Synopses & Reviews
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.
Synopsis
Geared 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.
Synopsis
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.