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9780817642235

Nonlinear Physics With Mathematica for Scientists and Engineers

by ;
  • ISBN13:

    9780817642235

  • ISBN10:

    0817642234

  • Edition: CD
  • Format: Hardcover
  • Copyright: 2001-06-01
  • Publisher: Birkhauser

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Summary

Nonlinear physics continues to be an area of dynamic modern research, with applications to physics, engineering, chemistry, mathematics, computer science, biology, medicine and economics. In this text extensive use is made of the Mathematica computer algebra system. No prior knowledge of Mathematica or programming is assumed. The authors have included a CD-ROM that contains over 130 annotated Mathematica files. These files may be used to solve and explore the text's 400 problems. This book includes 33 experimental activities that are designed to deepen and broaden the reader's understanding of nonlinear physics. These activities are correlated with Part I, the theoretical framework of the text.Additional features:* User-friendly, accessible presentation integrating theory, experiments, and the provided Mathematica notebooks; as the concepts of nonlinear science are developed, readers are gently introduced to Mathematica as an auxiliary tool* CD-ROM includes a wide variety of illustrative nonlinear examples solved with Mathematica--command structures introduced on a need-to-know basis* Notebooks designed to make use of Mathematica's sound capability* Mathematica notebook using the EulerEquation command incorporated into the textThis work is an excellent text for undergraduate and graduate students as well as a useful resource for working scientists.Reviewer comments on the Maple edition of NONLINEAR PHYSICS:"An...excellent book...the authors have been able to cover an extraordinary range of topics and hopefully excite a wide audience to investigate nonlinear phenomena...accessible to advanced undergraduates and yet challenging enough for graduate students and working scientists.... The reader is guided through it all with sound advice and humor.... I hope that many will adopt the text."-American Journal of Physics"Its organization of subject matter, clarity of writing, and smooth integration of analytic and computational techniques put it among the very best...Richard Enns and George McGuire have written an excellent text for introductory nonlinear physics."-Computers in Physics"...correctly balances a good treatment of nonlinear, but also nonchaotic, behavior of systems with some of the exciting findings about chaotic dynamics...one of the book's strength is the diverse selection of examples from mechanical, chemical, electronic, fluid and many other systems .... Another strength of the book is the diversity of approaches that the student is encouraged to take...the authors have chosen well, and the trio of text,...software, and lab manual gives the newcomer to nonlinear physics quite an effective set of tools.... Basic ideas are explained clearly and illustrated with many examples."-Physics Today"... the care that the authors have taken to ensure that their text is as comprehensive, versatile, interactive, and student-friendly as possible place this book far above the average."-Scientific Computing World

Table of Contents

Preface xi
I THEORY 1(510)
Introduction
3(36)
It's a Nonlinear World
3(3)
Symbolic Computation
6(29)
Examples of Mathematica Operations
7(19)
Getting Mathematica Help
26(1)
Use of Mathematica in Studying Nonlinear Physics
27(8)
Nonlinear Experimental Activities
35(2)
Scope of Part I (Theory)
37(2)
Nonlinear Systems. Part I
39(42)
Nonlinear Mechanics
39(14)
The Simple Pendulum
39(7)
The Eardrum
46(2)
Nonlinear Damping
48(3)
Nonlinear Lattice Dynamics
51(2)
Competition Phenomena
53(15)
Volterra-Lotka Competition Equations
54(5)
Population Dynamics of Fox Rabies in Europe
59(3)
Selection and Evolution of Biological Molecules
62(2)
Laser Beam Competition Equations
64(2)
Rapoport's Model for the Arms Race
66(2)
Nonlinear Electrical Phenomena
68(8)
Nonlinear Inductance
68(1)
An Electronic Oscillator (the Van der Pol Equation)
69(7)
Chemical and Other Oscillators
76(5)
Chemical Oscillators
76(4)
The Beating Heart
80(1)
Nonlinear Systems. Part II
81(44)
Pattern Formation
81(15)
Chemical Waves
81(2)
Snowflakes and Other Fractal Structures
83(6)
Rayleigh-Benard Convection
89(1)
Cellular Automata and the Game of Life
90(6)
Solitons
96(15)
Shallow Water Waves (KdV and Other Equations)
99(4)
Sine-Gordon Equation
103(4)
Self-Induced Transparency
107(1)
Optical Solitons
107(3)
The Jovian Great Red Spot (GRS)
110(1)
The Davydov Soliton
111(1)
Chaos and Maps
111(14)
Forced Oscillators
112(3)
Lorenz and Rossler Systems
115(2)
Poincare Sections and Maps
117(2)
Examples of One- and Two-Dimensional Maps
119(6)
Topological Analysis
125(42)
Introductory Remarks
125(4)
Types of Simple Singular Points
129(4)
Classifying Simple Singular Points
133(5)
Poincare's Theorem for the Vortex (Center)
137(1)
Examples of Phase Plane Analysis
138(16)
The Simple Pendulum
138(3)
The Laser Competition Equations
141(6)
Example of a Higher Order Singularity
147(7)
Bifurcations
154(3)
Isoclines
157(2)
3-Dimensional Nonlinear Systems
159(8)
Analytic Methods
167(56)
Introductory Remarks
167(1)
Some Exact Methods
168(25)
Separation of Variables
171(4)
The Bernoulli Equation
175(2)
The Riccati Equation
177(2)
Equations of the Structure d2y/dx2 = f(y)
179(14)
Some Approximate Methods
193(17)
Mathematica Generated Taylor Series Solution
193(3)
The Perturbation Approach: Poisson's Method
196(7)
Lindstedt's Method
203(7)
The Krylov-Bogoliubov (KB) Method
210(6)
Ritz and Galerkin Methods
216(7)
The Numerical Approach
223(42)
Finite-Difference Approximations
224(3)
Euler and Modified Euler Methods
227(11)
Euler Method
228(4)
The Modified Euler Method
232(6)
Runge-Kutta (RK) Methods
238(9)
The Basic Approach
238(3)
Examples of Common RK Algorithms
241(6)
Adaptive Step Size
247(6)
A Simple Example
247(2)
The Step Doubling Approach
249(1)
The RKF 45 Algorithm
250(3)
Stiff Equations
253(5)
Implicit and Semi-Implicit Schemes
258(5)
Some Remarks on NDSolve
263(2)
Limit Cycles
265(28)
Stability Aspects
265(8)
Relaxation Oscillations
273(5)
Bendixson's First Theorem
278(3)
Bendixson's Negative Criterion
278(1)
Proof of Theorem
278(2)
Applications
280(1)
The Poincare-Bendixson Theorem
281(4)
Poincare-Bendixson Theorem
282(1)
Application of the Theorem
282(3)
The Brusselator Model
285(6)
Prigogine-Lefever (Brusselator) Model
285(1)
Application of the Poincare-Bendixson Theorem
286(5)
3-Dimensional Limit Cycles
291(2)
Forced Oscillators
293(62)
Duffing's Equation
293(11)
The Harmonic Solution
296(2)
The Nonlinear Response Curves
298(6)
The Jump Phenomenon and Hysteresis
304(4)
Subharmonic & Other Periodic Oscillations
308(8)
Power Spectrum
316(8)
Chaotic Oscillations
324(11)
Entrainment and Quasiperiodicity
335(4)
Entrainment
335(2)
Quasiperiodicity
337(2)
The Rossler and Lorenz Systems
339(3)
The Rossler Attractor
339(1)
The Lorenz Attractor
340(2)
Hamiltonian Chaos
342(13)
Hamiltonian Formulation of Classical Mechanics
342(1)
The Henon-Heiles Hamiltonian
343(12)
Nonlinear Maps
355(58)
Introductory Remarks
355(1)
The Logistic Map
356(7)
Introduction
356(2)
Geometrical Representation
358(5)
Fixed Points and Stability
363(3)
The Period-Doubling Cascade to Chaos
366(3)
Period Doubling in the Real World
369(3)
The Lyapunov Exponent
372(3)
Stretching and Folding
375(3)
The Circle Map
378(5)
Chaos versus Noise
383(5)
2-Dimensional Maps
388(6)
Introductory Remarks
388(2)
Classification of Fixed Points
390(1)
Delayed Logistic Map
391(1)
Mandelbrot Map
392(2)
Mandelbrot and Julia Sets
394(2)
Nonconservative versus Conservative Maps
396(2)
Controlling Chaos
398(6)
3-Dimensional Maps: Saturn's Rings
404(9)
Nonlinear PDE Phenomena
413(38)
Introductory Remarks
413(1)
Burgers' Equation
414(11)
Backlund Transformations
425(7)
The Basic Idea
425(1)
Examples
425(4)
Nonlinear Superposition
429(3)
Solitary Waves
432(19)
The Basic Approach
432(1)
Phase Plane Analysis
433(4)
KdV Equation
437(5)
Sine-Gordon Equation
442(3)
The Three-Wave Problem
445(6)
Numerical Simulation
451(40)
Finite Difference Approximations
451(6)
Explicit Methods
457(16)
Diffusion Equation
457(9)
Fisher's Nonlinear Diffusion Equation
466(1)
Klein-Gordon Equation
467(3)
KdV Solitary Wave Collisions
470(3)
Von Neumann Stability Analysis
473(3)
Linear Diffusion Equation
473(1)
Burgers' Equation
474(2)
Implicit Methods
476(3)
Method of Characteristics
479(7)
Colliding Laser Beams
479(3)
General Equation
482(2)
Sine-Gordon Equation
484(2)
Higher Dimensions
486(5)
2-Dimensional Reaction-Diffusion Equations
487(1)
3-Dimensional Light Bullet Collisions
488(3)
Inverse Scattering Method
491(20)
Lax's Formulation
492(3)
Application to KdV Equation
495(6)
Direct Problem
495(2)
Time Evolution of the Scattering Data
497(3)
The Inverse Problem
500(1)
Multi-Soliton Solutions
501(2)
General Input Shapes
503(2)
The Zakharov-Shabat/AKNS Approach
505(6)
II EXPERIMENTAL ACTIVITIES 511(144)
Introduction to Nonlinear Experiments
513(4)
Magnetic Force
517(4)
Magnetic Tower
521(4)
Spin Toy Pendulum
525(4)
Driven Eardrum
529(4)
Nonlinear Damping
533(4)
Anharmonic Potential
537(6)
Iron Core Inductor
543(4)
Nonlinear LRC Circuit
547(6)
Tunnel Diode Negative Resistance Curve
553(6)
Tunnel Diode Self-Excited Oscillator
559(4)
Forced Duffing Equation
563(6)
Focal Point Instability
569(6)
Compound Pendulum
575(2)
Damped Simple Pendulum
577(2)
Stable Limit Cycle
579(8)
Van der Pol Limit Cycle
587(4)
Relaxation Oscillations: Neon Bulb
591(6)
Relaxation Oscillations: Drinking Bird
597(4)
Relaxation Oscillations: Tunnel Diode
601(4)
Hard Spring
605(4)
Nonlinear Resonance Curve: Mechanical
609(4)
Nonlinear Resonance Curve: Electrical
613(4)
Nonlinear Resonance Curve: Magnetic
617(4)
Subharmonic Response: Period Doubling
621(2)
Diode: Period Doubling
623(4)
Five-Well Magnetic Potential
627(6)
Power Spectrum
633(4)
Entrainment and Quasiperiodicity
637(2)
Quasiperiodicity
639(2)
Chua's Butterfly
641(4)
Route to Chaos
645(4)
Driven Spin Toy
649(2)
Mapping
651(4)
Bibliography 655(14)
Index 669

Supplemental Materials

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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

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