图书介绍

NUMERICAL METHODS AN INTRODUCTION WITH APPLICATIONS USING MATLAB SECOND EDITION SI VERSIONPDF|Epub|txt|kindle电子书版本网盘下载

AMOS GILAT VISH SUBRAMANIAM 著
出版社： COPYRIGHT
ISBN：0470873748
出版时间：2011
标注页数：460页
文件大小：69MB
文件页数：477页
主题词：

PDF下载

点此进入-本书在线PDF格式电子书下载【推荐-云解压-方便快捷】直接下载PDF格式图书。移动端-PC端通用
种子下载[BT下载速度快]温馨提示：（请使用BT下载软件FDM进行下载）软件下载地址页直链下载[便捷但速度慢] [在线试读本书] [在线获取解压码]

点击复制MD5值：e2b171ad306f70cbcbf75c85582d1516

下载说明

NUMERICAL METHODS AN INTRODUCTION WITH APPLICATIONS USING MATLAB SECOND EDITION SI VERSIONPDF格式电子书版下载

下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。

点击复制85GB完整离线版磁力链接到迅雷FDM等BT下载工具进行下载详情点击-查看共享计划

建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！

（文件页数要大于标注页数，上中下等多册电子书除外）

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

图书目录

Chapter 1 Introduction1

1.1 Background1

1.2 Representation of Numbers on a Computer4

1.3 Errors in Numerical Solutions10

1.3.1 Round-Off Errors10

1.3.2 Truncation Errors13

1.3.3 Total Error14

1.4 Computers and Programming15

1.5 Problems18

Chapter 2 Solving Nonlinear Equations23

2.1 Background23

2.2 Estimation of Errors in Numerical Solutions25

2.3 Bisection Method27

2.4 Regula Falsi Method30

2.5 Newton’s Method32

2.6 Secant Method37

2.7 Fixed-Point Iteration Method40

2.8 Use of MATLAB Built-In Functions for Solving Nonlinear Equations43

2.8.1 The fzero Command44

2.8.2 The roots Command45

2.9 Equations with Multiple Solutions45

2.10 Systems of Nonlinear Equations47

2.10.1 Newton s Method for Solving a System of Nonlinear Equations48

2.10.2 Fixed-Point Iteration Method for Solving a System of Nonlinear Equations52

2.11 Problems54

Chapter 3 Solving a System of Linear Equations65

3.1 Background65

3.1.1 Overview of Numerical Methods for Solving a System of Linear Algebraic Equations66

3.2 Gauss Elimination Method68

3.2.1 Potential Difficulties When Applying the Gauss Elimination Method76

3.3 Gauss Elimination with Pivoting78

3.4 Gauss-Jordan Elimination Method81

3.5 LU Decomposition Method84

3.5.1 LU Decomposition Using the Gauss Elimination Procedure86

3.5.2 LU Decomposition Using Crouts Method87

3.5.3 LU Decomposition with Pivoting94

3.6 Inverse of a Matrix94

3.6.1 Calculating the Inverse with the LU Decomposition Method95

3.6.2 Calculating the Inverse Using the Gauss-Jordan Method97

3.7 Iterative Methods98

3.7.1 Jacobi Iterative Method99

3.7.2 Gauss-Seidel Iterative Method99

3.8 Use of MATLAB Built-In Functions for Solving a System of Linear Equations102

3.8.1 Solving a System of Equations Using MATLABs Left and Right Division102

3.8.2 Solving a System of Equations Using MATLABs Inverse Operation103

3.8.3 MATLABs Built-In Function for L U Decomposition104

3.8.4 Additional MATLAB Built-In Functions105

3.9 Tridiagonal Systems of Equations107

3.10 Error，Residual，Norms，and Condition Number112

3.10.1 Error and Residual112

3.10.2 Norms and Condition Number114

3.11 Ill-Conditioned Systems117

3.12 Eigenvalues and Eigenvectors121

3.12.1 The Basic Power Method124

3.12.2 The Inverse Power Method128

3.12.3 The Shifted Power Method129

3.12.4 The QR Factorization and Iteration Method129

3.12.5 Use of MA TLAB Built-In Functions for Determining Eigenvalues and Eigenvectors139

3.13 Problems141

Chapter 4 Curve Fitting and Interpolation153

4.1 Background153

4.2 Curve Fitting with a Linear Equation155

4.2.1 Measuring How Good Is a Fit155

4.2.2 Linear Least-Squares Regression157

4.3 Curve Fitting with Nonlinear Equation by Writing the Equation in a Linear Form161

4.4 Curve Fitting with Quadratic and Higher-Order Polynomials165

4.5 Interpolation Using a Single Polynomial170

4.5.1 Lagrange Interpolating Polynomials172

4.5.2 Newton’s Interpolating Polynomials176

4.6 Piecewise （Spline） Interpolation183

4.6.1 Linear Splines183

4.6.2 Quadratic Splines185

4.6.3 Cubic Splines189

4.7 Use of MATLAB Built-In Functions for Curve Fitting and Interpolation196

4.8 Curve Fitting with a Linear Combination of Nonlinear Functions198

4.9 Problems201

Chapter 5 Numerical Differentiation211

5.1 Background211

5.2 Finite Difference Approximation of the Derivative213

5.3 Finite Difference Formulas Using Taylor Series Expansion218

5.3.1 Finite Difference Formulas of First Derivative218

5.3.2 Finite Difference Formulas for the Second Derivative223

5.4 Summary of Finite Difference Formulas for Numerical Differentiation225

5.5 Differentiation Formulas Using Lagrange Polynomials227

5.6 Differentiation Using Curve Fitting228

5.7 Use of MATLAB Built-In Functions for Numerical Differentiation228

5.8 Richardson’s Extrapolation230

5.9 Error in Numerical Differentiation233

5.10 Numerical Partial Differentiation235

5.11 Problems238

Chapter 6 Numerical Integration249

6.1 Background249

6.1.1 Overview ofApproaches in Numerical Integration250

6.2 Rectangle and Midpoint Methods252

6.3 Trapezoidal Method254

6.3.1 Composite Trapezoidal Method255

6.4 Simpson’s Methods258

6.4.1 Simpson s 1/3 Method258

6.4.2 Simpson s 3/8 Method261

6.5 Gauss Quadrature263

6.6 Evaluation of Multiple Integrals269

6.7 Use of MATLAB Built-In Functions for Integration270

6.8 Estimation of Error in Numerical Integration272

6.9 Richardson’s Extrapolation274

6.10 Romberg Integration277

6.11 Improper Integrals280

6.11.1 Integrals with Singularities280

6.11.2 Integrals with Unbounded Limits281

6.12 Problems282

Chapter 7 Ordinary Differential Equations：Initial-Value Problems293

7.1 Background293

7.2 Euler’s Methods298

7.2.1 Euler’s Explicit Method298

7.2.2 Analysis of Truncation Error in Euler’s Explicit Method302

7.2.3 Euler’s Implicit Method306

7.3 Modified Euler’s Method309

7.4 Midpoint Method312

7.5 Runge-Kutta Methods313

7.5.1 Second-Order Runge-Kutta Methods314

7.5.2 Third-Order Runge Kutta Methods318

7.5.3 Fourth-Order Runge-Kutta Methods319

7.6 Multistep Methods325

7.6.1 Adams-Bashforth Method326

7.6.2 Adams-Moulton Method327

7.7 Predictor-Corrector Methods328

7.8 System of First-Order Ordinary Differential Equations330

7.8.1 Solving a System of First-Order ODEs Using Euler’s Explicit Method332

7.8.2 Solving a System ofFirst-Order ODEs Using Second-Order Runge-Kutta Method （Modified Euler Version）332

7.8.3 Solving a System of First-Order ODEs Using the Classical Fourth-Order Runge-Kutta Method339

7.9 Solving a Higher-Order Initial Value Problem340

7.10 Use of MATLAB Built-In Functions for Solving Initial-Value Problems345

7.10.1 Solving a Single First-Order ODE Using MA TLAB346

7.10.2 Solving a System of First-Order ODEs Using MATLAB352

7.11 Local Truncation Error in Second-Order Range-Kutta Method355

7.12 Step Size For Desired Accuracy356

7.13 Stability360

7.14 Stiff Ordinary Differential Equations362

7.15 Problems365

Chapter 8 Ordinary Differential Equations：Boundary-Value Problems377

8.1 Background377

8.2 The Shooting Method380

8.3 Finite Difference Method388

8.4 Use of MATLAB Built-In Functions for Solving Boundary Value Problems398

8.5 Error and Stability in Numerical Solution of Boundary Value Problems403

8.6 Problems405

Appendix A Introductory MATLAB415

A.1 Background415

A.2 Starting with MATLAB415

A.3 Arrays420

A.4 Mathematical Operations with Arrays425

A.5 Script Files430

A.6 Plotting432

A.7 User-Defined Functions and Function Files434

A.8 Anonymous Functions436

A.9 Function functions438

A.10 Subfunctions441

A.11 Programming in MATLAB443

A.11.1 Relational and Logical Operators443

A.11.2 Conditional Statements，if-else Structures444

A.11.3 Loops447

A.12 Problems448

Appendix B MATLAB Programs453

Index457