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Synopsis
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. A classical example is given in the differential equation problem that models the maximum weight that a column can support without buckling.
The author has assumed a fairly high level of mathematical sophistication. However, the pace of exposition is relatively leisurely, and the book is essentially self-contained. Upon completing the book, the reader will be well equipped to make rapid progress through the existing literature in the broad field of nonlinear analysis.
This book is highly recommended for self-study for mathematicians and students interest 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.
This text has been adopted at: California State University, Hayward University of Michigan, Ann Arbor Montana State University, Bozeman
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Review
"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
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