Following in the wake of his groundbreaking work War in the Age of Intelligent Machines, Manuel De Landa presents a brilliant, radical synthesis of historical development of the last thousand years. 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 Félix Guattari, while engaging — in an entirely unprecedented manner — the critical new understanding of material processes derived from the sciences of dynamics. Working against prevailing attitudes that see history merely as the 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. The result is an entirely novel approach to the study of human societies and their always mobile, semi-stable forms, cities, economies, technologies, and languages. De Landa attacks three domains that have given shape to human societies: economics, biology, and linguistics. In each case, De Landa discloses 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 for its urban, institutional, and technological forms. The source of all concrete forms in the West’s history, rather, is shown to derive from internal morphogenetic capabilities that lie within the flow of matter—energy itself. A Swerve Edition.

The aim of this book is to develop a unified approach to nonlinear science, which does justice to its multiple facets and to the diversity and richness of the concepts and tools developed in this field over the years. Nonlinear science emerged in its present form following a series of closely related and decisive analytic, numerical and experimental developments that took place over the past three decades. It appeals to an extremely large variety of subject areas, but, at the same time, introduces into science a new way of thinking based on a subtle interplay between qualitative and quantitative techniques, topological and metric considerations and deterministic and statistical views. Special effort has been made throughout the book to illustrate both the development of the subject and the mathematical techniques, by reference to simple models. Each chapter concludes with a set of problems. This book will be of great value to graduate students in physics, applied mathematics, chemistry, engineering and biology taking courses in nonlinear science and its applications.

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.

Nonlinear, now in its 4th edition, is an easy-to-understand handbook about the popular world of digital nonlinear editing. It's written in nontechnical language for both professionals and students, as well as for interested bystanders. Profusely illustrated. The first edition was designed for professionals in Hollywood's film and video industry, to bridge the chasm between film editors (older, non-technological, mechanical), videotape editors (younger, highly technical, electronic), and computer users (prosumers, cost-conscious, digital) in casual language. Today, Nonlinear has not only penetrated the professional industry, but has been expanded for consumer use. Widely used in colleges, universities, and professional organizations. Although nonlinear editing technology began to explode in 1991, nonlinear systems had already been around for almost 5 years. Nonlinear became the Rosetta Stone of the industry: it was a universal translator -- between film and video, video and computer, computer and film. It still covers virtually everything anyone would want to know about the new world of electronic post production, without the geeky mumbo jumbo that characterizes most professional texts. While the book is useful for anyone investigating or wishing to purchase a digital editing system, it is not meant to be a buyer's guide. It is designed not to go out of date every time a new new product is introduced or software release comes out. It is about essentials. Fundamentals. Concepts. And language. With over 25,000 copies in print, Nonlinear is the best selling textbook on nonlinear editing in the world today.

Nonlinear analysis, formerly a subsidiary of linear analysis, has advanced as an individual discipline, with its own methods and applications. Moreover, students can now approach this highly active field without the preliminaries of linear analysis. As this text demonstrates, the concepts of nonlinear analysis are simple, their proofs direct, and their applications clear. No prerequisites are necessary beyond the elementary theory of Hilbert spaces; indeed, many of the most interesting results lie in Euclidean spaces. In order to remain at an introductory level, this volume refrains from delving into technical difficulties and sophisticated results not in current use. Applications are explained as soon as possible, and theoretical aspects are geared toward practical use. Topics range from very smooth functions to nonsmooth ones, from convex variational problems to nonconvex ones, and from economics to mechanics. Background notes, comments, bibliography, and indexes supplement the text.

A collection of prestigious postgraduate lectures, Nonlinear Dynamics and Spatial Complexity in Optical Systems reviews developments in the theory and practice of nonlinear dynamics and structural complexity, and explores modern-day applications in nonlinear optics. The book addresses systems including both singlemode and multimode lasers, bistable and multistable devices, optical fibers, counter-propagating beam interactions, nonlinear mixing, and related optical phenomena.

A self-contained treatment appropriate for advanced undergraduate and graduate students, this volume offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, the text advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.