An Introduction to Differentiable Manifolds and Riemannian Geometry (Pure and Applied Mathematics, Volume 120)

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9780121160531: An Introduction to Differentiable Manifolds and Riemannian Geometry (Pure and Applied Mathematics, Volume 120)

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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From the Back Cover:

Differentiable manifolds and 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).

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