A Topological Introduction to Nonlinear An...

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Beschreibung

This third edition is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully-expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. Included in this new edition are several new chapters that present the fixed point index and its applications. The exposition and mathematical content is improved throughout.

This book is ideal for self-study for mathematicians and students interested in such areas of geometric and algebraic topology, functional analysis, differential equations, and applied mathematics. It is a sharply focused and highly readable view of nonlinear analysis by a practicing topologist who has seen a clear path to understanding.

"For the topology-minded reader, the book indeed has a lot to offer: written in a very personal, eloquent and instructive style it makes one of the highlights of nonlinear analysis accessible to a wide audience."-Monatshefte fur Mathematik (2006)

Über den Autor

Robert F. Brown is a Professor of Mathematics at UCLA. His research area includes algebraic topology that is included within topological fixed point theory. Professor Brown's most recent research concerns the fixed point theory of fiber maps of fiberings with singularities.

Zusammenfassung

3rd Edition provides new content and expanded coverage of key topics

New section discusses the fixed point index and its many applications

Concise presentation and clear exposition make it an ideal resource for classroom use or self study

Includes supplementary material: [...]

Inhaltsverzeichnis

Preface.- Part I Fixed Point Existence Theory.- The Topological Point of View.- Ascoli-Arzela Theory.- Brouwer Fixed Point Theory.- Schauder Fixed Point Theory.- The Forced Pendulum.- Equilibrium Heat Distribution.- Generalized Bernstain Theory.- Part II Degree Theory.- Brouwer Degree.- Properties of the Brouwer Degree.- Leray-Schauder Degree.- Properties of the Leray-Schauder Degree.- The Mawhin Operator.- The Pendulum Swings back.- Part III Fixed Point Index Theory.- A Retraction Theorum.- The Fixed Point Index.- The Tubulur Reactor.- Fixed Points in a Cone.- Eigenvalues and Eigenvectors.- Part IV Bifurcation Theory.- A Separation Theorem.- Compact Linear Operators.- The Degree Calculation.- The Krasnoselskii-Rabinowitz Theorem.- Nonlinear Strum Liouville Theory.- More Strum Liouville Theory.- Euler Buckling.- Part V Appendices.

Details

Erscheinungsjahr:	2014
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	252
Inhalt:	x 240 S. 42 s/w Illustr. 240 p. 42 illus.
ISBN-13:	9783319117935
ISBN-10:	3319117939
Sprache:	Englisch
Herstellernummer:	86279643
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Brown, Robert F.
Auflage:	3rd ed. 2014
Hersteller:	Springer International Publishing
Maße:	235 x 155 x 14 mm
Von/Mit:	Robert F. Brown
Erscheinungsdatum:	09.12.2014
Gewicht:	0,388 kg

preigu-id: 105124031