Complex Dynamical Systems In Education
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Complex Dynamical Systems In Education
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Author : Matthijs Koopmans
language : en
Publisher: Springer
Release Date : 2016-02-19
Complex Dynamical Systems In Education written by Matthijs Koopmans and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-19 with Education categories.
This book capitalizes on the developments in dynamical systems and education by presenting some of the most recent advances in this area in seventeen non-overlapping chapters. The first half of the book discusses the conceptual framework of complex dynamical systems and its applicability to educational processes. The second half presents a set of empirical studies that that illustrate the use of various research methodologies to investigate complex dynamical processes in education, and help the reader appreciate what we learn about dynamical processes in education from using these approaches.
Dynamical Systems
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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-24
Dynamical Systems written by Jürgen Jost and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-24 with Science categories.
Breadth of scope is unique Author is a widely-known and successful textbook author Unlike many recent textbooks on chaotic systems that have superficial treatment, this book provides explanations of the deep underlying mathematical ideas No technical proofs, but an introduction to the whole field that is based on the specific analysis of carefully selected examples Includes a section on cellular automata
Complex And Adaptive Dynamical Systems
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Author : Claudius Gros
language : en
Publisher: Springer
Release Date : 2015-04-01
Complex And Adaptive Dynamical Systems written by Claudius Gros and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-01 with Science categories.
This primer offers readers an introduction to the central concepts that form our modern understanding of complex and emergent behavior, together with detailed coverage of accompanying mathematical methods. All calculations are presented step by step and are easy to follow. This new fourth edition has been fully reorganized and includes new chapters, figures and exercises. The core aspects of modern complex system sciences are presented in the first chapters, covering network theory, dynamical systems, bifurcation and catastrophe theory, chaos and adaptive processes, together with the principle of self-organization in reaction-diffusion systems and social animals. Modern information theoretical principles are treated in further chapters, together with the concept of self-organized criticality, gene regulation networks, hypercycles and coevolutionary avalanches, synchronization phenomena, absorbing phase transitions and the cognitive system approach to the brain. Technical course prerequisites are the standard mathematical tools for an advanced undergraduate course in the natural sciences or engineering. Each chapter includes exercises and suggestions for further reading, and the solutions to all exercises are provided in the last chapter. From the reviews of previous editions: This is a very interesting introductory book written for a broad audience of graduate students in natural sciences and engineering. It can be equally well used both for teac hing and self-education. Very well structured and every topic is illustrated with simple and motivating examples. This is a true guidebook to the world of complex nonlinear phenomena. (Ilya Pavlyukevich, Zentralblatt MATH, Vol. 1146, 2008) Claudius Gros’ Complex and Adaptive Dynamical Systems: A Primer is a welcome addition to the literature. A particular strength of the book is its emphasis on analytical techniques for studying complex systems. (David P. Feldman, Physics Today, July, 2009).
Chaos And Dynamical Systems
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Author : David P. Feldman
language : en
Publisher: Princeton University Press
Release Date : 2019-08-06
Chaos And Dynamical Systems written by David P. Feldman and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-06 with Mathematics categories.
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.
The Dynamical Systems Approach To Cognition
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Author : Wolfgang Tschacher
language : en
Publisher: World Scientific
Release Date : 2003
The Dynamical Systems Approach To Cognition written by Wolfgang Tschacher and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Psychology categories.
The shared platform of the articles collected in this volume is used to advocate a dynamical systems approach to cognition. It is argued that recent developments in cognitive science towards an account of embodiment, together with the general approach of complexity theory and dynamics, have a major impact on behavioral and cognitive science. The book points out that there are two domains that follow naturally from the stance of embodiment: first, coordination dynamics is an established empirical paradigm that is best able to aid the approach; second, the obvious goal-directedness of intelligent action (i.e., intentionality) is nicely addressed in the framework of the dynamical synergetic approach.
Complex Dynamic Systems Theory And L2 Writing Development
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Author : Gary G. Fogal
language : en
Publisher: John Benjamins Publishing Company
Release Date : 2020-06-04
Complex Dynamic Systems Theory And L2 Writing Development written by Gary G. Fogal and has been published by John Benjamins Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-04 with Foreign Language Study categories.
This volume integrates complex dynamic systems theory (CDST) and L2 writing scholarship through a collection of in-depth studies and commentary across a range of writing constructs, learning contexts, and second and foreign languages. The text is arranged thematically across four topics: (i) perspectives on complexity, accuracy, and fluency, (ii) new constructs, approaches, and domains of L2-writing scholarship, (iii) methodological issues, and finally (iv) curricular perspectives. This work should appeal to graduate students and academics interested in expanded discussions on CDST, highlighting its utility for theorizing and researching language change, and to L2 writing scholars curious about how this fresh approach to researching L2 development can inform understandings of how L2 writing develops. As a CDST approach to language change has matured and taken a place among the dominant epistemologies in the field, students and researchers of L2 development alike will benefit from this volume.
Modeling And Simulation Of Complex Dynamical Systems
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Author : Vladimir Ryzhov
language : en
Publisher: Springer Nature
Release Date : 2021-07-16
Modeling And Simulation Of Complex Dynamical Systems written by Vladimir Ryzhov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-16 with Science categories.
This book highlights the practical aspects of computer modelling and simulation of complex dynamical systems for students. Mechanical systems are considered in the book as representative examples of dynamical systems. Wolfram SystemModeler, in combination with Learning Management System Sakai, is used as an instrument for studying features of various physical and technical phenomena and processes. Each of the presented virtual labs may be considered a stand-alone mini project to enable students to go through all the steps of mathematical modelling and computer simulation—from the problem statement to mathematical and physical analysis of the obtained result. The book is useful for teachers to organize the educational process, allowing gradual monitoring of the learning process and assessment of students’ competencies. It also allows tutors to design individual educational trajectories for students to achieve educational properties. The subject of the book is an extension of activity started by the international team of authors within the InMotion project of the European programme ERASMUS+.
Chaos
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Author : Angelo Vulpiani
language : en
Publisher: World Scientific
Release Date : 2010
Chaos written by Angelo Vulpiani and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.
Lines Of Inquiry In Mathematical Modelling Research In Education
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Author : Gloria Ann Stillman
language : en
Publisher: Springer
Release Date : 2019-05-16
Lines Of Inquiry In Mathematical Modelling Research In Education written by Gloria Ann Stillman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-16 with Education categories.
This open access book is based on selected presentations from Topic Study Group 21: Mathematical Applications and Modelling in the Teaching and Learning of Mathematics at the 13th International Congress on Mathematical Education (ICME 13), held in Hamburg, Germany on July 24–31, 2016. It contributes to the theory, research and teaching practice concerning this key topic by taking into account the importance of relations between mathematics and the real world. Further, the book addresses the “balancing act” between developing students’ modelling skills on the one hand, and using modelling to help them learn mathematics on the other, which arises from the integration of modelling into classrooms. The contributions, prepared by authors from 9 countries, reflect the spectrum of international debates on the topic, and the examples presented span schooling from years 1 to 12, teacher education, and teaching modelling at the tertiary level. In addition the book highlights professional learning and development for in-service teachers, particularly in systems where the introduction of modelling into curricula means reassessing how mathematics is taught. Given its scope, the book will appeal to researchers and teacher educators in mathematics education, as well as pre-service teachers and school and university educators
Chaos
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Author : Kathleen Alligood
language : en
Publisher: Springer
Release Date : 2012-12-06
Chaos written by Kathleen Alligood and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.