An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised (Pure and Applied Mathematics) | 
 enlarge | Creator: William M. Boothby
Publisher: Academic Press
Category: Book
List Price: $101.00
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Rating:  5 reviews
Sales Rank: 286749
Media: Paperback
Edition: 2nd
Pages: 400
Number Of Items: 1
Shipping Weight (lbs): 1.2
Dimensions (in): 9 x 6 x 0.9
ISBN: 0121160513
Dewey Decimal Number: 516.36
EAN: 9780121160517
Publication Date: August 5, 2002
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Product Description
The second edition of this text has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject.
Line and surface integrals
Divergence and curl of vector fields
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| Customer Reviews:
 This is a book for REAL mathematicians April 16, 2005
T. Baillie Arnold (Brunswick, ME)
11 out of 11 found this review helpful
This book is an wonderful introduction to Differential Geometry for the serious student of mathematics. However, it is not aimed at engineers, physicists or even applied mathaticians.
The author assumes the reader has an extensive knowledge of abstract algebra and at least one course in analysis. Likewise, he has chosen to emphasis applications of the subject to Lie Groups, homotopy theory, and group actions, rather than the physical applications that applied mathematicians are looking for. But, for the student of pure mathematics, this text is a great starting point into the rich world of differential geometry.
Also, while this book is an introduction and requires no previous knowledge of the subject, it covers enough ground to be followed up by such topics as the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet's Theorem, or Morse Theory.
great introductory text March 27, 2002
Alex (MTL)
13 out of 17 found this review helpful
My first course on manifolds was based on this book, and I believe that it is the best introduction to the subject (especially for beginners). I thoroughly enjoyed it! I should also recommend Conlon's 'Differentiable Manifolds' (2ed, Birkhauser), as it is the perfect follow-up to Boothby. --A
Great book October 9, 2008
Great introductory differential geometry text! I used this book to help me pass my qualifying exam. Yay Boothby!
Very Nice Nontrivial Introduction June 1, 2000
Kevin R. Vixie (Los Alamos, NM)
17 out of 18 found this review helpful
This book is a careful treatment of the subjects in the title. It is an introduction, but it manages to cover quite a bit of ground with lots of examples to illustrate. One of it's distinguishing points is the way in which the concrete, coordinate based calculations are emphasized even while usually presenting the more abstract, coordinate free approach as well. The book does a good job at stimulating those studying it to develop intuition. I found the book helpful when I was first studying the subject.
 When accountants and soldiers take interest in geometry..... March 31, 2005
9 out of 29 found this review helpful
One day, accountants and soldiers may take an interest in differential geometry. If and when such a day comes to pass, this book will have a role to play. Until then, engineers, physicists and mathematicians alike have better alternatives, such as the inspiring texts, with complementary qualities, by Burke, "Applied Differential Geometry"; by do Carmo, "Riemannian Geometry", or by Spivak, "A Comprehensive Introduction to Differential Geometry".
Even more advanced books such as Lang's or Petersen's are more readable: in them the extra formalism brings the reward of more powerful results. Here the retentive attention to the trees at the expense of the forest is merely a barrier to entry for the uninitiated. This text's popularity in some areas of engineering must have played a role in the slow acceptance of Riemannian geometric methods.
Manuel Tenide
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