Introduction to Differentiable Manifolds (Universitext) - Hardcover

Lang, Serge

Hardcover

ISBN 10: 0387954775 ISBN 13: 9780387954776

Publisher: Springer, 2002

Synopsis

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

About this title

From the 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

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)

Edition details

• Publisher: Springer
• Publication date: 2002
• ISBN 10: 0387954775
• ISBN 13: 9780387954776
• Binding: Hardcover
• Language: English
• Number of pages: 261