The Joy of x

Die Schönheit der Mathematik

Author: Steven Strogatz

Publisher: Kein & Aber AG

ISBN: 3036992693

Category: Mathematics

Page: 352

View: 9710

Mathematik durchdringt den ganzen Kosmos. Das weiß jeder, doch nur die wenigsten verstehen die Zusammenhänge wirklich. Steven Strogatz nimmt uns bei der Hand und spaziert mit uns durch diese Welt der Weisheit, Klarheit und Eleganz. Als Reiseleiter geht er neue, erfrischende Wege, deutet auf Besonderheiten, schildert Hintergründe und erklärt die unsichtbaren Mechanismen. Wir erfahren unter anderem von dem Wunder des Zählens, der genialen Einfachheit der Algebra, dem ewigen Erbe Newtons, dem Tango mit Quadraten, der Zweisamkeit von Primzahlen und der Macht des Unendlichen. Mit all seiner Begeisterung, seinem Scharfblick und seinem leichtem Ton hat Steven Strogatz ein herrliches Buch für alle geschrieben, die ihr Verständnis von Mathematik auf eine neue Art vertiefen möchten.

Die Erforschung des Chaos

Dynamische Systeme

Author: John Argyris,Gunter Faust,Maria Haase,Rudolf Friedrich

Publisher: Springer-Verlag

ISBN: 3662545462

Category: Computers

Page: 913

View: 6278

Der Band ist Lehrbuch und wissenschaftliche Monografie in einem und enthält zahlreiche Beispiele, Bilder und Simulationen. „Inhalt des Buches ist eine in sich geschlossene, in jeder Weise überzeugende Darstellung des Themengebiets naturwissenschaftliche Chaosforschung. Sie richtet sich in gleicher Weise an den, der sich mit der Chaosphysik und der Nichtlinearen Dynamik intensiv auseinandersetzen möchte, wie auch an den, der sich erstmalig mit Aufgaben, Zielen und Ergebnissen dieses Arbeitsgebiets vertraut machen will." Werner Martienssen, Frankfurt.

Die Erforschung des Chaos

Eine Einführung in die Theorie nichtlinearer Systeme

Author: John Argyris,Gunter Faust,Maria Haase,Rudolf Friedrich

Publisher: Springer

ISBN: 9783540710714

Category: Mathematics

Page: 893

View: 3701

Der Band ist Lehrbuch und wissenschaftliche Monografie in einem und enthält zahlreiche Beispiele, Bilder und Simulationen. „Inhalt des Buches ist eine in sich geschlossene, in jeder Weise überzeugende Darstellung des Themengebiets naturwissenschaftliche Chaosforschung. Sie richtet sich in gleicher Weise an den, der sich mit der Chaosphysik und der Nichtlinearen Dynamik intensiv auseinandersetzen möchte, wie auch an den, der sich erstmalig mit Aufgaben, Zielen und Ergebnissen dieses Arbeitsgebiets vertraut machen will." Werner Martienssen, Frankfurt.

An Experimental Approach to Nonlinear Dynamics and Chaos

Author: Nicholas Tufillaro,Tyler Abbott

Publisher: Addison Wesley Publishing Company


Category: Chaotic behavior in systems.

Page: 420

View: 5217

This essential handbook provides the theoretical and experimental tools necessary to begin researching the nonlinear behavior of mechanical, electrical, optical, and other systems. The book describes several nonlinear systems which are realized by desktop experiments, such as an apparatus showing chaotic string vibrations, an LRC circuit displaying strange scrolling patterns, and a bouncing ball machine illustrating the period doubling route to chaos. Fractal measures, periodic orbit extraction, and symbolic analysis are applied to unravel the chaotic motions of these systems. The simplicity of the examples makes this an excellent book for undergraduate and graduate-level physics and mathematics courses, new courses in dynamical systems, and experimental laboratories.

Nonlinear Dynamics and Chaos, 2nd ed. SET with Student Solutions Manual

Author: Steven H. Strogatz

Publisher: Westview Press

ISBN: 9780813350844

Category: Mathematics

Page: 932

View: 4539

Steven H. Strogatz's Nonlinear Dynamics and Chaos, second edition, is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. The Student Solutions Manual, by Mitchal Dichter, includes solutions to the odd-numbered exercises featured in Nonlinear Dynamics and Chaos, second edition. Complete with graphs and worked-out solutions, the Student Solutions Manual demonstrates techniques for students to analyze differential equations, bifurcations, chaos, fractals, and other subjects explored in Strogatz's popular book.

Global Nonlinear Dynamics for Engineering Design and System Safety

Author: Stefano Lenci,Giuseppe Rega

Publisher: Springer

ISBN: 3319997106

Category: Technology & Engineering

Page: 318

View: 1227

This is the first book which exploits concepts and tools of global nonlinear dynamics for bridging the gap between theoretical and practical stability of systems/structures, and for possibly enhancing the engineering design in macro-, micro- and nano-mechanics. Addressed topics include complementing theoretical and practical stability to achieve load carrying capacity; dynamical integrity for analyzing global dynamics, for interpreting/predicting experimental behavior, for getting hints towards engineering design; techniques for control of chaos; response of uncontrolled and controlled system/models in applied mechanics and structural dynamics by also considerung the effect of system imperfections; from relatively simple systems to multidimensional models representative of real world applications; potential and expected impact of global dynamics for engineering design.

Chaos and Nonlinear Dynamics

An Introduction for Scientists and Engineers

Author: Robert C. Hilborn,Amanda and Lisa Cross Professor of Physics Robert Hilborn

Publisher: Oxford University Press on Demand

ISBN: 9780198507239

Category: Mathematics

Page: 650

View: 9924

This is a comprehensive introduction to the exciting scientific field of nonlinear dynamics for students, scientists, and engineers, and requires only minimal prerequisites in physics and mathematics. The book treats all the important areas in the field and provides an extensive and up-to-date bibliography of applications in all fields of science, social science, economics, and even the arts.

Nonlinear Dynamics and Chaos

Author: J. M. T. Thompson,Michael Thompson,H. B. Stewart

Publisher: John Wiley & Sons

ISBN: 9780471876847

Category: Mathematics

Page: 437

View: 5727

Nonlinear dynamics and chaos involves the study of apparent randomhappenings within a system or process. The subject has wideapplications within mathematics, engineering, physics and otherphysical sciences. Since the bestselling first edition waspublished, there has been a lot of new research conducted in thearea of nonlinear dynamics and chaos. * Expands on the bestselling, highly regarded first edition * A new chapter which will cover the new research in the area sincefirst edition * Glossary of terms and a bibliography have been added * All figures and illustrations will be 'modernised' * Comprehensive and systematic account of nonlinear dynamics andchaos, still a fast-growing area of applied mathematics * Highly illustrated * Excellent introductory text, can be used for an advancedundergraduate/graduate course text

Nonlinearity and Chaos in Molecular Vibrations

Author: Guozhen Wu

Publisher: Elsevier

ISBN: 9780080459073

Category: Science

Page: 318

View: 3107

Nonlinearity and Chaos in Molecular Vibrations deals systematically with a Lie algebraic approach to the study of nonlinear properties of molecular highly excited vibrations. The fundamental concepts of nonlinear dynamics such as chaos, fractals, quasiperiodicity, resonance, and the Lyapunov exponent, and their roles in the study of molecular vibrations are presented. The 20 chapters cover the basic ideas, the concept of dynamical groups, the integrable two-mode SU(2) system, the unintegrable three-mode SU(3) system, the noncompact su(1,1) algebraic application, su(3) symmetry breaking and its application and the quantal effect of asymmetric molecular rotation. Emphasis is given to: resonance and chaos, the fractal structure of eigencoefficients, the C-H bend motion of acetylene, regular and chaotic motion of DCN, the existence of approximately conserved quantum numbers, one-electronic motion in multi-sites, the Lyapunov exponent, actions of periodic trajectories and quantization, the H function and its application in vibrational relaxation as well as the Dixon dip and its destruction and chaos in the transitional states. This approach bridges the gap between molecular vibrational spectroscopy and nonlinear dynamics. The book presents a framework of information that readers can use to build their knowledge, and is therefore highly recommended for all those working in or studying molecular physics, molecular spectroscopy, chemical physics and theoretical physics. * Discusses nonlinearity and chaotic phenomena in molecular vibrations * Approaches the complicated highly excited molecular vibration * Provides clear information for students and researchers looking to expand knowledge in this field

Clinical Chaos

A Therapist's Guide to Nonlinear Dynamics and Therapeutic Change

Author: Linda L. Chamberlain,Michael R. Bütz

Publisher: Psychology Press

ISBN: 9780876309261

Category: Psychology

Page: 225

View: 1212

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

Report of the Research Briefing Panel on Order, Chaos, and Patterns

Aspects of Nonlinearity

Author: Committee on Science, Engineering, and Public Policy (U.S.). Research Briefing Panel on Order, Chaos, and Patterns : Aspects of Nonlinearity,Mitchell J. Feigenbaum,Martin David Kruskal

Publisher: National Academies


Category: Chaotic behavior in systems

Page: 14

View: 3873


Nonlinear Dynamics in Human Behavior

Author: William H. Sulis,Allan Combs

Publisher: World Scientific

ISBN: 9789810227425

Category: Psychology

Page: 411

View: 6615

This book represents a selection of papers presented at the Fourth Annual Conference of the Society for Chaos Theory in Psychology and the Life Sciences, held at Johns Hopkins University in Baltimore, June 24-27, 1995. The book reflects the Society as a whole, consisting of applications of nonlinear methodology in psychophysics, neurophysiology, business and social science as well as applications of the nonlinear paradigm to issues arising in psychotherapy and the study of creativity. Unique are contributions on the use of Boolean networks in the study of psychosis and quality of life. Review articles on the appropriate use of time series methods in psychology and psychophysics provide a valuable reference.

Erfahrung Mathematik

Author: P.J. Davis,R. Hersh

Publisher: Springer-Verlag

ISBN: 3034850409

Category: Science

Page: 466

View: 5945

ie ältesten uns bekannten mathematischen Schriftta D feln stammen aus der Zeit um 2400 v. ehr. ; aber wir dürfen davon ausgehen, daß das Bedürfnis, Mathematik zu schaffen, ein Ausdruck der menschlichen Zivilisation an sich ist. In vier bis fünf Jahrtausenden hat sich ein gewalti ges System von Praktiken und Begriffen - die Mathematik herangebildet, die in vielfältiger Weise mit unserem Alltag verknüpft ist. Was ist Mathematik? Was bedeutet sie? Wo mit befaßt sie sich? Was sind ihre Methoden? Wie wird sie geschaffen und benützt? Wo ist ihr Platz in der Vielgestalt der menschlichen Erfahrung? Welchen Nutzen bringt sie? Was für Schaden richtet sie an? Welches Gewicht kommt ihr zu? Diese schwierigen Fragen werden noch zusätzlich kompliziert durch die Fülle des Materials und die weitver zweigten Querverbindungen, die es dem einzelnen verun möglichen, alles zu begreifen, geschweige denn, es in seiner Gesamtheit zu erfassen und zwischen den Deckeln eines normalen Buches unterzubringen. Um von dieser Material fülle nicht erdrückt zu werden, haben sich die Autoren für eine andere Betrachtungsweise entschieden. Die Mathema tik ist seit Tausenden von Jahren ein Feld menschlicher Ak tivität. In begrenztem Rahmen ist jeder von uns ein Mathe matiker und betreibt bewußt Mathematik, wenn er zum Beispiel auf dem Markt einkauft, Tapeten ausmißt oder ei nen Keramiktopf mit einem regelmäßigen Muster verziert. In bescheidenem Ausmaß versucht sich auch jeder von uns als mathematischer Denker. Schon mit dem Ausruf «Aber Zahlen lügen nicht!» befinden wir uns in der Gesellschaft von Plato oder Lakatos.

Growth Theory, Nonlinear Dynamics, and Economic Modelling

Scientific Essays of William Allen Brock

Author: William A. Brock

Publisher: Edward Elgar Publishing

ISBN: 9781782543046

Category: Business & Economics

Page: 443

View: 6288

'Buz Brock's contribution to economic theory in general and economic dynamics in particular are characterized by an unmatched richness of ideas and by deep theoretical, empirical as well as computational analysis. Brock's contribution to economic dynamics range from one extreme of the field, global stability of stochastic optimal growth models, to another extreme, market instability and nonlinearity in economic and financial modelling and data analysis. But his work also includes environmental and economic policy issues and, more recently, the modelling of markets as complex adaptive systems. This collection of essays reflects Brock's richness of ideas that have motivated economists for more than three decades already and will continue to influence many economists for the next decades to come.' - Cars H. Hommes, University of Amsterdam, The Netherlands 'Buz Brock has been, from the beginning of his career, one of the most original thinkers in dynamic economics. His early work showed that growth with random elements could be studied effectively and above all posed exactly the right questions. His more recent work has brought complexity theory to the fore and shown its implications for financial and other markets. In the process, he has both introduced and used econometric tools to show the relevance of his work to empirically observed phenomena. It is very useful to have his work in collected form.' - Kenneth J. Arrow, Stanford University, US This outstanding collection of William Brock's essays illustrates the power of dynamic modelling to shed light on the forces for stability and instability in economic systems. The articles selected reflect his best work and are indicative both of the type of policy problem that he finds challenging and the complex methodology that he uses to solve them. Also included is an introduction by Brock to his own work, which helps tie together the main aspects of his research to date.

Universality of Nonclassical Nonlinearity

Applications to Non-Destructive Evaluations and Ultrasonics

Author: Pier Paolo Delsanto

Publisher: Springer Science & Business Media

ISBN: 038735851X

Category: Science

Page: 546

View: 1679

This book presents the results of two major international research projects on phenomenology, theory and applications of Nonclassical Nonlinearity. It conveys concepts, experimental techniques and applications which were previously found in specialized journals. It also allows for an interdisciplinary audience to better understand the range of practical applications, and is timely and interesting to both researchers and professionals.

Nonlinear Dynamics in the Life and Social Sciences

Author: William H. Sulis,Irina Nikolaevna Trofimova

Publisher: IOS Press

ISBN: 9781586030209

Category: Mathematics

Page: 417

View: 9501

Incorporating chaos theory into psychology and the life sciences, this text includes empirical studies of neural encoding, memory, eye movements, warfare, business cycles and selection of time series analysis algorithms. There are theoretical chapters on emergence and social dynamics, and clinical contributions dealing with: the measurement of quality of life for psychiatric patients; psychosis; the organization of self; and the role of love in family dynamics. Finally ideas from non-linear dynamics are applied to understanding the creative process.

Quantum Chaos

A New Paradigm of Nonlinear Dynamics

Author: Katsuhiro Nakamura

Publisher: CUP Archive

ISBN: 9780521467469

Category: Mathematics

Page: 224

View: 9430

Past studies on chaos have been concerned with classical systems but this book is one of the first to deal with quantum chaos.

Chaos and Complexity Theory for Management: Nonlinear Dynamics

Nonlinear Dynamics

Author: Banerjee, Santo

Publisher: IGI Global

ISBN: 1466625104

Category: Business & Economics

Page: 449

View: 2804

Although chaos theory refers to the existence between seemingly random events, it has been gaining the attention of science, technology and managements fields. The shift from traditional procedures to the dynamics of chaos and complexity theory has resulted in a new element of complexity thinking, allowing for a greater capability for analyzing and understanding key business processes. Chaos and Complexity Theory for Management: Nonlinear Dynamics explores chaos and complexity theory and its relationship with the understanding of natural chaos in the business environment. Utilizing these theories aids in comprehending the development of businesses as a complex adaptive system.