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Applied Numerical Methods with MATLAB for Engineers and Scientists
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【核心代码】
CONTENTS About the Author iv Preface xiv Part One Modeling, Computers, and Error Analysis 1 1.1 Motivation 1 1.2 Part Organization 2 CHAPTER 1 Mathematical Modeling, Numerical Methods, and Problem Solving 4 1.1 A Simple Mathematical Model 5 1.2 Conservation Laws in Engineering and Science 12 1.3 Numerical Methods Covered in This Book 13 1.4 Case Study: It’s a Real Drag 17 Problems 20 CHAPTER 2 MATLAB Fundamentals 27 2.1 The MATLAB Environment 28 2.2 Assignment 29 2.3 Mathematical Operations 36 2.4 Use of Built-In Functions 39 2.5 Graphics 42 2.6 Other Resources 46 2.7 Case Study: Exploratory Data Analysis 46 Problems 49 CHAPTER 3 Programming with MATLAB 53 3.1 M-Files 54 3.2 Input-Output 61 cha97962_fm_i-xvi.indd 5 07/11/16 8:25 pm vi CONTENTS 3.3 Structured Programming 65 3.4 Nesting and Indentation 79 3.5 Passing Functions to M-Files 81 3.6 Case Study: Bungee Jumper Velocity 87 Problems 91 CHAPTER 4 Roundoff and Truncation Errors 99 4.1 Errors 100 4.2 Roundoff Errors 106 4.3 Truncation Errors 114 4.4 Total Numerical Error 125 4.5 Blunders, Model Errors, and Data Uncertainty 130 Problems 131 Part Two Roots and Optimization 135 2.1 Overview 135 2.2 Part Organization 136 CHAPTER 5 Roots: Bracketing Methods 138 5.1 Roots in Engineering and Science 139 5.2 Graphical Methods 140 5.3 Bracketing Methods and Initial Guesses 141 5.4 Bisection 146 5.5 False Position 152 5.6 Case Study: Greenhouse Gases and Rainwater 156 Problems 159 CHAPTER 6 Roots: Open Methods 164 6.1 Simple Fixed-Point Iteration 165 6.2 Newton-Raphson 169 6.3 Secant Methods 174 6.4 Brent’s Method 176 6.5 MATLAB Function: fzero 181 6.6 Polynomials 183 6.7 Case Study: Pipe Friction 186 Problems 191 cha97962_fm_i-xvi.indd 6 07/11/16 8:25 pm CONTENTS vii CHAPTER 7 Optimization 198 7.1 Introduction and Background 199 7.2 One-Dimensional Optimization 202 7.3 Multidimensional Optimization 211 7.4 Case Study: Equilibrium and Minimum Potential Energy 213 Problems 215 Part Three Linear Systems 223 3.1 Overview 223 3.2 Part Organization 225 CHAPTER 8 Linear Algebraic Equations and Matrices 227 8.1 Matrix Algebra Overview 229 8.2 Solving Linear Algebraic Equations with MATLAB 238 8.3 Case Study: Currents and Voltages in Circuits 240 Problems 244 CHAPTER 9 Gauss Elimination 248 9.1 Solving Small Numbers of Equations 249 9.2 Naive Gauss Elimination 254 9.3 Pivoting 261 9.4 Tridiagonal Systems 264 9.5 Case Study: Model of a Heated Rod 266 Problems 270 CHAPTER 10 LU Factorization 274 10.1 Overview of LU Factorization 275 10.2 Gauss Elimination as LU Factorization 276 10.3 Cholesky Factorization 283 10.4 MATLAB Left Division 286 Problems 287 cha97962_fm_i-xvi.indd 7 07/11/16 8:25 pm viii CONTENTS CHAPTER 11 Matrix Inverse and Condition 288 11.1 The Matrix Inverse 288 11.2 Error Analysis and System Condition 292 11.3 Case Study: Indoor Air Pollution 297 Problems 300 CHAPTER 12 Iterative Methods 305 12.1 Linear Systems: Gauss-Seidel 305 12.2 Nonlinear Systems 312 12.3 Case Study: Chemical Reactions 320 Problems 323 CHAPTER 13 Eigenvalues 326 13.1 Mathematical Background 328 13.2 Physical Background 331 13.3 The Power Method 333 13.4 MATLAB Function: eig 336 13.5 Case Study: Eigenvalues and Earthquakes 337 Problems 340 Part Four Curve Fitting 343 4.1 Overview 343 4.2 Part Organization 345 CHAPTER 14 Linear Regression 346 14.1 Statistics Review 348 14.2 Random Numbers and Simulation 353 14.3 Linear Least-Squares Regression 358 14.4 Linearization of Nonlinear Relationships 366 14.5 Computer Applications 370 14.6 Case Study: Enzyme Kinetics 373 Problems 378 cha97962_fm_i-xvi.indd 8 07/11/16 8:25 pm CONTENTS ix CHAPTER 15 General Linear Least-Squares and Nonlinear Regression 385 15.1 Polynomial Regression 385 15.2 Multiple Linear Regression 389 15.3 General Linear Least Squares 391 15.4 QR Factorization and the Backslash Operator 394 15.5 Nonlinear Regression 395 15.6 Case Study: Fitting Experimental Data 397 Problems 399 CHAPTER 16 Fourier Analysis 404 16.1 Curve Fitting with Sinusoidal Functions 405 16.2 Continuous Fourier Series 411 16.3 Frequency and Time Domains 414 16.4 Fourier Integral and Transform 415 16.5 Discrete Fourier Transform (DFT) 418 16.6 The Power Spectrum 423 16.7 Case Study: Sunspots 425 Problems 426 CHAPTER 17 Polynomial Interpolation 429 17.1 Introduction to Interpolation 430 17.2 Newton Interpolating Polynomial 433 17.3 Lagrange Interpolating Polynomial 441 17.4 Inverse Interpolation 444 17.5 Extrapolation and Oscillations 445 Problems 449 CHAPTER 18 Splines and Piecewise Interpolation 453 18.1 Introduction to Splines 453 18.2 Linear Splines 455 18.3 Quadratic Splines 459 18.4 Cubic Splines 462 18.5 Piecewise Interpolation in MATLAB 468 18.6 Multidimensional Interpolation 473 18.7 Case Study: Heat Transfer 476 Problems 480 cha97962_fm_i-xvi.indd 9 07/11/16 8:25 pm x CONTENTS Part Five Integration and Differentiation 485 5.1 Overview 485 5.2 Part Organization 486 CHAPTER 19 Numerical Integration Formulas 488 19.1 Introduction and Background 489 19.2 Newton-Cotes Formulas 492 19.3 The Trapezoidal Rule 494 19.4 Simpson’s Rules 501 19.5 Higher-Order Newton-Cotes Formulas 507 19.6 Integration with Unequal Segments 508 19.7 Open Methods 512 19.8 Multiple Integrals 512 19.9 Case Study: Computing Work with Numerical Integration 515 Problems 518 CHAPTER 20 Numerical Integration of Functions 524 20.1 Introduction 524 20.2 Romberg Integration 525 20.3 Gauss Quadrature 530 20.4 Adaptive Quadrature 537 20.5 Case Study: Root-Mean-Square Current 540 Problems 544 CHAPTER 21 Numerical Differentiation 548 21.1 Introduction and Background 549 21.2 High-Accuracy Differentiation Formulas 552 21.3 Richardson Extrapolation 555 21.4 Derivatives of Unequally Spaced Data 557 21.5 Derivatives and Integrals for Data with Errors 558 21.6 Partial Derivatives 559 21.7 Numerical Differentiation with MATLAB 560 21.8 Case Study: Visualizing Fields 565 Problems 567 cha97962_fm_i-xvi.indd 10 07/11/16 8:25 pm CONTENTS xi Part six Ordinary Differential Equations 573 6.1 Overview 573 6.2 Part Organization 577 CHAPTER 22 Initial-Value Problems 579 22.1 Overview 581 22.2 Euler’s Method 581 22.3 Improvements of Euler’s Method 587 22.4 Runge-Kutta Methods 593 22.5 Systems of Equations 598 22.6 Case Study: Predator-Prey Models and Chaos 604 Problems 609 CHAPTER 23 Adaptive Methods and Stiff Systems 615 23.1 Adaptive Runge-Kutta Methods 615 23.2 Multistep Methods 624 23.3 Stiffness 628 23.4 MATLAB Application: Bungee Jumper with Cord 634 23.5 Case Study: Pliny’s Intermittent Fountain 635 Problems 640 CHAPTER 24 Boundary-Value Problems 646 24.1 Introduction and Background 647 24.2 The Shooting Method 651 24.3 Finite-Difference Methods 658 24.4 MATLAB Function: bvp4c 665 Problems 668 APPENDIX A: MATLAB BUILT-IN FUNCTIONS 674 APPENDIX B: MATLAB M-FILE FUNCTIONS 676 APPENDIX C: INTRODUCTION TO SIMULINK 677 BIBLIOGRAPHY 685 INDEX 687
Applied Numerical Methods with MATLAB for Engineers and Scientists.pdf
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