This book was planned and written as a text for a two-semester course designed, it is hoped, to overcome, or at least to minimize, some of these difficulties. It has, in fact, been used successfully several times in preliminary form as class notes for a two-semester course intended to lead the student from a reasonable mastery of advanced (multivariable) calculus and a rudimentary knowledge of differentiable manifolds, including some facility in working with the basic tools of manifold theory: tensors, differential forms, Lie and covariant derivatives, multiple integrals, and so on. Although in overall content this book necessarily overlaps the several available excellent books on manifold theory, there are differences in presentation and emphasis which, it is hoped, will make it particularly suitable as an introductory text.
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Book Description
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. --This text refers to an alternate Paperback edition.
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. --This text refers to an alternate Paperback edition.
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).
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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,
By
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,
By
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,
By
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
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Key Phrases - Statistically Improbable Phrases (SIPs):
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contracting mapping theorem, single coordinate neighborhood, regular submanifold, admissible neighborhoods, coordinate neighborhoods, maximal integral manifold, covariant tensor fields, covector field, vector field along the curve, parallel curvature, orthonormal frame field, diffeomorphic image, covering mapping, exterior differential forms, differentiability class, regular covering, isolated fixed point, local isometry, parallel vector fields, geodesic segment, differentiable structure, identity isomorphism, countable basis, immersed submanifold, content zero Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Proof Let, Example Let, Lemma Let, Corollary Let, Proof Suppose, Prove Corollary, Definition Let, Proof According, Using Exercise, Prove Theorem, Use Exercise, Proof First, Prove Lemma, Theorem Every, Using Remark, Elie Cartan, Theorem Any, Proof Given Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
contracting mapping theorem, single coordinate neighborhood, regular submanifold, admissible neighborhoods, coordinate neighborhoods, maximal integral manifold, covariant tensor fields, covector field, vector field along the curve, parallel curvature, orthonormal frame field, diffeomorphic image, covering mapping, exterior differential forms, differentiability class, regular covering, isolated fixed point, local isometry, parallel vector fields, geodesic segment, differentiable structure, identity isomorphism, countable basis, immersed submanifold, content zero Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Let, Proof Let, Example Let, Lemma Let, Corollary Let, Proof Suppose, Prove Corollary, Definition Let, Proof According, Using Exercise, Prove Theorem, Use Exercise, Proof First, Prove Lemma, Theorem Every, Using Remark, Elie Cartan, Theorem Any, Proof Given Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
58
books
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- Computer Vision-ECCV 2002: 7th European Conference on Computer Vision, Copenhagen, Denmark, May 28-31, 2002 - Proceedings, Part 2 by Anders Heyden on page 29, and page 744
- Real Reductive Groups I, Vol. 132 (Pure and Applied Mathematics) by Nolan R. Wallach in Index (1), and Index (2)
- Representations of *-Algebras, Locally Compact Groups, and Benach *-Algebraic Bundles, Two Volume Set: Representations of *-Algebras, Locally Compact ... and Algebras (Pure and Applied Mathematics) by J. M.G. Fell in Back Matter (1), and Back Matter (2)
- Representations of *-Algebras, Locally Compact Groups, and Benach *-Algebraic Bundles, Two Volume Set: Representations of *-Algebras, Locally Compact ... Analysis (Pure and Applied Mathematics) by J. M.G. Fell in Back Matter (1), and Back Matter (2)
- Invariance, déformations et reconnaissance de formes (Mathématiques et Applications) (French Edition) by Laurent Younes in Back Matter
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