Introduction to Differentiable Manifolds by Serge Lang (English) Paperback Book

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This book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. 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.

FORMATPaperback LANGUAGEEnglish CONDITIONBrand New Publisher Description

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.

Notes

This book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. The author's book, Fundamentals of Differential Geometry, can be viewed as a continuation of the present book. Since this book is intended as a text to follow advanced calculus, manifolds are assumed finite dimensional. The author has made numerous corrections to this new edition, and he has also added a chapter on applications of Stokes' Theorem.

Back Cover

"This book contains essential material that every graduate student must know. Written with Serge Lang's inimitable wit and clarity, the volume introduces the reader to manifolds, differential forms, Darboux's theorem, Frobenius, and all the central features of the foundations of differential geometry. Lang lays the basis for further study in geometric analysis, and provides a solid resource in the techniques of differential topology. The book will have a key position on my shelf. Steven Krantz, Washington University in St. Louis "This is an elementary, finite dimensional version of the author's classic monograph, Introduction to Differentiable Manifolds (1962), which served as the standard reference for infinite dimensional manifolds. It provides a firm foundation for a beginner's entry into geometry, topology, and global analysis. The exposition is unencumbered by unnecessary formalism, notational or otherwise, which is a pitfall few writers of introductory texts of the subject manage to avoid. The author's hallmark characteristics of directness, conciseness, and structural clarity are everywhere in evidence. A nice touch is the inclusion of more advanced topics at the end of the book, including the computation of the top cohomology group of a manifold, a generalized divergence theorem of Gauss, and an elementary residue theorem of several complex variables. If getting to the main point of an argument or having the key ideas of a subject laid bare is important to you, then you would find the reading of this book a satisfying experience." Hung-Hsi Wu, University of California, Berkeley

Table of Contents

Differential Calculus.- Manifolds.- Vector Bundles.- Vector Fields and Differential Equations.- Operations on Vector Fields and Differential Forms.- The Theorem of Frobenius.- Metrics.- Integration of Differential Forms.- Stokes' Theorem.- Applications of Stokes' Theorem.

Review

From the reviews:"This volume is an introduction to differential manifolds which is intended for post-graduate or advanced undergraduate students. … Basic concepts are presented, which are used in differential topology, differential geometry, and differential equations. Charts are used systematically … . The book is well readable, and it is of interest not only for mathematicians, but also for theory-oriented researchers in applied sciences, who need an introduction to this important topic." (I. Troch, Internationale Mathematische Nachrichten, Issue 196, 2004)"The author recommends his text to 'the first year graduate level or advanced undergraduate level' … . his explanation is very precise, with rich formalism and with maximum generality … . In summary, this is an ideal text for people who like a more general and abstract approach to the topic." (EMS, June, 2003)"The book offers a quick introduction to basic concepts which are used in differential topology, differential geometry and differential equations. … The bibliography contains important new titles in studying differential geometry. A large index is also included. This is an interesting Universitext (for students – the first year graduate level or advanced undergraduate level), with important concepts concerning the general basic theory of differential manifolds." (Corina Mohorianu, Zentralblatt MATH, Vol. 1008, 2003)

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Long Description

This book contains essential material that every graduate student must know. Written with Serge Lang's inimitable wit and clarity, the volume introduces the reader to manifolds, differential forms, Darboux's theorem, Frobenius, and all the central features of the foundations of differential geometry. Lang lays the basis for further study in geometric analysis, and provides a solid resource in the techniques ofdifferential topology. The book will have a key position on my shelf.-Steven Krantz, Washington University in St. LouisThis is an elementary, finite dimensional version of the author's classic monograph, Introduction to Differentiable Manifolds (1962), which served as the standard reference for infinite dimensional manifolds. It provides a firm foundation for a beginner's entry into geometry, topology, and globalanalysis. The exposition is unencumbered by unnecessary formalism, notational or otherwise, which is a pitfall few writers of introductory texts of the subject manage to avoid. The author's hallmark characteristics of directness, conciseness, and structural clarity are everywhere in evidence. A nice touch is the inclusion of more advanced topics at the end of the book, including the computation of the top cohomology group of a manifolds, a generalized divergence theorem of Gauss, and an elementary residuetheorem of several complex variables. If getting to the main point of an argument or having the key ideas of a subject laid bare is important to you, then you would find the reading of this book a satisfying experience.

Review Quote

From the reviews:"This volume is an introduction to differential manifolds which is intended for post-graduate or advanced undergraduate students. Basic concepts are presented, which are used in differential topology, differential geometry, and differential equations. Charts are used systematically . The book is well readable, and it is of interest not only for mathematicians, but also for theory-oriented researchers in applied sciences, who need an introduction to this important topic." (I. Troch, Internationale Mathematische Nachrichten, Issue 196, 2004)"The author recommends his text to the first year graduate level or advanced undergraduate level " . his explanation is very precise, with rich formalism and with maximum generality . In summary, this is an ideal text for people who like a more general and abstract approach to the topic." (EMS, June, 2003)"The book offers a quick introduction to basic concepts which are used in differential topology, differential geometry and differential equations. The bibliography contains important new titles in studying differential geometry. A large index is also included. This is an interesting Universitext (for students " the first year graduate level or advanced undergraduate level), with important concepts concerning the general basic theory of differential manifolds." (Corina Mohorianu, Zentralblatt MATH, Vol. 1008, 2003)

Description for Sales People

This book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. The author's book, Fundamentals of Differential Geometry, can be viewed as a continuation of the present book. Since this book is intended as a text to follow advanced calculus, manifolds are assumed finite dimensional. The author has made numerous corrections to this new edition, and he has also added a chapter on applications of Stokes' Theorem.

Details ISBN1441930191 Author Serge Lang Series Universitext Year 2010 ISBN-10 1441930191 ISBN-13 9781441930194 Format Paperback Publication Date 2010-12-03 Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States DEWEY 510 Birth 1927 Short Title INTRO TO DIFFERENTIABLE MANIFO Language English Media Book Residence New Haven, CT, US Death 2005 DOI 10.1007/978-0-387-21772-7 AU Release Date 2010-12-03 NZ Release Date 2010-12-03 US Release Date 2010-12-03 UK Release Date 2010-12-03 Illustrations XI, 250 p. Pages 250 Publisher Springer-Verlag New York Inc. Edition Description Softcover reprint of the original 1st ed. 2002 Alternative 9780387954776 Audience Professional & Vocational We've got this

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