An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics) [Paperback]

William M. Boothby (Author, Editor)

Book Description

ISBN-10: 0121160513 | ISBN-13: 978-0121160517 | Publication Date: August 19, 2002 | Edition: 2

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

Editorial Reviews

From the Back Cover

Differentiable manifolds abd the differential and integral calculus of their associated structures, such as vectors, tensors, and differential forms are of great importance in many areas of mathematics and its applications. Although basically and extension of advanced, or multivariable calculus, the leap from Euclidean space to manifolds can often be difficult. It takes time and patience, and it is easy to become mirred in abstraction and generalization.
In this text the author draws on his extensive experience in teaching this subject to minimize these difficulties. The pace is relatively liesurely, inessential abstraction and generality are avoided, the essential ideas used from the prerequisite subjects are reviewed, and there is an abundance of accessible and carefully developed examples to illuminate new concepts and to motivate the reader by illustrating their power. There are more than 400 exercises for the reader.
This book has been in constant, successful use for more than 25 years and has helped several generations of students as well as working mathemeticians, physicists and engineers to gain a good working knowledge of manifolds and to appreciate their importance, beauty and extensive applications.

About the Author

William Boothby received his Ph.D. at the University of Michigan and was a professor of mathematics for over 40 years. In addition to teaching at Washington University, he taught courses in subjects related to this text at the University of Cordoba (Argentina), the University of Strasbourg (France), and the University of Perugia (Italy).

William Boothby received his Ph.D. at the University of Michigan and was a professor of mathematics for over 40 years. In addition to teaching at Washington University, he taught courses in subjects related to this text at the University of Cordoba (Argentina), the University of Strasbourg (France), and the University of Perugia (Italy).

Product Details

• Paperback: 400 pages
• Publisher: Academic Press; 2 edition (August 19, 2002)
• Language: English
• ISBN-10: 0121160513
• ISBN-13: 978-0121160517
• Product Dimensions: 8.9 x 6 x 1.1 inches
• Shipping Weight: 1.3 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #667,732 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

15 of 15 people found the following review helpful:

5.0 out of 5 stars This is a book for REAL mathematicians, April 16, 2005

By 

T. Baillie Arnold (Brunswick, ME) - See all my reviews
(REAL NAME)   

This review is from: An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, Volume 120, Second Edition (Pure and Applied Mathematics) (Paperback)

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.

21 of 23 people found the following review helpful:

4.0 out of 5 stars Very Nice Nontrivial Introduction, May 31, 2000

By 

Kevin R. Vixie (Los Alamos, NM) - See all my reviews
(REAL NAME)   

This review is from: An Introduction to Differentiable Manifolds and Riemannian Geometry (Pure and Applied Mathematics, Volume 120) (Paperback)

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.

17 of 22 people found the following review helpful:

5.0 out of 5 stars great introductory text, March 27, 2002

By 

Alex "supermanifold" (MTL) - See all my reviews

This review is from: An Introduction to Differentiable Manifolds and Riemannian Geometry (Pure and Applied Mathematics, Volume 120) (Paperback)

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