工程中的数值方法第3版PDF电子书下载

CONTENTS 3

PART ONE MODELING,COMPUTERS,AND ERROR ANALYSIS 3

PT 1.1 Motivation 3

PT 1.2 Mathematical Background 5

PT 1.3 Orientation 8

CHAPTER 1 Mathematical Modeling and Engineering Problem-Solving 11

1.1 A Simple Mathematical Model 11

1.2 Conservation Laws and Engineering 18

Problems 21

CHAPTER 2 Computers and Software 24

2.1 Computing Environments 25

2.2 The Software Development Process 26

2.3 Algorithm Design 30

2.4 Program Composition 40

2.5 Quality Control 43

2.6 Documentation and Maintenance 47

2.7 Software Strategy 48

Problems 53

CHAPTER 3 Approximations and Round-Off Errors 56

3.1 Significant Figures 57

3.2 Accuracy and Precision 59

3.3 Error Definitions 60

3.4 Round-Off Errors 63

Problems 78

CHAPTER 4 Truncation Errors and the Taylor Series 79

4.1 The Taylor Series 79

4.2 Error Propagation 95

4.3 Total Numerical Error 99

4.4 Blunders,Formulation Errors,and Data Uncertainty 101

Problems 103

EpILOGUE:PART ONE 105

PT 1.4 Trade-Offs 105

PT 1.6 Advanced Methods and Additional References 108

PT 1.5 Important Relationships and Formulas 108

PART TWO ROOTS OF EQUATIONS 111

PT 2.1 Motivation 111

PT 2.2 Mathematical Background 113

PT 2.3 Orientation 114

CHAPTER 5 Bracketing Methods 118

5.1 Graphical Methods 118

5.2 The Bisection Method 122

5.3 The False-Position Method 132

5.4 Incremental Searches and Determining Initial Guesses 137

Problems 138

CHAPTER 6 Open Methods 141

6.1 Simple Fixed-Point Iteration 142

6.2 The Newton-Raphson Method 147

6.3 The Secant Method 153

6.4 Multiple Roots 158

6.5 Systems of Nonlinear Equations 161

Problems 165

CHAPTER 7 Roots of Polynomials 167

7.1 Polynomials in Engineering and Science 167

7.2 Computing with Polynomials 170

7.3 Conventional Methods 173

7.4 Müeller's Method 174

7.5 Bairstow's Method 178

7.6 Other Methods 183

7.7 Root Location with Libraries and Packages 183

Problems 193

CHAPTER 8 Engineering Applications:Roots of Equations 194

8.1 Ideal and Nonideal Gas Laws(Chemicol/Petroleum Engineering) 194

8.2 Open-Channel Flow(Civil/Environmental Engineering) 197

8.3 Design of an Electric Circuit(Electrical Engineering) 201

8.4 Vibration Analysis(Mechanical/Aerospace Engineering) 203

Problems 210

PT 2.4 Trade-Offs 215

EPILOGUE:PART TWO 215

PT 2.5 Important Relationships and Formulas 216

PT 2.6 Advanced Methods and Additional References 216

PART THREE LINEAR ALGEBRAIC EQUATIONS 219

PT 3.1 Motivation 219

PT 3.2 Mathematical Background 221

PT 3.3 Orientation 229

CHAPTER 9 Gauss Elimination 233

9.1 Solving Small Numbers of Equations 233

9.2 Naive Gauss Elimination 240

9.3 Pitfalls of Elimination Methods 246

9.4 Techniques for Improving Solutions 252

9.5 Complex Systems 259

9.6 Nonlinear Systems of Equations 259

9.7 Gauss-Jordan 261

Problems 263

9.8 Summary 263

CHAPTER 10 LU Decomposition and Matrix Inversion 266

10.1 LU Decomposition 266

10.2 The Matrix Inverse 275

10.3 Error Analysis and System Condition 279

Problems 287

CHAPTER 11 Special Matrices and Gauss-Seidel 288

11.1 Special Matrices 288

11.2 Gauss-Seidel 292

11.3 Linear Algebraic Equations with Libraries and Packages 299

Problems 307

CHAPTER 12 Engineering Applications:Linear Algebraic Equations 309

12.1 Steady-State Analysis of a System of Reactors (Chemical/Petroleum Engineering) 309

12.2 Analysis of a Statically Determinate Truss(Civil/Environmental Engineering) 312

12.3 Currents and Voltages in Resistor Circuits(Electrical Engineering) 316

12.4 Spring-Mass Systems (Mechanical/Aerospace Engineering) 318

Problems 321

PT 3.4 Trade-Offs 327

EPlLOGUE:PART THREE 327

PT 3.5 Important Relationships and Formulas 328

PT 3.6 Advanced Methods and Additional References 328

PART FOUR OPTIMIZATION 331

PT 4.1 Motivation 331

PT 4.2 Mathematical Background 336

PT 4.3 Orientation 337

CHAPTER 13 One-dimensional Unconstrained Optimization 341

13.1 Golden-Section Search 342

13.2 Quadratic Interpolation 349

13.3 Newton's Method 351

Problems 353

CHAPTER 14 Multidimensional Unconstrained Optimization 355

14.1 Direct Methods 356

14.2 Gradient Methods 360

Problems 373

15.1 Linear Programming 375

CHAPTER 15 Constrained Optimization 375

15.2 Nonlinear Constrained Optimization 386

15.3 Optimization with Packages 387

Problems 397

CHAPTER 16 Engineering Applications:Optimization 399

16.1 Least-Cost Design of a Tank(Chemical/Petroleum Engineering) 399

16.2 Least-Cost Treatment of Wastewater(Civil/Environmental Engineering) 403

16.3 Maximum Power Transfer for a Circuit(Electrical Engineering) 408

16.4 Mountain Bike Design (Mechanical/Aerospace Engineering) 412

Problems 414

EPILOGUE:PART FOUR 420

PT 4.4 Trade-Offs 420

PT 4.5 Additional References 421

PART FIVE CURVE FITTING 423

PT 5.1 Motivation 423

PT 5.2 Mathematical Background 425

PT 5.3 Orientation 434

17.1 Linear Regression 438

CHAPTER 17 Least-Squares Regression 438

17.2 Polynomial Regression 454

17.3 Multiple Linear Regression 460

17.4 General Linear Least-Squares 463

17.5 Nonlinear Regression 468

Problems 471

CHAPTER 18 Interpolation 473

18.1 Newton's Divided-Difference Interpolating Polynomials 474

18.2 Logrange Interpolating Polynomials 485

18.3 Coefficients of an Interpolating Polynomial 490

18.4 Inverse Interpolation 490

18.5 Additional Comments 491

18.6 Spline Interpolation 494

Problems 505

CHAPTER 19 Fourier Approximation 507

19.1 Curve Fitting with Sinusoidal Functions 508

19.2 Continuous Fourier Series 514

19.3 Frequency and Time Domains 517

19.4 Fourier Integral and Transform 521

19.5 Discrete Fourier Transform (DFT) 523

19.6 Fast Fourier Transform (FFT) 525

19.7 The Power Spectrum 532

19.8 Curve Fitting with Libraries and Packages 533

Problems 544

CHAPTER 20 Engineering Applications:Curve Fitting 546

20.1 Linear Regression and Population Models(Chemical/Petroleum Engineering) 546

20.2 Use of Splines to Estimate Heat Transfer (Civil/Environmental Engineering) 550

20.3 Fourier Analysis(Electrical Engineering) 552

20.4 Analysis of Experimental Data(Mechonical/Aerospace Engineering) 553

Problems 555

EPILOGUE:PART FIVE 561

PT 5.4 Trade-Offs 561

PT 5.5 Important Relationships and Formulas 562

PT 5.6 Advanced Methods and Additional References 564

PT 6.1 Motivation 567

PART SIX NUMERICAL DIFFERENTIATION AND INTEGRATION 567

PT 6.2 Mathematical Background 576

PT 6.3 Orientation 579

CHAPTER 21 Newton-Cotes Integration of Equations 582

21.1 The Trapezoidal Rule 584

21.2 Simpson's Rules 595

21.3 Integration with Unequal Segments 604

21.4 Open Integration Formulas 607

Problems 607

CHAPTER 22 Integration of Equations 610

22.1 Newton-Cotes Algorithms for Equations 610

22.2 Romberg Integration 612

22.3 Gauss Quadrature 617

22.4 Improper Integrals 624

Problems 628

23.1 High-Accuracy Differentiation Formulas 629

CHAPTER 23 Numerical Differentiation 629

23.2 Richardson Extrapolation 632

23.3 Derivatives of Unequally Spaced Data 634

23.4 Derivatives and Integrals for Data with Errors 635

23.5 Numerical Integration/Differentiation Formulas with Libraries and Packages 636

Problems 641

CHAPTER 24 Engineering Applications:Numerical Integration and Differentiation 643

24.1 Integration to Determine the Total Quantity of Heat (Chemical/Petroleum Engineering) 643

24.2 Effective Force on the Mast of a Racing Sailboat (Civil/Environmental Engineering) 645

24.3 Root-Mean-Square Current by Numerical Integration(Electrical Engineering) 647

24.4 Numerical Integration to Compute Work (Mechanical/Aerospace Engineering) 650

Problems 654

EPILOGUE:PART SIX 661

PT 6.4 Trade-Offs 661

PT 6.5 Important Relationships and Formulas 662

PT 6.6 Advanced Methods and Additional References 662

PT 7.1 Motivation 665

PART SEVEN ORDINARY DIFFERENTIAL EQUATIONS 665

PT 7.2 Mathematical Background 669

PT 7.3 Orientation 671

CHAPTER 25 Runge-Kutta Methods 675

25.1 Euler's Method 676

25.2 Improvements of Euler's Method 687

25.3 Runge-Kutta Method 695

25.4 Systems of Equations 705

25.5 Adaptive Runge-Kutta Method 710

Problems 718

CHAPTER 26 Stiffness and Multistep Methods 719

26.1 Stiffness 719

26.2 Multistep Methods 723

Problems 743

CHAPTER 27 Boundary-Value and Eigenvalue Problems 745

27.1 General Methods of Boundary-Value Problems 746

27.2 Eigenvalue Problems 752

27.3 ODEs and Eigenvalues with Libraries and Packages 768

Problems 775

CHAPTER 28 Engineering Applications:Ordinary Differential Equations 　 777

28.1 Using ODEs to Analyze the Transient Response of a Reactor(Chemical/Petroleum Engineering) 777

28.2 Predator-Prey Models and Chaos(Civil/Environmental Engineering) 784

28.3 Simulating Transient Current for an Electronic Circuit(Electrical Engineering) 788

28.4 The Swinging Pendulum(Mechanicol/Aerospace Engineering) 793

Problems 796

EPILOGUE:PART SEVEN 800

PT 7.4 Trade-Offs 800

PT 7.5 Important Relationships and Formulas 801

PT 7.6 Advanced Methods and Additional References 801

PART EIGHT PARTIAL DIFFERENTIAL EQUATIONS 805

PT 8.1 Motivation 805

PT 8.2 Orientation 808

29.1 The Laplace Equation 812

CHAPTER 29 Finite Difference:Elliptic Equations 812

29.2 Solution Techniques 814

29.3 Boundary Conditions 820

29.4 The Control Volume Approach 826

29.5 Software to Solve Elliptic Equations 829

Problems 830

CHAPTER 30 Finite Difference:Parabolic Equations 832

30.1 The Heat Conduction Equation 832

30.2 Explicit Methods 833

30.3 A Simple Implicit Method 837

30.4 The Crank-Nicholson Method 841

30.5 Parabolic Equations in Two Spatial Dimenstons 844

Problems 848

CHAPTER 31 Finite Element Method 849

31.1 The General Approach 850

31.2 Finite-Element Application in One Dimension 854

31.3 Two-Dimensional Problems 863

31.4 PDEs with Libraries and Packages 867

Problems 874

CHAPTER 32 Engineering Applications:Partial Differential Equations 876

32.1 One-Dimensional Mass Balance of a Reactor (Chemical/Petroleum Engineering) 876

32.2 Deflections of a Plate(Civil/Environmental Engineering) 880

32.3 Two-Dimensional Electrostatic Field Problems(Electrical Engineering) 882

32.4 Finite-Element Solution of a Series of Springs(Mechanical/Aerospace Engineering) 885

Problems 889

PT 8.4 Important Relationships and Formulas 891

EPILOGUE:PART EIGHT 891

PT 8.3 Trade-Offs 891

PT 8.5 Advanced Methods and Additional References 892

APPENDIX A:THE FOURIER SERIES 893

APPENDIX B:GETTING STARTED WITH MATHCAD 895

APPENDIX C:GETTING STARTED WITH MATLAB 905

BIBLIOGRAPHY 913

INDEX 916