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A Topological Introduction to Nonlinear Analysis / Edition 2

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Overview

"The book is highly recommended as a text for an introductory course in nonlinear analysis and bifurcation theory . . . reading is fluid and very pleasant . . . style is informal but far from being imprecise."

—MATHEMATICAL REVIEWS (Review of the First Edition)

Here is a book that will be a joy 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.

New to the second edition: New chapters will supply additional applications of the theory and techniques presented in the book.

• Several new proofs, making the second edition more self-contained.

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Editorial Reviews

From the Publisher
"The book is highly recommended as a text for an introductory course in nonlinear analysis and bifurcation theory... reading is fluid and very pleasant... style is informal but far from being imprecise."

- Mathematical Reviews (Review of the first edition)

"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 für Mathematik

"Written by an expert in fixed point theory who is well aware of the important applications of this area to nonlinear analysis and differential equations, the first edition of this book has been very well received, and has helped both topologists in learning nonlinear analysis and analysts in appreciating topological fixed point theory. The second edition has kept the freshness and clarity of style of the first one. The new version remains more than even an excellent introduction to the sue of topological techniques in dealing with nonlinear problems." —-Mathematical Society

Booknews
Based on ideas from several branches of topology, and illustrated by numerous figures that attest to the geometric nature of the exposition, provides mathematically sophisticated readers with an understanding of the mathematics of the nonlinear phenomena that characterize the real world. A classical example is given in the differential equation problem that models the maximum weight that a column can support without buckling. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780817632588
  • Publisher: Birkhauser Verlag
  • Publication date: 12/12/2003
  • Edition description: 2nd ed. 2004
  • Edition number: 2
  • Pages: 184
  • Product dimensions: 0.42 (w) x 6.14 (h) x 9.21 (d)

Meet the Author

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.
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Table of Contents

Preface
Pt. I Fixed Point Existence Theory
1 The Topological Point of View 3
2 Ascoli-Arzela Theory 9
3 Brouwer Fixed Point Theory 19
4 Schauder Fixed Point Theory 23
5 The Forced Pendulum 29
6 Equilibrium Heat Distribution 39
7 Generalized Bernstein Theory 45
Pt. II Degree Theory
8 Brouwer Degree 51
9 Properties of the Brouwer Degree 55
10 Leray-Schauder Degree 63
11 Properties of the Leray-Schauder Degree 69
12 The Mawhin Operator 79
13 The Pendulum Swings Back 85
Pt. III Bifurcation Theory
14 A Separation Theorem 95
15 Compact Linear Operators 99
16 The Degree Calculation 111
17 The Krasnoselskii-Rabinowitz Bifurcation Theorem 119
18 Nonlinear Sturm-Liouville Theory 133
19 More Sturm-Liouville Theory 143
20 Euler Buckling 155
Pt. IV Appendices
A Singular Homology 163
B Additivity and Product Properties 169
C Bounded Linear Transformations 175
References 181
Index 183
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