Encounters With Chaos And Fractals Second Edition
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Encounters With Chaos And Fractals Second Edition
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Author : Denny Gulick
language : en
Publisher: CRC Press
Release Date : 2012-04-26
Encounters With Chaos And Fractals Second Edition written by Denny Gulick and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
Now with an extensive introduction to fractal geometry Revised and updated, Encounters with Chaos and Fractals, Second Edition provides an accessible introduction to chaotic dynamics and fractal geometry for readers with a calculus background. It incorporates important mathematical concepts associated with these areas and backs up the definitions and results with motivation, examples, and applications. Laying the groundwork for later chapters, the text begins with examples of mathematical behavior exhibited by chaotic systems, first in one dimension and then in two and three dimensions. Focusing on fractal geometry, the author goes on to introduce famous infinitely complicated fractals. He analyzes them and explains how to obtain computer renditions of them. The book concludes with the famous Julia sets and the Mandelbrot set. With more than enough material for a one-semester course, this book gives readers an appreciation of the beauty and diversity of applications of chaotic dynamics and fractal geometry. It shows how these subjects continue to grow within mathematics and in many other disciplines.
Encounters With Chaos And Fractals
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Author : Denny Gulick
language : en
Publisher: CRC Press
Release Date : 2012-04-26
Encounters With Chaos And Fractals written by Denny Gulick and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
Revised and updated, this second edition provides an accessible introduction to both chaotic dynamics and fractal geometry for readers with a calculus background. This edition contains new and expanded material on fractals that illustrates how to obtain computer renderings of them and covers Julia and Mandelbrot sets. It also includes a substantial number of new exercises at the end of each section and MATLAB programs in the appendix, with selected solutions at the back of the book.
Encounters With Chaos And Fractals
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Author : Denny Gulick
language : en
Publisher: CRC Press
Release Date : 2024-05-10
Encounters With Chaos And Fractals written by Denny Gulick and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-10 with Mathematics categories.
Encounters with Chaos and Fractals, Third Edition provides an accessible introduction to chaotic dynamics and fractal geometry. It incorporates important mathematical concepts and backs up the definitions and results with motivation, examples, and applications. The Third Edition updates this classic book for a modern audience. New applications on contemporary topics, like data science and mathematical modelling, appear throughout. Coding activities are transitioned to open-source programming languages, including Python. The text begins with examples of mathematical behavior exhibited by chaotic systems, first in one dimension and then in two and three dimensions. Focusing on fractal geometry, the authors introduce famous infinitely complicated fractals. How to obtain computer renditions of them are explained. The book concludes with Julia sets and the Mandelbrot set. The Third Edition includes: v More coding activities included in each section. The code is expanded to include pseudo-code, with specific examples in MATLAB (or it's open-source cousin Octave) and Python. v Many more and updated exercises from previous editions. v Proof writing exercises for a more theoretical course. v Sections revised to include historical context. v Short sections added to explain applied problems developing the mathematics. This edition reveals how these ideas are continuing to be applied in the 21st century, while connecting to the long and winding history of dynamical systems. The primary focus is the beauty and diversity of these ideas. Offering more than enough material for a one-semester course, the authors show how these subjects continue to grow within mathematics and in many other disciplines.
Problems And Solutions Nonlinear Dynamics Chaos And Fractals
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Author : Willi-hans Steeb
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-03-02
Problems And Solutions Nonlinear Dynamics Chaos And Fractals written by Willi-hans Steeb and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Science categories.
This book presents a collection of problems for nonlinear dynamics, chaos theory and fractals. Besides the solved problems, supplementary problems are also added. Each chapter contains an introduction with suitable definitions and explanations to tackle the problems.The material is self-contained, and the topics range in difficulty from elementary to advanced. While students can learn important principles and strategies required for problem solving, lecturers will also find this text useful, either as a supplement or text, since concepts and techniques are developed in the problems.
Discrete Encounters
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Author : Craig Bauer
language : en
Publisher: CRC Press
Release Date : 2020-05-14
Discrete Encounters written by Craig Bauer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-14 with Mathematics categories.
Eschewing the often standard dry and static writing style of traditional textbooks, Discrete Encounters provides a refreshing approach to discrete mathematics. The author blends traditional course topics and applications with historical context, pop culture references, and open problems. This book focuses on the historical development of the subject and provides fascinating details of the people behind the mathematics, along with their motivations, deepening readers’ appreciation of mathematics. This unique book covers many of the same topics found in traditional textbooks, but does so in an alternative, entertaining style that better captures readers’ attention. In addition to standard discrete mathematics material, the author shows the interplay between the discrete and the continuous and includes high-interest topics such as fractals, chaos theory, cellular automata, money-saving financial mathematics, and much more. Not only will readers gain a greater understanding of mathematics and its culture, they will also be encouraged to further explore the subject. Long lists of references at the end of each chapter make this easy. Highlights: Features fascinating historical context to motivate readers Text includes numerous pop culture references throughout to provide a more engaging reading experience Its unique topic structure presents a fresh approach The text’s narrative style is that of a popular book, not a dry textbook Includes the work of many living mathematicians Its multidisciplinary approach makes it ideal for liberal arts mathematics classes, leisure reading, or as a reference for professors looking to supplement traditional courses Contains many open problems Profusely illustrated
Fractal Worlds
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Author : Michael Frame
language : en
Publisher: Yale University Press
Release Date : 2016-01-01
Fractal Worlds written by Michael Frame and has been published by Yale University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-01 with Mathematics categories.
In this essential primer, mathematician Michael Frame, a close collaborator with Benoit Mandelbrot, the founder of fractal geometry, and poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology
Chaos A Mathematical Introduction
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Author : John Banks
language : en
Publisher: Cambridge University Press
Release Date : 2003-05-08
Chaos A Mathematical Introduction written by John Banks and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-08 with Mathematics categories.
When new ideas like chaos first move into the mathematical limelight, the early textbooks tend to be very difficult. The concepts are new and it takes time to find ways to present them in a form digestible to the average student. This process may take a generation, but eventually, what originally seemed far too advanced for all but the most mathematically sophisticated becomes accessible to a much wider readership. This book takes some major steps along that path of generational change. It presents ideas about chaos in discrete time dynamics in a form where they should be accessible to anyone who has taken a first course in undergraduate calculus. More remarkably, it manages to do so without discarding a commitment to mathematical substance and rigour. The book evolved from a very popular one-semester middle level undergraduate course over a period of several years and has therefore been well class-tested.
Nonlinear Dynamics And Chaos
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Author : Steven H. Strogatz
language : en
Publisher: CRC Press
Release Date : 2018-05-04
Nonlinear Dynamics And Chaos written by Steven H. Strogatz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
This textbook 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.
Advanced Linear Algebra
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Author : Nicholas A. Loehr
language : en
Publisher: CRC Press
Release Date : 2024-06-21
Advanced Linear Algebra written by Nicholas A. Loehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-21 with Mathematics categories.
Designed for advanced undergraduate and beginning graduate students in linear or abstract algebra, Advanced Linear Algebra covers theoretical aspects of the subject, along with examples, computations, and proofs. It explores a variety of advanced topics in linear algebra that highlight the rich interconnections of the subject to geometry, algebra, analysis, combinatorics, numerical computation, and many other areas of mathematics. The author begins with chapters introducing basic notation for vector spaces, permutations, polynomials, and other algebraic structures. The following chapters are designed to be mostly independent of each other so that readers with different interests can jump directly to the topic they want. This is an unusual organization compared to many abstract algebra textbooks, which require readers to follow the order of chapters. Each chapter consists of a mathematical vignette devoted to the development of one specific topic. Some chapters look at introductory material from a sophisticated or abstract viewpoint, while others provide elementary expositions of more theoretical concepts. Several chapters offer unusual perspectives or novel treatments of standard results. A wide array of topics is included, ranging from concrete matrix theory (basic matrix computations, determinants, normal matrices, canonical forms, matrix factorizations, and numerical algorithms) to more abstract linear algebra (modules, Hilbert spaces, dual vector spaces, bilinear forms, principal ideal domains, universal mapping properties, and multilinear algebra). The book provides a bridge from elementary computational linear algebra to more advanced, abstract aspects of linear algebra needed in many areas of pure and applied mathematics.
An Introduction To Dynamical Systems And Chaos
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Author : G.C. Layek
language : en
Publisher: Springer
Release Date : 2015-12-01
An Introduction To Dynamical Systems And Chaos written by G.C. Layek and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-01 with Mathematics categories.
The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonian flows and symmetries of nonlinear systems are among the main focuses of this book. Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.