throughout and only in cases where they encourage mathematical thinking, otherwise the reader is referred to the original literature.
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