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Dover Books on Mathematics Ser.: Introduction to Global Analysis by Donald W. Kahn (2007, Perfect)
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About this product
Product Identifiers
PublisherDover Publications, Incorporated
ISBN-100486457826
ISBN-139780486457826
eBay Product ID (ePID)57199622
Product Key Features
Number of Pages352 Pages
Publication NameIntroduction to Global Analysis
LanguageEnglish
SubjectDifferential Equations / General, Geometry / Algebraic
Publication Year2007
TypeTextbook
AuthorDonald W. Kahn
Subject AreaMathematics
SeriesDover Books on Mathematics Ser.
FormatPerfect
Dimensions
Item Height0.7 in
Item Weight13 Oz
Item Length8.5 in
Item Width5.7 in
Additional Product Features
Intended AudienceCollege Audience
LCCN2006-047093
Dewey Edition22
IllustratedYes
Dewey Decimal510
SynopsisGeared toward advanced undergraduates and graduate students, this text introduces the methods of mathematical analysis as applied to manifolds. In addition to examining the roles of differentiation and integration, it explores infinite-dimensional manifolds, Morse theory, Lie groups, dynamical systems, and the roles of singularities and catastrophes. 1980 edition., 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 Poincar 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., 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., This text introduces the methods of mathematical analysis as applied to manifolds, including the roles of differentiation and integration, infinite dimensions, Morse theory, Lie groups, and dynamical systems. 1980 edition.
LC Classification NumberQA614.K34 2007
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