The Geometry of Physics: An Introduction, Second Edition | 
 enlarge | Author: Theodore Frankel
Publisher: Cambridge University Press
Category: Book
List Price: $55.00
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Rating:  17 reviews
Sales Rank: 309108
Media: Paperback
Edition: 2
Pages: 720
Number Of Items: 1
Shipping Weight (lbs): 2.7
Dimensions (in): 9.9 x 6.9 x 1.4
ISBN: 0521539277
Dewey Decimal Number: 530.15636
EAN: 9780521539272
Publication Date: November 24, 2003
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Condition: Brand new item. Over 3.5 million customers served. Order now. Selling online since 1995. Few left in stock - order soon. Code: C20080812190856B
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Product Description
Theodore Frankel explains those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms essential to a better understanding of classical and modern physics and engineering. Key highlights of his new edition are the inclusion of three new appendices that cover symmetries, quarks, and meson masses; representations and hyperelastic bodies; and orbits and Morse-Bott Theory in compact Lie groups. Geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. First Edition Hb (1997): 0-521-38334-X First Edition Pb (1999): 0-521-38753-1
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: Read 12 more reviews...
 THE modern Differential Geometry book for Physicists February 21, 2000
A graduate student of Physics (Santa Barbara, CA)
78 out of 84 found this review helpful
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.
The perfect first book in differential geometry January 28, 2005
Liviu I. Nicolaescu (Notre Dame, IN)
16 out of 19 found this review helpful
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.
over and over and over again July 25, 2003
Kevin Roberge (Old Town, Maine United States)
11 out of 13 found this review helpful
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.
You should buy this, despite its flaws March 3, 2006
E. M. Stoudenmire (Santa Barbara, CA)
10 out of 11 found this review helpful
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.
a book worth keeping April 30, 2007
Hexogen (Naperville, IL)
1 out of 1 found this review helpful
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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