Introduction to Global Analysis (Dover Books on Mathematics)

Book Details

• Author: Donald W. Kahn

• Brand: Dover

• Binding: Paperback

• Format: Import

• Number of Pages: 352

• Release Date: 29th March 2007

• ISBN: 9780486457826

• Package Dimensions: 8.5 x 5.4 x 0.8 inches

• Languages: English

About The Book
Introduction to Global Analysis by Donald W. Kahn is a comprehensive and accessible textbook designed to introduce students to the complex field of global analysis. Ideal for advanced undergraduates and graduate students, the book starts with fundamental concepts such as finite-dimensional differential manifolds and builds up to more advanced topics in global analysis.

Kahn's approach includes clear explanations and proofs of significant theorems, such as the Whitney embedding theorem and the Sard theorem. As the book progresses, it explores the tangent bundle to a manifold, vector bundles, differential operators on manifolds, and important concepts in algebra like differential forms, Stokes' theorem, and deRham cohomology.

The text also delves into more advanced areas of study, including infinite-dimensional manifolds, Morse theory, Lie groups, and the dynamics of singularities and catastrophes. Each chapter concludes with a set of problems and projects to enhance understanding and provide opportunities for further study.

This book is a vital resource for students pursuing studies in mathematics, particularly those with an interest in differential geometry and the applications of global analysis.