An introduction to nonlinear analysis
著者
書誌事項
An introduction to nonlinear analysis
Kluwer Academic, c2003
- Theory
- Applications
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注記
Includes bibliographical references and index
内容説明・目次
- 巻冊次
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Theory ISBN 9780306473920
内容説明
An Introduction to Nonlinear Analysis: Theory is an overview of some basic, important aspects of Nonlinear Analysis, with an emphasis on those not included in the classical treatment of the field. Today Nonlinear Analysis is a very prolific part of modern mathematical analysis, with fascinating theory and many different applications ranging from mathematical physics and engineering to social sciences and economics. Topics covered in this book include the necessary background material from topology, measure theory and functional analysis (Banach space theory). The text also deals with multivalued analysis and basic features of nonsmooth analysis, providing a solid background for the more applications-oriented material of the book An Introduction to Nonlinear Analysis: Applications by the same authors.
The book is self-contained and accessible to the newcomer, complete with numerous examples, exercises and solutions. It is a valuable tool, not only for specialists in the field interested in technical details, but also for scientists entering Nonlinear Analysis in search of promising directions for research.
目次
Theory:- List of Figures. Preface. Acknowledgements. 1. Elements of Topology. 2. Elements of Measure Theory. 3. Banach Spaces. 4. Set-valued Analysis. 5. Nonsmooth Analysis. References. Index.
- 巻冊次
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Applications ISBN 9780306474569
内容説明
This book offers an exposition of the main applications of Nonlinear Analysis, beginning with a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics. The presentation is supplemented with the inclusion of many exercises and their solutions.
目次
Applications:- List of Figures. Preface. 1. Nonlinear Operators and Fixed Points. 2. Ordinary Differential Equations. 3. Partial Differential Equations. 4. Optimal Control and Calculus of Variations. 5. Mathematical Economics. References. Index.
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