Introduction to Global Analysis

Nonfiction, Science & Nature, Mathematics, Differential Equations
Cover of the book Introduction to Global Analysis by Donald W. Kahn, Dover Publications
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Donald W. Kahn ISBN: 9780486152295
Publisher: Dover Publications Publication: November 7, 2013
Imprint: Dover Publications Language: English
Author: Donald W. Kahn
ISBN: 9780486152295
Publisher: Dover Publications
Publication: November 7, 2013
Imprint: Dover Publications
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Dover Publications

Cover of the book Elementary Theory of Numbers by Donald W. Kahn
Cover of the book The Quantum Mechanics of Many-Body Systems by Donald W. Kahn
Cover of the book Montgomery Ward Fashions of the Twenties by Donald W. Kahn
Cover of the book Bold Script Alphabets by Donald W. Kahn
Cover of the book Ornamental Borders, Scrolls and Cartouches in Historic Decorative Styles by Donald W. Kahn
Cover of the book Adventures with a Microscope by Donald W. Kahn
Cover of the book Tangrams by Donald W. Kahn
Cover of the book Abstract Analytic Number Theory by Donald W. Kahn
Cover of the book Classical Dynamics by Donald W. Kahn
Cover of the book Applied Matrix Algebra in the Statistical Sciences by Donald W. Kahn
Cover of the book Arban's Complete Conservatory Method for Trumpet by Donald W. Kahn
Cover of the book Lessons on Figure Drawing by Donald W. Kahn
Cover of the book Rotary-Wing Aerodynamics by Donald W. Kahn
Cover of the book Art Nouveau Floral Ornament in Color by Donald W. Kahn
Cover of the book The 36 Fantasias for Keyboard by Donald W. Kahn
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy