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Author: Klaus Deimling
Publisher: Springer Science & Business Media
ISBN: 3662005476
Category : Mathematics
Languages : en
Pages : 465
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Book Description
topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, where infinite dimensions first appear, one should be familiar with the essential step of consider ing a sequence or a function of some sort as a point in the corresponding vector space of all such sequences or functions, whenever this abstraction is worthwhile. One should also work out the things which are proved in § 7 and accept certain basic principles of linear functional analysis quoted there for easier references, until they are applied in later chapters. In other words, even the 'completely linear' sections which we have included for your convenience serve only as a vehicle for progress in nonlinearity. Another point that makes the text introductory is the use of an essentially uniform mathematical language and way of thinking, one which is no doubt familiar from elementary lectures in analysis that did not worry much about its connections with algebra and topology. Of course we shall use some elementary topological concepts, which may be new, but in fact only a few remarks here and there pertain to algebraic or differential topological concepts and methods.
Author: Klaus Deimling
Publisher: Springer Science & Business Media
ISBN: 3662005476
Category : Mathematics
Languages : en
Pages : 465
Get Book Here
Book Description
topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, where infinite dimensions first appear, one should be familiar with the essential step of consider ing a sequence or a function of some sort as a point in the corresponding vector space of all such sequences or functions, whenever this abstraction is worthwhile. One should also work out the things which are proved in § 7 and accept certain basic principles of linear functional analysis quoted there for easier references, until they are applied in later chapters. In other words, even the 'completely linear' sections which we have included for your convenience serve only as a vehicle for progress in nonlinearity. Another point that makes the text introductory is the use of an essentially uniform mathematical language and way of thinking, one which is no doubt familiar from elementary lectures in analysis that did not worry much about its connections with algebra and topology. Of course we shall use some elementary topological concepts, which may be new, but in fact only a few remarks here and there pertain to algebraic or differential topological concepts and methods.
Author: Manuel De Landa
Publisher: Princeton University Press
ISBN:
Category : History
Languages : en
Pages : 342
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Book Description
More than a simple expository history, A Thousand Years of Nonlinear History sketches the outlines of a renewed materialist philosophy of history in the tradition of Fernand Braudel, Gilles Deleuze, and F lix Guattari, while also engaging the critical new understanding of material processes derived from the sciences of dynamics.Following in the wake of his groundbreaking War in the Age of Intelligent Machines, Manuel De Landa presents a radical synthesis of historical development over the last one thousand years. More than a simple expository history, A Thousand Years of Nonlinear History sketches the outlines of a renewed materialist philosophy of history in the tradition of Fernand Braudel, Gilles Deleuze, and F lix Guattari, while also engaging the critical new understanding of material processes derived from the sciences of dynamics. Working against prevailing attitudes that see history as an arena of texts, discourses, ideologies, and metaphors, De Landa traces the concrete movements and interplays of matter and energy through human populations in the last millennium. De Landa attacks three domains that have given shape to human societies: economics, biology, and linguistics. In every case, what one sees is the self-directed processes of matter and energy interacting with the whim and will of human history itself to form a panoramic vision of the West free of rigid teleology and naive notions of progress, and even more important, free of any deterministic source of its urban, institutional, and technological forms. Rather, the source of all concrete forms in the West's history are shown to derive from internal morphogenetic capabilities that lie within the flow of matter-energy itself.
Author: Jack K. Hale
Publisher: Courier Dover Publications
ISBN: 0486803260
Category : Mathematics
Languages : en
Pages : 193
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Book Description
By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction provides a unified approach for obtaining periodic solutions to nonautonomous and autonomous differential equations. 1963 edition.
Author: Zdzisław Denkowski
Publisher: Springer Science & Business Media
ISBN: 9780306473920
Category : Applied mathematics
Languages : en
Pages : 708
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Book Description
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.
Author: Juha Heinonen
Publisher: Courier Dover Publications
ISBN: 0486830462
Category : Mathematics
Languages : en
Pages : 417
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Book Description
A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.
Author: Mateusz Michałek
Publisher: American Mathematical Society
ISBN: 1470453673
Category : Mathematics
Languages : en
Pages : 243
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Book Description
Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and fast-developing area. It is not an extensive encyclopedia of known results, but rather a first introduction to the subject, allowing the reader to enter into more advanced topics. It was designed as the next step after linear algebra and well before abstract algebraic geometry. The book presents both classical topics—like the Nullstellensatz and primary decomposition—and more modern ones—like tropical geometry and semidefinite programming. The focus lies on interactions and applications. Each of the thirteen chapters introduces fundamental concepts. The book may be used for a one-semester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.
Author: Robert Haber
Publisher: Springer Science & Business Media
ISBN: 9780792358572
Category : Computers
Languages : en
Pages : 428
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Book Description
This is the second part of a two-volume handbook presenting a comprehensive overview of nonlinear dynamic system identification. The books include many aspects of nonlinear processes such as modelling, parameter estimation, structure search, nonlinearity and model validity tests.
Author: Robert Boyd
Publisher: Academic Press
ISBN: 0323148204
Category : Science
Languages : en
Pages : 494
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Book Description
Contemporary Nonlinear Optics discusses the different activities in the field of nonlinear optics. The book is comprised of 10 chapters. Chapter 1 presents a description of the field of nonlinear guided-wave optics. Chapter 2 surveys a new branch of nonlinear optics under the heading optical solitons. Chapter 3 reviews recent progress in the field of optical phase conjugation. Chapter 4 discusses ultrafast nonlinear optics, a field that is growing rapidly with the ability of generating and controlling femtosecond optical pulses. Chapter 5 examines a branch of nonlinear optics that may be termed nonlinear quantum optics. Chapter 6 reviews the new field of photorefractive adaptive neural networks. Chapter 7 presents a discussion of recent successes in the development of nonlinear optical media based on organic materials. Chapter 8 reviews the field of nonlinear optics in quantum confined structures. Chapter 9 reviews the field of nonlinear laser spectroscopy, with emphasis on advances made during the 1980s. Finally, Chapter 10 reviews the field of nonlinear optical dynamics by considering nonlinear optical systems that exhibit temporal, spatial, or spatio-temporal instabilities. This book is a valuable source for physicists and other scientists interested in optical systems and neural networks.
Author: A. Cuyt
Publisher: Elsevier
ISBN: 0080872476
Category : Computers
Languages : en
Pages : 289
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Book Description
While most textbooks on Numerical Analysis discuss linear techniques for the solution of various numerical problems, this book introduces and illustrates nonlinear methods. It presents several nonlinear techniques resulting mainly from the use of Padé approximants and rational interpolants.
Author: Thomas L. Carroll
Publisher: World Scientific
ISBN: 9789810224387
Category : Science
Languages : en
Pages : 352
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Book Description
This volume describes the use of simple analog circuits to study nonlinear dynamics, chaos and stochastic resonance. The circuit experiments that are described are mostly easy and inexpensive to reproduce, and yet these experiments come from the forefront of nonlinear dynamics research. The individual chapters describe why analog circuits are so useful for studying nonlinear dynamics, and include theoretical as well as experimental results from some of the leading researchers in the field. Most of the articles contain some tutorial sections for the less experienced readers.The audience for this book includes researchers in nonlinear dynamics, chaos and statistical physics as well as electrical engineering, and graduate and advanced undergraduate students in these fields.
