BOOTHBY AN INTRODUCTION TO DIFFERENTIABLE MANIFOLDS PDF

About this title 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. 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.

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About this title 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. 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 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.

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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DIFFERENTIABLE MANIFOLDS BOOTHBY PDF

Voodoonris Chris Shaver rated it liked it May 20, Just a moment while we sign you in to your Goodreads account. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6, copies since publication booyhby and this revision will make it even more useful. Account Options Sign in. Thus a smooth surface, the topic of the B3 course, is an example of a 2-dimensional manifold. Partitions of unity, integration on oriented manifolds.

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