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Introduction to Differentiable Manifolds

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Author is well-known and established book author (all Serge Lang books are now published by Springer); Presents a brief introduction to the subject; All manifolds are assumed finite dimensional in order not to frighten some readers; Complete proofs are given; Use of manifolds cuts across disciplines and includes physics, engineering and economics

Author(s): Serge Lang
Edition: 1
Year: 2002

Language: English
Pages: 264

Cover......Page 1
Introduction to
Differentiable Manifolds,
Second Edition......Page 3
Universitext......Page 2
ISBN 0387954775......Page 4
Foreword......Page 5
Acknowledgments......Page 7
Contents......Page 8
CHAPTER I
Differential Calculus......Page 11
CHAPTER II
Manifolds......Page 30
CHAPTER III
Vector Bundles......Page 47
CHAPTER IV
Vector Fields and Differential
Equations......Page 70
CHAPTER V
Operations on Vector Fields
and Differential Forms......Page 115
CHAPTER VI
The Theorem of Frobenius......Page 153
CHAPTER VII
Metrics......Page 168
CHAPTER VIII
Integration of Differential
Forms......Page 190
CHAPTER IX
Stokes’ Theorem......Page 210
CHAPTER X
Applications of Stokes’
Theorem......Page 224
Bibliography......Page 252