Introduction to Differentiable Manifolds
“Introduction to Differentiable Manifolds” by Serge Lang, published by Springer New York on December 3, 2010, is a softcover reprint of the original first edition from 2002, comprising 250 pages. This book provides an introduction to fundamental concepts in differential topology, differential geometry, and differential equations, focusing on the essential theories of differential manifolds. It serves as a foundational text for readers who have completed advanced calculus, assuming familiarity with finite-dimensional manifolds.
Readers will find a comprehensive overview of the basic theories that underpin these mathematical fields, allowing for a smoother transition to more advanced studies. The new edition includes numerous corrections and an additional chapter on applications of Stokes’ Theorem, enhancing its utility for students and educators alike. Topics such as mathematics, topology, and geometry are woven throughout the text, making it a valuable resource for those looking to deepen their understanding of these areas.
Official synopsis Publisher
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.
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