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.

Klappentext

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

Inhalt

Foreword * Acknowledgments * 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