应用数值方法 使用MATLAB和C语言PDF|Epub|txt|kindle电子书版本网盘下载

应用数值方法 使用MATLAB和C语言PDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

CHAPTER 1 Numerical Computation1

1.1 Motivation and Objectives1

1.1.1 A Simple Calculation1

1.1.2 Chapter Objectives2

1.1.3 Mathematical Background3

1.2 Number Representation3

1.2.1 Binary,Decimal,and Hexadecimal3

1.2.2 Integers6

1.2.3 Floats7

1.3 Machine Precision8

1.4 Round-Off Error10

1.4.1 Chopping and Rounding10

1.4.2 Error Propagation11

1.5 Truncation Error14

1.6 Random Number Generation15

1.6.1 Uniform Distribution15

1.6.2 Gaussian Distribution19

1.7 Numerical Software22

1.7.1 A Numerical Library:NLIB23

1.7.2 NLIB Example Browser24

1.7.3 Pseudo-Prototypes25

1.8 Applications26

1.8.1 Throwing Darts to Estimate π:MATLAB26

1.8.2 Monte Carlo Integration:C29

1.9 Summary32

Problems34

1.10.1 Analysis34

1.10.2 Computation35

CHAPTER 2 Linear Algebraic Systems37

2.1 Motivation and Objectives37

2.1.1 Robotic Arm38

2.1.2 Converter Circuit38

2.1.3 DC Motor39

2.1.4 Chapter Objectives40

2.2 Gauss-Jordan Elimination41

2.3 Gaussian Elimination50

2.4 LU Decomposition54

2.5.1 LU Factorization55

2.5.2 Forward and Back Substitution59

2.5.3 Tridiagonal Systems62

2.5 Ill-Conditioned Systems64

2.5.1 Vector and Matrix Norms64

2.5.2 Condition Number66

2.5.3 Approximate Condition Number68

2.5.4 Iterative Improvement69

2.6 Iterative Methods70

2.6.1 Jacobi's Method71

2.6.2 Gauss-Seidel Method73

2.6.3 Relaxation Methods74

2.6.4 Convergence77

2.7 Applications79

2.7.1 Chemical Absorption Process:MATLAB79

2.7.2 Planar Truss:C82

2.7.3 DC Bridge Circuit:MATLAB84

2.7.4 Mass-Spring-Damper System:C86

2.8 Summary89

Problems91

2.9.1 Analysis91

2.9.2 Computation93

CHAPTER 3 Eigenvalues and Eigenvectors96

3.1 Motivation and Objectives97

3.1.1 Seismograph97

3.1.2 Convergence of Iterative Methods99

3.1.3 Chapter Objectives101

3.2 The Characteristic Polynomial102

3.3 Power Methods105

3.3.1 Direct Power Method105

3.3.2 Inverse Power Method109

3.4 Jacobi's Method111

3.5 Householder Transformation113

3.6 QR Method116

3.6.1 Deflation118

3.6.2 Shifting119

3.7 Danilevsky's Method120

3.8 Polynomial Roots124

3.9 Applications126

3.9.1 Transient Analysis of an Absorption Process:C126

3.9.2 Population Growth Model:MATLAB130

3.9.3 Telescope Position Control:C133

3.9.4 Rotating Masses and Torsional Springs:MATLAB136

3.10 Summary140

Problems141

3.11.1 Analysis142

3.11.2 Computation143

CHAPTER 4 Curve Fitting145

4.1 Motivation and Objectives146

4.1.1 Gravitational Acceleration146

4.1.2 Circadian Rhythms147

4.1.3 Chapter Obiectives148

4.2 Interpolating149

4.2.1 Piecewise-Linear Interpolation150

4.2.2 Polynomial Interpolation151

4.2.3 Lagrange Interpolation Polynomials153

4.2.4 Polynomials155

4.3 Newton's Difference Formula156

4.4 Cubic Splines158

4.5 Least Squares165

4.5.1 Straight Line Fit166

4.5.2 Polynomial Fit168

4.5.3 Orthogonal Polynomials168

4.6 Two-Dimensional Interpolation174

4.7 Applications177

4.7.1 Pressure-Temperature Curves:MATLAB177

4.7.2 Water Resource Management:C180

4.7.3 Voltage Regulator Circuit:MATLAB182

4.7.4 Nonlinear Friction Model:C185

4.8 Summary188

Problems189

4.9.1 Analysis190

4.9.2 Computation191

CHAPTER 5 Root Finding193

5.1 Motivation and Objectives194

5.1.1 Tunnel Diode Circuit194

5.1.2 Leaky Tank196

5.1.3 Bacterial Chemostat197

5.1.4 Chapter Objectives198

5.2 Bracketing Methods199

5.2.1 Bisection Method199

5.2.2 False Position Method202

5.3 Contraction Mapping Method205

5.3.1 Root Finding207

5.3.2 Aitken Extrapolation209

5.4 Secant Method210

5.5 Muller's Method212

5.6 Newton's Method216

5.7 Polynomial Roots219

5.7.1 Quadratic Formula219

5.7.2 Synthetic Division221

5.7.3 Laguerre's Method224

5.8 Nonlinear Systems of Equations228

5.9 Applications232

5.9.1 Propane Cylinder:C232

5.9.2 Bacterial Chemostat:MATLAB236

5.9.3 Industrial High-Temperature Oven:C238

5.9.4 Suspension Cable:MATLAB241

5.10 Summary244

Problems246

5.11.1 Analysis246

5.11.2 Computation247

CHAPTER 6 Optimization250

6.1 Motivation and Objectives251

6.1.1 Nonlinear Regression251

6.1.2 Electrical Load Design252

6.1.3 Container Design253

6.1.4 Chapter Objectives254

6.2 Local and Global Minima255

6.3 Line Searches257

6.3.1 Golden Section257

6.3.2 Derivative Bisection262

6.3.3 Inverse Parabolic Interpolation263

6.4 Steepest Descent Method265

6.5 Conjugate-Gradient Method268

6.6 Quasi-Newton Methods270

6.7 Penalty Functions274

6.8 Simulated Annealing278

6.8.1 Annealing Schedules280

6.8.2 Constrained Optimization281

6.9 Applications286

6.9.1 Heat Exchanger:MATLAB286

6.9.2 Transportation Planning:C291

6.9.3 Maximum Power Extraction:MATLAB295

6.9.4 Container Design:C298

6.10 Summary300

Problems302

6.11.1 Analysis302

6.11.2 Computation304

CHAPTER 7 Differentiation and Integration307

7.1 Motivation and Objectives308

7.1.1 Magnetic Levitation308

7.1.2 Mechanical Work309

7.1.3 Water Management310

7.1.4 Chapter Objectives311

7.2 Numerical Differentiation312

7.2.1 First Derivative312

7.2.2 Second Derivative315

7.2.3 Richardson Extrapolation317

7.3 Noise-Corrupted Data319

7.4 Newton-Cotes Integration Formulas321

7.4.1 Trapezoid Rule323

7.4.2 Simpson's Rules324

7.4.3 Midpoint Rule325

7.5 Romberg Integration328

7.6 Gauss Quadrature331

7.6.1 Legendre Polynomials332

7.6.2 Chebyshev Polynomials334

7.6.3 Laguerre Polynomials335

7.6.4 Hermite Polynomials336

7.7 Improper Integrals337

7.8 Multiple Integrals340

7.8.1 Parameterization Method340

7.8.2 Monte Carlo Integration342

7.9 Applications345

7.9.1 Change in Enthalpy:C345

7.9.2 Dam Design:MATLAB347

7.9.3 RC Network:C350

7.9.4 Link of Robotic Arm:MATLAB353

7.10 Summary354

Problems357

7.11.1 Analysis357

7.11.2 Computation358

CHAPTER 8 Ordinary Differential Equations361

8.1 Motivation and Objectives362

8.1.1 Satellite Attitude Control363

8.1.2 Pendulum364

8.1.3 Predator-Prey Ecological System364

8.1.4 Chapter Objectives365

8.2 Euler's Method366

8.3 Runge-Kutta Methods368

8.4 Step Size Control372

8.4.1 Interval Halving373

8.4.2 Runge-Kutta-Fehlberg Method374

8.4.3 Step Size Adjustment375

8.5 MultiStep Methods378

8.5.1 Adams-Bashforth Predictor378

8.5.2 Adams-Moulton Corrector379

8.6 Bulirsch-Stoer Extrapolation Methods382

8.6.1 Modified Midpoint Method382

8.6.2 Richardson Extrapolation383

8.7 Stiff Differential Equations387

8.7.1 Implicit Methods389

8.7.2 Semi-Implicit Extrapolation Method391

8.7.3 Differential-Algebraic Systems394

8.8 Boundary Value Problems395

8.8.1 Shooting Method396

8.8.2 Finite Difference Method398

8.9 Applications401

8.9.1 Chemical Reactor:MATLAB401

8.9.2 Cantilever Beam:C404

8.9.3 Phase-Locked Loop:MATLAB406

8.9.4 Turbulent Flow and Chaos:C410

8.10 Summary413

Problems415

8.11.1 Analysis415

8.11.2 Computation416

CHAPTER 9 Partial Differential Equations422

9.1 Motivation and Obiectives423

9.1.1 Laplace's Equation423

9.1.2 Heat Equation424

9.1.3 Wave Equation425

9.1.4 Equation Classification426

9.1.5 Chapter Objectives427

9.2 Elliptic Equations428

9.2.1 Central Difference Method428

9.2.2 Boundary Conditions431

9.2.3 Iterative Solution Methods432

9.3 One-Dimensional Parabolic Equations437

9.3.1 Explicit Forward Euler Method437

9.3.2 Implicit Backward Euler Method440

9.3.3 Crank-Nicolson Method442

9.4 Two-Dimensional Parabolic Equations444

9.5 One-Dimensional Hyperbolic Equations448

9.5.1 d'Alembert's Solution449

9.5.2 Explicit Central Difference Method452

9.6 Two-Dimensional Hyperbolic Equations455

9.7 Applications459

9.7.1 Heated Rod:C460

9.7.2 Plate Deflection:MATLAB462

9.7.3 Electrostatic Field:C464

9.7.4 Twisted Bar:MATLAB466

9.8 Summary468

Problems469

9.9.1 Analysis469

9.9.2 Computation472

CHAPTER 10 Digital Signal Processing475

10.1 Motivation and Objectives476

10.1.1 Harmonic Distortion476

10.1.2 Radar477

10.1.3 Chapter Objectives477

10.2 Fourier Transform478

10.3 Fast Fourier Transform(FFT)480

10.4 Correlation487

10.5 Convolution490

10.5.1 Pulse Response491

10.5.2 Stability493

10.6 Digital Filters495

10.6.1 Frequency Response495

10.6.2 FIR Filter Design497

10.7 Two-Dimensional FFT502

10.8 System Identification506

10.8.1 Least-Squares Method507

10.8.2 Adaptive LMS Method511

10.9 Applications514

10.9.1 Heat Exchanger Frequency Response:MATLAB514

10.9.2 Flagpole Motion:C516

10.9.3 Band Pass Filter:MATLAB519

10.9.4 Helicopter Noise:C522

10.10 Summary524

Problems526

10.11.1 Analysis526

10.11.2 Computation527

References and Further Reading530

APPENDIX 1 NLIB Using MATLAB533

1.1 A Numerical Toolbox:NLIB534

1.1.1 Toolbox Installation534

1.1.2 NLIB Example Browser535

1.2 Main-Program Support536

1.2.1 Tabular Display536

1.2.2 Graphical Display538

1.2.3 Utility Functions542

1.3 Linear Algebraic Systems544

1.4 Eigenvalues and Eigenvectors548

1.5 Curve Fitting552

1.6 Root Finding555

1.7 Optimization558

1.8 Differentiation and Integration563

1.9 Ordinary Differential Equations567

1.10 Partial Differential Equations571

1.11 Digital Signal Processing578

APPENDIX 2 NLIB Using C584

2.1 A Numerical Library:NLIB585

2.1.1 NLIB Installation585

2.1.2 Library Usage585

2.1.3 NLIB Example Browser587

2.2 NLIB Data Types588

2.2.1 Scalars588

2.2.2 Vectors588

2.2.3 Matrices589

2.2.4 Precision590

2.3 NLIB Core591

2.3.1 Vector and Matrix Allocation591

2.3.2 Vector and Matrix Input/Output594

2.3.3 Matrix Algebra598

2.3.4 Complex Arithmetic600

2.3.5 Random Number Generation602

2.3.6 Utility Functions604

2.4 Tabular Display605

2.4.1 Screen605

2.4.2 Keyboard606

2.4.3 Printer607

2.5 Graphical Display608

2.5.1 Curves609

2.5.2 Surfaces612

2.6 Linear Algebraic Systems614

2.7 Eigenvalues and Eigenvectors619

2.8 Curve Fitting623

2.9 Root Finding626

2.10 Optimization631

2.11 Differentiation and Integration637

2.12 Ordinary Differential Equations641

2.13 Partial Differential Equations646

2.14 Digital Signal Processing653

APPENDIX 3 Vectors and Matrices661

3.1 Vector and Matrix Notation661

3.2 Basic Operations663

3.3 Matrix Inverse665

3.4 Eigenvalues and Eigenvectors666

3.5 Vector Norms668

APPENDIX 4 Answers to Selected Problems669

Index703