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The Geometry of Physics: An Introduction Hardcover – November 24, 2003

ISBN-13: 978-0521833301 ISBN-10: 0521833302 Edition: 2nd

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Product Details

  • Hardcover: 720 pages
  • Publisher: Cambridge University Press; 2 edition (November 24, 2003)
  • Language: English
  • ISBN-10: 0521833302
  • ISBN-13: 978-0521833301
  • Product Dimensions: 1.6 x 7.2 x 10.3 inches
  • Shipping Weight: 3.1 pounds
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #3,005,118 in Books (See Top 100 in Books)

Editorial Reviews

Review

"...highly readable and enjoyable ...The book will make an excellent course text or self-study manual for this interesting subject." Physics Today

"If you're looking for a well-written and well-motivated introduction to differential geometry, this one looks hard to beat." MAA On Line, Mathematical Association of America

Book Description

This book is intended to provide a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should be of interest also to mathematics students. This book will be useful to graduate and advanced undergraduate students of physics, engineering and mathematics. It can be used as a course text or for self study.

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Customer Reviews

4.3 out of 5 stars
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See all 7 customer reviews
The writing is not good: sentences are often not comprehensible, and the punctuation is often confusing.
Fredrik Meyer
The author never hesitate to use graphs and diagrams to illustrate points, and stroke nice balance in between mathematics rigor and physical insight.
Hexogen
I've attempted to wade through a number of books on differential geometry in the last year+ and this is by far the best.
Zac

Most Helpful Customer Reviews

24 of 28 people found the following review helpful By Liviu I. Nicolaescu on January 28, 2005
Format: Paperback Verified Purchase
Differential geometry can be a very intimidating subject due to its heavy formalism. There are complete books (such as Kobayashi& Nomizu) very good as reference books, and there very few books that show the reader the picture behind the formulas.

This is one such book. It tells you the intuition behind each construction and from this point of view it has many things in common with Arnold's famous book on Math. Methods in Classical Mechanics. But where as Arnold does not pay too much attention to formalism, this book achieves this task as well. It shows the reader how to do those impossible computations as well.

This is definitely the first place to look at if you want to really learn differential geometry. If it seems difficult it is only because the subject is so.
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6 of 6 people found the following review helpful By Eboue! from arsecast on May 13, 2010
Format: Paperback Verified Purchase
this is a damn hard book to understand. i am a theoretical physicist who already knows the stuff here and i find the explanations sometimes very confusing. it's not a simple book to read. you have to pay close attention to every line, and this is a major pain since the book is so big. also some sentences are very bloated. i know the author spent a lot of time on this book. but he should have gotten a better copy editor.

it has a lot going for it. the emphasis on physics is nice. but unless you have a lot of patience and haven't read any other books (so you don't confused about the unorthodox notation), this book may drive you crazy.

its really too bad, because this is the only book that i know of which tries to really "explain" bundles in a non-pedantic way. unfortunately, it is not that successful. (the part on bundles is perhaps the most transparent and easiest part of the book though).

if you have patience and are willing to decipher some of the prose which is ambiguous, or difficult to understand because there are like 5 commas in a single sentence, then this is absolutely a 5 STAR book. the material is wonderful, and there is an enormous amount of insight shared.

otherwise, if you are a typical math guy (like me) you are probably better off going with a thinner and more mathematical book like Darling's differential geometry book or Morita's book or the new book on differential geometry by Tu.

it is of course an alternative to Nakahara. but Nakahara isn't a proper textbook. it's a collection of examples. in summary, despite the book's flaws, i have not seen anyone write a better story in a single volume of how to combine math and physics at an "elementary" level than Frankel.
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6 of 6 people found the following review helpful By Hexogen on April 30, 2007
Format: Paperback
This book can be quite confusing if you start without any background on the idea of manifold or knows nothing about general relativity. However, it does have strong points:

1. The notation is very up-to-date, and is entirely coordinate-independant approach.

2. The author explains in great details of formulation of modern differential geometry, and the details are comparatively lacking in other reference books.

3. The author never hesitate to use graphs and diagrams to illustrate points, and stroke nice balance in between mathematics rigor and physical insight.

Although it appears quite verbose at some point, it is mainly because differential geometry is such a heavy subject. Another book nice to have as companion reading is Goldburg's "Tensor analysis on Manifold", a terse, well-written text book.
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1 of 1 people found the following review helpful By Zac on October 30, 2011
Format: Paperback Verified Purchase
I'm an engineer primarily interested in learning differential geometry to apply it to dynamics and control problems. I've attempted to wade through a number of books on differential geometry in the last year+ and this is by far the best. It is extremely clear and intuitive, and the exercises given are at a level where they aid understanding but don't burden the reader with lots of computation. I highly recommend this book to engineers and/or scientists who want a good self-study book and who would rather have physical and intuitive explanations than rigorous mathematical proofs.
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