Nonlinear Physics With Maple for Scientists and Engineers

, by Enns, Richard H.; McGuire, George C.

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780817641191 | 081764119X
Cover: Hardcover
Copyright: 12/1/1999

Rent

(Recommended)

$61.64

Term

Due

Price

Semester

Dec 13

$64.88

Quarter

Aug 16

$61.64

Short Term

Jul 5

$58.39

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping cart.
Buy New

Special Order: 1-2 Weeks

$88.64
eBook

Available Instantly

Online: 180 Days

Downloadable: 180 Days

$40.22

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.

Preface

I THEORY

(492)

Introduction

(32)

It's a Nonlinear World

(3)

Symbolic Computation

(25)

Examples of Maple Operations

(15)

Getting Maple Help

(1)

Use of Maple in Studying Nonlinear Physics

(8)

Nonlinear Experimental Activities

(1)

Scope of Part I (Theory)

(3)

Nonlinear Systems. Part I

(42)

Nonlinear Mechanics

(15)

The Simple Pendulum

(7)

The Eardrum

(2)

Nonlinear Damping

(3)

Nonlinear Lattice Dynamics

(3)

Competition Phenomena

(14)

Volterra--Lotka Competition Equations

(5)

Population Dynamics of Fox Rabies in Europe

(2)

Selection and Evolution of Biological Molecules

(3)

Laser Beam Competition Equations

(2)

Rapoport's Model for the Arms Race

(2)

Nonlinear Electrical Phenomena

(7)

Nonlinear Inductance

(1)

An Electronic Oscillator (the Van der Pol Equation)

(6)

Chemical and Other Oscillators

(6)

Chemical Oscillators

(4)

The Beating Heart

(2)

Nonlinear Systems. Part II

(44)

Pattern Formation

(16)

Chemical Waves

(2)

Snowflakes and Other Fractal Structures

(5)

Rayleigh--Benard Convection

(2)

Cellular Automata and the Game of Life

(7)

Solitons

(15)

Shallow Water Waves (KdV and Other Equations)

(4)

Sine-Gordon Equation

(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

Please wait while the item is added to your bag...

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Nonlinear Physics With Maple for Scientists and Engineers

Summary

Table of Contents

Supplemental Materials