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Differential Equations Dynamical Systems And An Introduction To Chaos

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Differential Equations Dynamical Systems and an Introduction to Chaos

Differential Equations  Dynamical Systems  and an Introduction to Chaos Book
Author : Morris W. Hirsch,Stephen Smale,Robert L. Devaney
Publisher : Academic Press
Release : 2004
ISBN : 0123497035
Language : En, Es, Fr & De

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Book Description :

This text is about the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It is an update of one of Academic Press's most successful mathematics texts ever published, which has become the standard textbook for graduate courses in this area. The authors are tops in the field of advanced mathematics. Steve Smale is a Field's Medalist, which equates to being a Nobel prize winner in mathematics. Bob Devaney has authored several leading books in this subject area. Linear algebra prerequisites toned down from first edition Inclusion of analysis of examples of chaotic systems, including Lorenz, Rosssler, and Shilnikov systems Bifurcation theory included throughout.

Differential Equations Dynamical Systems and an Introduction to Chaos

Differential Equations  Dynamical Systems  and an Introduction to Chaos Book
Author : Morris W. Hirsch,Stephen Smale,Robert L. Devaney
Publisher : Academic Press
Release : 2013
ISBN : 0123820103
Language : En, Es, Fr & De

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Book Description :

Hirsch, Devaney, and Smale's classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems. Classic text by three of the world's most prominent mathematicians Continues the tradition of expository excellence Contains updated material and expanded applications for use in applied studies

Differential Equations Dynamical Systems and an Introduction to Chaos

Differential Equations  Dynamical Systems  and an Introduction to Chaos Book
Author : Morris William Hirsch,Stephen Smale,Robert L. Devaney
Publisher : Unknown
Release : 2004-01-01
ISBN : 9788181474254
Language : En, Es, Fr & De

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Book Description :

Download Differential Equations Dynamical Systems and an Introduction to Chaos book written by Morris William Hirsch,Stephen Smale,Robert L. Devaney, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Differential Equations Dynamical Systems and an Introduction to Chaos

Differential Equations  Dynamical Systems  and an Introduction to Chaos Book
Author : Morris W. Hirsch,Stephen Smale,Robert L. Devaney
Publisher : Academic Press
Release : 2004
ISBN : 0123497035
Language : En, Es, Fr & De

GET BOOK

Book Description :

This text is about the dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. It is an update of one of Academic Press's most successful mathematics texts ever published, which has become the standard textbook for graduate courses in this area. The authors are tops in the field of advanced mathematics. Steve Smale is a Field's Medalist, which equates to being a Nobel prize winner in mathematics. Bob Devaney has authored several leading books in this subject area. Linear algebra prerequisites toned down from first edition Inclusion of analysis of examples of chaotic systems, including Lorenz, Rosssler, and Shilnikov systems Bifurcation theory included throughout.

Chaos

Chaos Book
Author : Kathleen Alligood,Tim Sauer,J.A. Yorke
Publisher : Springer
Release : 2012-12-06
ISBN : 3642592813
Language : En, Es, Fr & De

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Book Description :

BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.

Dynamical Systems

Dynamical Systems Book
Author : D. Arrowsmith,C.M. Place
Publisher : CRC Press
Release : 1992-08-01
ISBN : 9780412390807
Language : En, Es, Fr & De

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Book Description :

This text discusses the qualitative properties of dynamical systems including both differential equations and maps. The approach taken relies heavily on examples (supported by extensive exercises, hints to solutions and diagrams) to develop the material, including a treatment of chaotic behavior. The unprecedented popular interest shown in recent years in the chaotic behavior of discrete dynamic systems including such topics as chaos and fractals has had its impact on the undergraduate and graduate curriculum. However there has, until now, been no text which sets out this developing area of mathematics within the context of standard teaching of ordinary differential equations. Applications in physics, engineering, and geology are considered and introductions to fractal imaging and cellular automata are given.

Invitation to Dynamical Systems

Invitation to Dynamical Systems Book
Author : Edward R. Scheinerman
Publisher : Courier Corporation
Release : 2013-05-13
ISBN : 0486275329
Language : En, Es, Fr & De

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Book Description :

This text is designed for those who wish to study mathematics beyond linear algebra but are unready for abstract material. Rather than a theorem-proof-corollary exposition, it stresses geometry, intuition, and dynamical systems. 1996 edition.

Differential Dynamical Systems

Differential Dynamical Systems Book
Author : James D. Meiss
Publisher : SIAM
Release : 2007-01-01
ISBN : 0898716357
Language : En, Es, Fr & De

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Book Description :

Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems conceptsflow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems. Audience This textbook is intended for senior undergraduates and first-year graduate students in pure and applied mathematics, engineering, and the physical sciences. Readers should be comfortable with elementary differential equations and linear algebra and should have had exposure to advanced calculus. Contents List of Figures; Preface; Acknowledgments; Chapter 1: Introduction; Chapter 2: Linear Systems; Chapter 3: Existence and Uniqueness; Chapter 4: Dynamical Systems; Chapter 5: Invariant Manifolds; Chapter 6: The Phase Plane; Chapter 7: Chaotic Dynamics; Chapter 8: Bifurcation Theory; Chapter 9: Hamiltonian Dynamics; Appendix: Mathematical Software; Bibliography; Index

Linear Chaos

Linear Chaos Book
Author : Karl-G. Grosse-Erdmann,Alfred Peris Manguillot
Publisher : Springer Science & Business Media
Release : 2011-08-24
ISBN : 1447121708
Language : En, Es, Fr & De

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Book Description :

It is commonly believed that chaos is linked to non-linearity, however many (even quite natural) linear dynamical systems exhibit chaotic behavior. The study of these systems is a young and remarkably active field of research, which has seen many landmark results over the past two decades. Linear dynamics lies at the crossroads of several areas of mathematics including operator theory, complex analysis, ergodic theory and partial differential equations. At the same time its basic ideas can be easily understood by a wide audience. Written by two renowned specialists, Linear Chaos provides a welcome introduction to this theory. Split into two parts, part I presents a self-contained introduction to the dynamics of linear operators, while part II covers selected, largely independent topics from linear dynamics. More than 350 exercises and many illustrations are included, and each chapter contains a further ‘Sources and Comments’ section. The only prerequisites are a familiarity with metric spaces, the basic theory of Hilbert and Banach spaces and fundamentals of complex analysis. More advanced tools, only needed occasionally, are provided in two appendices. A self-contained exposition, this book will be suitable for self-study and will appeal to advanced undergraduate or beginning graduate students. It will also be of use to researchers in other areas of mathematics such as partial differential equations, dynamical systems and ergodic theory.

Chaos and Dynamical Systems

Chaos and Dynamical Systems Book
Author : David P. Feldman
Publisher : Princeton University Press
Release : 2019-08-06
ISBN : 0691189390
Language : En, Es, Fr & De

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Book Description :

Chaos and Dynamical Systems presents an accessible, clear introduction to dynamical systems and chaos theory, important and exciting areas that have shaped many scientific fields. While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview. In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder. Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.

Dynamical Systems with Applications using Python

Dynamical Systems with Applications using Python Book
Author : Stephen Lynch
Publisher : Springer
Release : 2018-10-09
ISBN : 3319781456
Language : En, Es, Fr & De

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Book Description :

This textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary oscillator computing. Dynamical Systems with Applications Using Python takes advantage of Python’s extensive visualization, simulation, and algorithmic tools to study those topics in nonlinear dynamical systems through numerical algorithms and generated diagrams. After a tutorial introduction to Python, the first part of the book deals with continuous systems using differential equations, including both ordinary and delay differential equations. The second part of the book deals with discrete dynamical systems and progresses to the study of both continuous and discrete systems in contexts like chaos control and synchronization, neural networks, and binary oscillator computing. These later sections are useful reference material for undergraduate student projects. The book is rounded off with example coursework to challenge students’ programming abilities and Python-based exam questions. This book will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a range of disciplines, such as biology, chemistry, computing, economics, and physics. Since it provides a survey of dynamical systems, a familiarity with linear algebra, real and complex analysis, calculus, and ordinary differential equations is necessary, and knowledge of a programming language like C or Java is beneficial but not essential.

Differential Equations Bifurcations and Chaos in Economics

Differential Equations  Bifurcations  and Chaos in Economics Book
Author : Wei-Bin Zhang
Publisher : World Scientific
Release : 2005
ISBN : 9812563334
Language : En, Es, Fr & De

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Book Description :

Although the application of differential equations to economics is a vast and vibrant area, the subject has not been systematically studied; it is often treated as a subsidiary part of mathematical economics textbooks. This book aims to fill that void by providing a unique blend of the theory of differential equations and their exciting applications to dynamic economics. Containing not just a comprehensive introduction to the applications of the theory of linear (and linearized) differential equations to economic analysis, the book also studies nonlinear dynamical systems, which have only been widely applied to economic analysis in recent years. It provides comprehensive coverage of the most important concepts and theorems in the theory of differential equations in a way that can be understood by any reader who has a basic knowledge of calculus and linear algebra. In addition to traditional applications of the theory to economic dynamics, the book includes many recent developments in different fields of economics.

Dynamical Systems

Dynamical Systems Book
Author : Pierre N.V. Tu
Publisher : Springer Science & Business Media
Release : 2013-11-11
ISBN : 3662027798
Language : En, Es, Fr & De

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Book Description :

Dynamic tools of analysis and modelling are increasingly used in Economics and Biology and have become more and more sophisticated in recent years, to the point where the general students without training in Dynamic Systems (DS) would be at a loss. No doubt they are referred to the original sources of mathematical theorems used in the various proofs, but the level of mathematics is generally beyond them. Students are thus left with the burden of somehow understanding advanced mathematics by themselves, with· very little help. It is to these general students, equipped only with a modest background of Calculus and Matrix Algebra that this book is dedicated. It aims at providing them with a fairly comprehensive box of dynamical tools they are expected to have at their disposal. The first three Chapters start with the most elementary notions of first and second order Differential and Difference Equations. For these, no matrix theory and hardly any calculus are needed. Then, before embarking on linear and nonlinear DS, a review of some Linear Algebra in Chapter 4 provides the bulk of matrix theory required for the study of later Chapters. Systems of Linear Differ ential Equations (Ch. 5) and Difference Equations (Ch. 6) then follow to provide students with a good background in linear DS, necessary for the subsequent study of nonlinear systems. Linear Algebra, reviewed in Ch. 4, is used freely in these and subsequent chapters to save space and time.

Dynamical Systems with Applications using MapleTM

Dynamical Systems with Applications using MapleTM Book
Author : Stephen Lynch
Publisher : Springer Science & Business Media
Release : 2009-12-23
ISBN : 0817646051
Language : En, Es, Fr & De

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Book Description :

Excellent reviews of the first edition (Mathematical Reviews, SIAM, Reviews, UK Nonlinear News, The Maple Reporter) New edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions Two new chapters on neural networks and simulation have also been added Wide variety of topics covered with applications to many fields, including mechanical systems, chemical kinetics, economics, population dynamics, nonlinear optics, and materials science Accessible to a broad, interdisciplinary audience of readers with a general mathematical background, including senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering A hands-on approach is used with Maple as a pedagogical tool throughout; Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author’s website with additional applications and further links of interest at Maplesoft’s Application Center

Dynamical Systems with Applications using MAPLE

Dynamical Systems with Applications using MAPLE Book
Author : Stephen Lynch
Publisher : Springer Science & Business Media
Release : 2001
ISBN : 9780817641504
Language : En, Es, Fr & De

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Book Description :

This introduction to the theory of dynamical systems utilizes MAPLE to facilitate the understanding of the theory and to deal with the examples, diagrams, and exercises. A wide range of topics in differential equations and discrete dynamical systems is discussed with examples drawn from many different areas of application, including mechanical systems and materials science, electronic circuits and nonlinear optics, chemical reactions and meteorology, and population modeling.

Differential Equations A Dynamical Systems Approach

Differential Equations  A Dynamical Systems Approach Book
Author : John H. Hubbard,Beverly H. West
Publisher : Springer Science & Business Media
Release : 1997-10-17
ISBN : 9780387972862
Language : En, Es, Fr & De

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Book Description :

This corrected third printing retains the authors'main emphasis on ordinary differential equations. It is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. The authors have taken the view that a differential equations theory defines functions; the object of the theory is to understand the behaviour of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods, and the companion software, MacMath, is designed to bring these notions to life.

Discrete and Continuous Dynamical Systems

Discrete and Continuous Dynamical Systems Book
Author : Anonim
Publisher : Unknown
Release : 2008
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Discrete and Continuous Dynamical Systems book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Mathematics of Complexity and Dynamical Systems

Mathematics of Complexity and Dynamical Systems Book
Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Release : 2011-10-05
ISBN : 1461418054
Language : En, Es, Fr & De

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Book Description :

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Dynamical Systems

Dynamical Systems Book
Author : Anonim
Publisher : CRC Press
Release : 1998-11-17
ISBN : 1482227878
Language : En, Es, Fr & De

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Book Description :

Several distinctive aspects make Dynamical Systems unique, including: treating the subject from a mathematical perspective with the proofs of most of the results included providing a careful review of background materials introducing ideas through examples and at a level accessible to a beginning graduate student

Vakantiecursus 2003

Vakantiecursus 2003 Book
Author : Anonim
Publisher : Unknown
Release : 2003
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Vakantiecursus 2003 book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.