Introduction to Differentiable Manifolds / Edition 1

Introduction to Differentiable Manifolds / Edition 1

by Serge Lang
     
 

ISBN-10: 0387954775

ISBN-13: 9780387954776

Pub. Date: 10/01/2002

Publisher: Springer New York

This book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. A certain number of concepts are essential for all three of these areas, and are so basic and elementary, that it is worthwhile to collect them together so that more advanced expositions can be given without having to start…  See more details below

Overview

This book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. A certain number of concepts are essential for all three of these areas, and are so basic and elementary, that it is worthwhile to collect them together so that more advanced expositions can be given without having to start from the very beginning. The concepts are concerned with the general basic theory of differential manifolds. As a result, this book can be viewed as a prerequisite to Fundamentals of Differential Geometry. Since this book is intended as a text to follow advanced calculus, manifolds are assumed finite dimensional.

In the new edition of this book, the author has made numerous corrections to the text and he has added a chapter on applications of Stokes' Theorem.

Product Details

ISBN-13:
9780387954776
Publisher:
Springer New York
Publication date:
10/01/2002
Series:
Universitext Series
Edition description:
2002
Pages:
250
Product dimensions:
0.63(w) x 6.14(h) x 9.21(d)

Table of Contents

Foreword
Acknowledgments
Ch. IDifferential Calculus1
Ch. IIManifolds20
Ch. IIIVector Bundles37
Ch. IVVector Fields and Differential Equations60
Ch. VOperations on Vector Fields and Differential Forms105
Ch. VIThe Theorem of Frobenius143
Ch. VIIMetrics158
Ch. VIIIIntegration of Differential Forms180
Ch. IXStokes' Theorem200
Ch. XApplications of Stokes' Theorem214
Bibliography243
Index247

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