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Dover Publications

Introduction to Global Analysis

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Title: Introduction to Global Analysis
Author: Donald W Kahn
ISBN: 9780486457826
Publisher: Dover Publications
Published: 2007
Binding: Paperback
Language: English
Condition: Used: Very Good
Clean, unmarked copy with some edge wear. Good binding. Dust jacket included if issued with one. We ship in recyclable American-made mailers. 100% money-back guarantee on all orders.

Science & Math 1615214

Publisher Description:
This accessible introduction to global analysis begins with a basic discussion of finite-dimensional differential manifolds. A Professor of Mathematics at the University of Minnesota, author Donald W. Kahn has geared his treatment toward advanced undergraduates and graduate students. Starting with those aspects that flow from the usual advanced calculus, he proceeds to proofs of versions of the Whitney embedding theorem, the theorem of Sard on the measure of the set of critical values, and the transversality lemma of Thom.
With the foundations set, the text turns to examinations of the tangent bundle to a manifold and the general theory of vector bundles. A study of differential operators on manifolds follows, including the algebra of differential forms, Stokes' theorem, the Poincaré lemma, and the basic definition of deRham cohomology. Additional topics include infinite-dimensional manifolds, Morse theory, Lie groups, dynamical systems, and the roles of singularities and catastrophes. Each chapter concludes with a selection of problems and projects.