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.
Rezensionen / Stimmen
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)
