Introduction to Discrete Dynamical Systems and Chaos (Wiley Series in Discrete Mathematics and Optimization) 1st Edition by Mario Martelli (PDF)

Description

A timely, accessible introduction to the mathematics of chaos. The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized. Introduction to Discrete Dynamical Systems and Chaos makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks. An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author’s 1993 book, but boasting at least 60% new, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field.

User’s Reviews

Editorial Reviews: Review “From the preface: ‘The purpose of this book is to present the fundamental ideas on discrete dynamical systems and chaos at the level of those undergraduates…who have completed the standard calculus sequence, with the inclusion of functions of several variables and linear algebra.'” (Mathematical Reviews, Issue 2001k) From the Inside Flap A timely, accessible introduction to the mathematics of chaos. The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized. Introduction to Discrete Dynamical Systems and Chaos makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks. An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author’s 1993 book, but boasting at least 60% new, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field. From the Back Cover A timely, accessible introduction to the mathematics of chaos. The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized. Introduction to Discrete Dynamical Systems and Chaos makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks. An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author’s 1993 book, but boasting at least 60% new, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field. About the Author MARIO MARTELLI, PhD, is Professor of Mathematics at California State University at Fullerton. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This text is about chaos and discrete dynamical systems, but the organization, presentation and discourse of these topics in this wonderful edition are anything but chaotic. The writing and context of the ideas laid out bristles with personality and clear focus for presenting the student with adequate examples and detail. This book serves as a superb introduction to the area, and is rich with a wide variety of situations and problems that will motivate the novice and still challenge those with background. I signed on to teach an introductory course on Chaos at New Mexico Highlands University (I’m am one of three math faculty at this institution). I spent considerable time searching for a text that adequately addressed chaos and dynamical systems, that was challenging and yet personable and reader friendly. We have a wide disparity of math students at NMHU, particularly with regard to background, ability and vocational aspirations. It was important to use a text, I felt, that did not sacrifice detail, but at the same time did not pre-suppose overly technical sophistication. Most of the texts that I sampled, were quite terse, demanding or pedagogically constipated. When I came across MArtelli’s text I was struck by the absence of these defects and then by the simple structure and sequence of topics that patiently build and reinforce concepts. The author’s enthusiasm for the material comes through clearly and reaction from students I test-sampled echoed this feeling. In fact, both students have decided to enroll in my spring course – I believe their postiive response to this text was more than a contributing factor. In exchange for their time, I promised I would relay encouragement for all who are considering similar course offerings and a companion text that supports and reinforces the excitement of this area of mathematics. This book is a great resource. Bravo, Mario !!

⭐The Introduction to Discrete Dynamical Systems and Chaos is an excellent text for those who just start sturying descrete dynamical systems and for those who already have some knowledge in the field. The book can be used as a textbook or as a guide for individual studies. In the first case the instructors will find a set of carefully chosen problems at the end of each chapter and several interesting projects for the students. While the first part of the book can be understood by a person without extensive mathematical background, the second part deals with topics such as nonlinear dynamical systems and chaotic behavior using Banach contraction principle, fractal dimension, etc.To illustrate the use of dynamical systems the book also describes few very common models: blood-sell population, predator-prey, Lorenz Model, and neural networks.The appendix on Mathematica and Dynamical Systems can be used by students to work on the sample projects offered by the author or by scientists to model and investigate the behavior of variety of dynamical system.

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