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9780817641191

Nonlinear Physics With Maple for Scientists and Engineers

by ;
  • ISBN13:

    9780817641191

  • ISBN10:

    081764119X

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 1999-12-01
  • Publisher: Birkhauser

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Supplemental Materials

What is included with this book?

Summary

Extensive use is made of the Maple computer algebra system. The authors have provided 74 Maple files, as well as 60 annotated Maple worksheets, on a CD-ROM. The files and worksheets may be used to solve and explore the text's 400 problems. Includes 30 experimental activities. DLC: Nonlinear theories--Data processing.

Table of Contents

Preface xi
I THEORY 1(492)
Introduction
3(32)
It's a Nonlinear World
3(3)
Symbolic Computation
6(25)
Examples of Maple Operations
7(15)
Getting Maple Help
22(1)
Use of Maple in Studying Nonlinear Physics
23(8)
Nonlinear Experimental Activities
31(1)
Scope of Part I (Theory)
32(3)
Nonlinear Systems. Part I
35(42)
Nonlinear Mechanics
35(15)
The Simple Pendulum
35(7)
The Eardrum
42(2)
Nonlinear Damping
44(3)
Nonlinear Lattice Dynamics
47(3)
Competition Phenomena
50(14)
Volterra--Lotka Competition Equations
50(5)
Population Dynamics of Fox Rabies in Europe
55(2)
Selection and Evolution of Biological Molecules
57(3)
Laser Beam Competition Equations
60(2)
Rapoport's Model for the Arms Race
62(2)
Nonlinear Electrical Phenomena
64(7)
Nonlinear Inductance
64(1)
An Electronic Oscillator (the Van der Pol Equation)
65(6)
Chemical and Other Oscillators
71(6)
Chemical Oscillators
71(4)
The Beating Heart
75(2)
Nonlinear Systems. Part II
77(44)
Pattern Formation
77(16)
Chemical Waves
77(2)
Snowflakes and Other Fractal Structures
79(5)
Rayleigh--Benard Convection
84(2)
Cellular Automata and the Game of Life
86(7)
Solitons
93(15)
Shallow Water Waves (KdV and Other Equations)
95(4)
Sine-Gordon Equation
99(4)
Self-Induced Transparency
103(1)
Optical Solitons
104(3)
The Jovian Great Red Spot (GRS)
107(1)
The Davydov Soliton
107(1)
Chaos and Maps
108(13)
Forced Oscillators
108(3)
Lorenz and Rossler Systems
111(2)
Poincare Sections and Maps
113(3)
Examples of One- and Two-Dimensional Maps
116(5)
Topological Analysis
121(42)
Introductory Remarks
121(4)
Types of Simple Singular Points
125(4)
Classifying Simple Singular Points
129(5)
Poincare's Theorem for the Vortex (Center)
134(1)
Examples of Phase Plane Analysis
134(16)
The Simple Pendulum
134(3)
The Laser Competition Equations
137(6)
Example of a Higher Order Singularity
143(7)
Bifurcations
150(3)
Isoclines
153(2)
3-Dimensional Nonlinear Systems
155(8)
Analytic Methods
163(52)
Introductory Remarks
163(1)
Some Exact Methods
164(22)
Separation of Variables
166(4)
The Bernoulli Equation
170(2)
The Riccati Equation
172(3)
Equations of the Structure d2y/dx2 = f(y)
175(11)
Some Approximate Methods
186(17)
Maple Generated Taylor Series Solution
187(1)
The Perturbation Approach: Poisson's Method
188(7)
Lindstedt's Method
195(8)
The Krylov--Bogoliubov (KB) Method
203(5)
Ritz and Galerkin Methods
208(7)
The Numerical Approach
215(40)
Finite-Difference Approximations
216(2)
Euler and Modified Euler Methods
218(11)
Euler Method
219(4)
The Modified Euler Method
223(6)
Runge-Kutta (RK) Methods
229(8)
The Basic Approach
229(3)
Examples of Common RK Algorithms
232(5)
Adaptive Step Size
237(7)
A Simple Example
237(3)
The Step Doubling Approach
240(1)
The RKF 45 Algorithm
241(3)
Stiff Equations
244(4)
Implicit and Semi-Implicit Schemes
248(7)
Limit Cycles
255(28)
Stability Aspects
255(8)
Relaxation Oscillations
263(4)
Bendixson's First Theorem
267(3)
Bendixson's Negative Criterion
267(1)
Proof of Theorem
267(2)
Applications
269(1)
The Poincare--Bendixson Theorem
270(4)
Poincare--Bendixson Theorem
271(1)
Application of the Theorem
271(3)
The Brusselator Model
274(6)
Prigogine--Lefever (Brusselator) Model
274(1)
Application of the Poincare--Bendixson Theorem
275(5)
3-Dimensional Limit Cycles
280(3)
Forced Oscillators
283(60)
Duffing's Equation
283(11)
The Harmonic Solution
286(2)
The Nonlinear Response Curves
288(6)
The Jump Phenomenon and Hysteresis
294(3)
Subharmonic & Other Periodic Oscillations
297(8)
Power Spectrum
305(7)
Chaotic Oscillations
312(12)
Entrainment and Quasiperiodicity
324(4)
Entrainment
324(2)
Quasiperiodicity
326(2)
The Rossler and Lorenz Systems
328(3)
The Rxsossler Attractor
328(2)
The Lorenz Attractor
330(1)
Hamiltonian Chaos
331(12)
Hamiltonian Formulation of Classical Mechanics
331(2)
The Henon-Heiles Hamiltonian
333(10)
Nonlinear Maps
343(58)
Introductory Remarks
343(1)
The Logistic Map
344(7)
Introduction
344(2)
Geometrical Representation
346(5)
Fixed Points and Stability
351(3)
The Period-Doubling Cascade to Chaos
354(3)
Period Doubling in the Real World
357(3)
The Lyapunov Exponent
360(3)
Stretching and Folding
363(3)
The Circle Map
366(5)
Chaos versus Noise
371(5)
2-Dimensional Maps
376(6)
Introductory Remarks
376(2)
Classification of Fixed Points
378(1)
Delayed Logistic Map
379(1)
Mandelbrot Map
380(2)
Mandelbrot and Julia Sets
382(2)
Nonconservative versus Conservative Maps
384(2)
Controlling Chaos
386(5)
3-Dimensional Maps: Saturn's Rings
391(10)
Nonlinear PDE Phenomena
401(36)
Introductory Remarks
401(1)
Burgers' Equation
402(8)
Backlund Transformations
410(6)
The Basic Idea
410(1)
Examples
410(3)
Nonlinear Superposition
413(3)
Solitary Waves
416(21)
The Basic Approach
416(1)
Phase Plane Analysis
417(4)
KdV Equation
421(7)
Sine-Gordon Equation
428(2)
The Three-Wave Problem
430(7)
Numerical Simulation
437(36)
Finite Difference Approximations
437(5)
Explicit Methods
442(16)
Diffusion Equation
442(9)
Fisher's Nonlinear Diffusion Equation
451(1)
Klein--Gordon Equation
452(3)
KdV Solitary Wave Collisions
455(3)
Von Neumann Stability Analysis
458(3)
Linear Diffusion Equation
458(1)
Burgers' Equation
459(2)
Implicit Methods
461(3)
Method of Characteristics
464(7)
Colliding Laser Beams
464(3)
General Equation
467(2)
Sine-Gordon Equation
469(2)
Higher Dimensions
471(2)
Inverse Scattering Method
473(20)
Lax's Formulation
474(2)
Application to KdV Equation
476(6)
Direct Problem
476(3)
Time Evolution of the Scattering Data
479(2)
The Inverse Problem
481(1)
Multi-Soliton Solutions
482(3)
General Input Shapes
485(2)
The Zakharov--Shabat/AKNS Approach
487(6)
II EXPERIMENTAL ACTIVITIES 493(134)
Introduction to Nonlinear Experiments
495(132)
1 Spin Toy Pendulum
499(4)
2 Driven Eardrum
503(4)
3 Nonlinear Damping
507(4)
4 Anharmonic Potential
511(6)
5 Iron Core Inductor
517(4)
6 Nonlinear LRC Circuit
521(6)
7 Tunnel Diode Negative Resistance Curve
527(6)
8 Tunnel Diode Self-Excited Oscillator
533(4)
9 Forced Duffing Equation
537(6)
10 Focal Point Instability
543(6)
11 Compound Pendulum
549(2)
12 Stable Limit Cycle
551(8)
13 Van der Pol Limit Cycle
559(4)
14 Relaxation Oscillations: Neon Bulb
563(6)
15 Relaxation Oscillations: Drinking Bird
569(4)
16 Relaxation Oscillations: Tunnel Diode
573(4)
17 Hard Spring
577(4)
18 Nonlinear Resonance Curve: Mechanical
581(4)
19 Nonlinear Resonance Curve: Electrical
585(4)
20 Nonlinear Resonance Curve: Magnetic
589(4)
21 Subharmonic Response: Period Doubling
593(2)
22 Diode: Period Doubling
595(4)
23 Five-Well Magnetic Potential
599(6)
24 Power Spectrum
605(4)
25 Entrainment and Quasiperiodicity
609(2)
26 Quasiperiodicity
611(2)
27 Chua's Butterfly
613(4)
28 Route to Chaos
617(4)
29 Driven Spin Toy
621(2)
30 Mapping
623(4)
Bibliography 627(14)
Index 641

Supplemental Materials

What is included with this book?

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