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Dynamical Systems with Applications using Mathematica® de Stephen Lynch

Dynamical Systems with Applications using Mathematica®

Autor Stephen Lynch
en Limba Engleză Paperback – 30 sep 2007

Observăm că în peisajul academic actual, studiul sistemelor dinamice a devenit indisociabil de utilizarea instrumentelor de calcul simbolic. Dynamical Systems with Applications using Mathematica® se poziționează ca un manual fundamental pentru cursurile de matematică aplicată, inginerie și științe naturale, oferind o punte esențială între rigoarea teoretică și implementarea computațională. Ediția de față, publicată de Birkhäuser, marchează o actualizare semnificativă, fiind recalibrată pentru a reflecta evoluția software-ului Mathematica până la versiunea 11.2, ceea ce asigură compatibilitatea codului cu cerințele moderne de cercetare.

Remarcăm o structură echilibrată ce ghidează cititorul printr-o progresie logică: de la o introducere tutorială în mediul Mathematica, la sisteme planare, teoria bifurcației și, în final, către subiecte avansate precum rețelele neuronale și controlul haosului. Spre deosebire de abordarea pur teoretică din Differential Equations, Dynamical Systems, and an Introduction to Chaos de Morris W. Hirsch, lucrarea lui Stephen Lynch prioritizează lărgimea spectrului de aplicabilitate în detrimentul detaliilor tehnice excesive ale demonstrațiilor. Este o alternativă pragmatică la Dynamical System and Chaos pentru cursurile de licență, având avantajul integrării directe a notebook-urilor Mathematica care permit vizualizarea imediată a fenomenelor neliniare.

Interesul autorului pentru accesibilitatea programării, vizibil și în lucrările sale recente dedicate limbajului Python, se traduce aici printr-un stil pedagogic transparent. Textul nu se rezumă la teorie, ci include secțiuni noi despre fractali Newton și procesare de imagini, oferind studenților resurse concrete pentru proiectele de cercetare individuală.

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Specificații

ISBN-13: 9780817644826
ISBN-10: 0817644822
Pagini: 484
Dimensiuni: 155 x 235 x 23 mm
Greutate: 0.69 kg
Ediția:2007
Editura: Birkhäuser Boston
Colecția Birkhäuser
Locul publicării:Boston, MA, United States

Public țintă

Research

De ce să citești această carte

Recomandăm această carte studenților și cercetătorilor care doresc să stăpânească modelarea sistemelor complexe fără a se pierde în demonstrații matematice abstracte. Cititorul câștigă competențe duble: o înțelegere intuitivă a dinamicii neliniare și abilitatea de a utiliza Mathematica pentru simulări avansate. Este un instrument de lucru indispensabil pentru proiecte de licență sau masterat în bio-matematică, econometrie sau fizică computațională, oferind soluții complete pentru toate exercițiile incluse.

Despre autor

Stephen Lynch este un autor și cercetător recunoscut pentru eforturile sale de a face matematica computațională accesibilă unui public larg. Expertiza sa se concentrează pe utilizarea pachetelor software moderne în educația științifică, fiind autorul unor volume de referință precum A Simple Introduction to Python și Python for Scientific Computing and Artificial Intelligence. În cadrul operei sale, Dynamical Systems with Applications using Mathematica® reprezintă pilonul central în ceea ce privește aplicarea calculului simbolic în sistemele dinamice, reflectând filosofia autorului de a pune instrumentele de programare direct în mâna cercetătorului pentru a facilita descoperirea științifică prin simulare și vizualizare.

Descriere

This book provides an introduction to the theory of dynamical systems with the ® aid of the Mathematica computer algebra system. It is written for both senior undergraduates and graduate students. The ?rst part of the book deals with c- tinuous systems using ordinary differential equations (Chapters 1–10), the second part is devoted to the study of discrete dynamical systems (Chapters 11–15), and Chapters 16 and 17 deal with both continuous and discrete systems. It should be pointedoutthatdynamicalsystemstheoryisnotlimitedtothesetopicsbutalso- compassespartialdifferentialequations,integralandintegrodifferentialequations, stochastic systems, and time-delay systems, for instance. References [1]–[4] given at the end of the Preface provide more information for the interested reader. The author has gone for breadth of coverage rather than ?ne detail and theorems with proofs are kept at a minimum. The material is not clouded by functional analytic and group theoretical de?nitions, and so is intelligible to readers with a general mathematical background. Some of the topics covered are scarcely covered el- where. Most of the material in Chapters 9, 10, 14, 16, and 17 is at a postgraduate levelandhasbeenin?uencedbytheauthor’sownresearchinterests. Thereismore theory in these chapters than in the rest of the book since it is not easily accessed anywhere else. It has been found that these chapters are especially useful as ref- ence material for senior undergraduate project work. The theory in other chapters of the book is dealt with more comprehensively in other texts, some of which may be found in the references section of the corresponding chapter.

Cuprins

PrefaceA Tutorial Introduction to MathematicaDifferential EquationsPlanar SystemsInteracting SpeciesLimit CyclesHamiltonian Systems, Lyapunov Functions, and StabilityBifurcation TheoryThree-Dimensional Autonomous Systems and ChaosPoincaré Maps and Nonautonomous Systems in the PlaneLocal and Global BifurcationsThe Second Part of David Hilbert's Sixteenth ProblemLinear Discrete Dynamical SystemsNonlinear Discrete Dynamical SystemsComplex Iterative MapsElectromagnetic Waves and Optical ResonatorsFractals and MultifractalsChaos Control and SynchronizationNeural NetworksExamination-Type QuestionsSolutions to ExercisesReferencesMathematica Program IndexIndex

Recenzii

From the reviews: "Stephen Lynch's book offers a comprehensive introduction to the theory and application of differential equations and dynamical systems methods. Its focus on applications and avoidance of overly technical arguments makes it a an equally good choice for teaching an undergraduate course in dynamical systems, as self-study for graduate students interested in dynamical systems, or as an introductory text for researchers seeking an overview of some current developments in applied dynamical systems. Most importantly, its content and presentation style convey the excitement that has drawn many students and researchers to dynamical systems in the first place.—Dynamical Systems Magazine
"This accessible university text shows how a wide range of differential equations work and begin to fail to work over a very wide range of solved and unsolvable applications. Mathematica is used throughout, from its tutorial introduction in Chapter 0 to the minimally chaotic neuromodule of the final section. This is the first work I have seen in which genuine self-education by computer is expected of the reader. The one-liner programs come to life when typed in, and the growing programming skill lends itself to inventing [one's] own extensions to the supplied problems.—Datafile, The Journal of the HPCC
“The book is a good introduction to dynamical systems theory. … This book presents an original, cheap and powerful solution to the problem of analysis of large data sets. … The text is aimed at graduate students and working scientists in various branches of applied mathematics, natural sciences and engineering. … recommend ‘Dynamical Systems with Applications using MATHEMATICA®’ as a good handbook for a diverse readership, for graduates and professionals in mathematics, physics, science and engineering.” (Damian Trif, Studia Universitatis Babeş-Bolyai. Mathematica, Vol. LIV (4), December, 2009)

Textul de pe ultima copertă

Dynamical Systems with Applications using Mathematica® provides an introduction to the theory of dynamical systems with the aid of the Mathematica computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks.
Mathematica’s symbolic, numerical, and graphical capabilities make it ideal for the study of nonlinear dynamical systems. An introductory chapter provides complete tutorials on how to use Mathematica’s text-based input commands and palettes, enabling new users to become familiar with the program, while providing a good reference source for experts. Working Mathematica notebooks will be available at http://library.wolfram.com/infocenter/Books/AppliedMathematics/.
Throughout the book, the author has focused on breadth of coverage rather than fine detail, with theorems and proofs being kept to a minimum. The first part of the book deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems. Some of the material presented is at the postgraduate level and has been influenced by the author’s own research interests. Exercises are included at the end of every chapter. A comprehensive bibliography including textbooks and research papers rounds out the work.
The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering. Many chapters of the book are especially useful as reference material for senior undergraduate independent project work.
Also by the author:
Dynamical Systems with Applications using MATLAB®, ISBN 978-0-8176-4321-8
Dynamical Systems with Applications using Maple, ISBN 978-0-8176-4150-4
 
 

Notă biografică

Stephen Lynch is Senior Lecturer in the Department of Computing and Mathematics at Manchester Metropolitan University.
Also by the author:
Dynamical Systems with Applications using Maple™, ISBN 978-0-8176-4389-8
Dynamical Systems with Applications using MATLAB®, ISBN 978-3-319-06819-0