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计算物理简明教程=AN INTRODUCTION TO COMPUTATIONAL PHYSICSPDF|Epub|txt|kindle电子书版本网盘下载

张海燕编著著
出版社：上海交通大学出版社
ISBN：9787313066688
出版时间：2010
标注页数：259页
文件大小：101MB
文件页数：40526706页
主题词：计算物理学－教材－英文

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图书目录

1 Approximations，Errors and the Taylor Series1

1.1 Approximations and Errors2

1.1.1 Approximations2

1.1.2 Round-off Errors4

1.1.3 Principles to Hold During the Numerical Calculations5

1.2 Truncation Errors and the Taylor Series7

1.2.1 Truncation Errors7

1.2.2 The Taylor Series8

1.2.3 Some Techniques in Numerical Computation11

1.3 Control of Total Numerical Error12

1.3.1 Truncation Error12

1.3.2 Total Numerical Error13

1.3.3 Control of Numerical Errors14

1.4 Problems for Chapter 115

1.5 Computer Work for Chapter 116

2 Interpolation and Finite Differences18

2.1 Finite Difference20

2.2 Newton Interpolation21

2.2.1 Basis Functions22

2.2.2 Newton Interpolation23

2.2.3 Newton’s Divided-difference Interpolating Polynomial25

2.2.4 Errors of Newton Interpolation28

2.3 Interpolation Formulae30

2.3.1 NGF Interpolation30

2.3.2 NGB Interpolation31

2.3.3 ST Interpolation31

2.4 Difference Quotients32

2.4.1 DNGF Formulae33

2.4.2 DNGB Formulae34

2.4.3 DST Formulae35

2.5 Problems for Chapter 238

2.6 Computer Work for Chapter 239

3 Numerical Integration41

3.1 Numerical Integration Methods41

3.2 Newton-Cotes Quadrature Rules43

3.2.1 The Trapezoid Rule44

3.2.2 Simpson’s Rule45

3.2.3 Error Estimation47

3.3 Composite and Adaptive Quadrature50

3.3.1 Composite Quadrature Rules50

3.3.2 Automatic and Adaptive Quadrature55

3.4 Numerical Integration of Multi-dimensional Integrals58

3.5 Problems for Chapter 361

3.6 Computer Work for Chapter 362

4 Matrix Algebra63

4.1 Types of Matrices64

4.2 Gauss Elimination and Back Substitution66

4.2.1 The Elimination of Unknowns66

4.2.2 The Algorithm of Gauss Elimination and Back Substitution67

4.2.3 Techniques for Improving Solutions72

4.3 LU Decomposition and Matrix Inversion74

4.3.1 Overview of LU Decomposition74

4.3.2 LU Decomposition Algorithm76

4.3.3 Procedure from Gauss Elimination79

4.3.4 The Matrix Inverse and Error Analysis83

4.4 Tridiagonal Matrices and Recursion Method85

4.4.1 Tri-diagonal Systems86

4.4.2 Recursion Method89

4.5 Iterative Methods92

4.6 Jacobi Method95

4.6.1 The Algorithm95

4.6.2 The Convergency96

4.7 Gauss-Seidel Method（GS）97

4.7.1 The Algorithm97

4.7.2 The Convergency99

4.8 Successive Over-Relaxation Method（SOR）99

4.9 Conjugate Gradient Method（CG）102

4.9.1 The Gradient104

4.9.2 Steepest Descent Method107

4.9.3 CG Method109

4.10 Problems for Chapter 4115

4.11 Computer Work for Chapter 4116

5 Ordinary Differential Equations118

5.1 Types of Differential Equations119

5.2 Euler Method122

5.2.1 Error Analysis124

5.2.2 Stability126

5.2.3 Application to Vector Equations130

5.3 The Leapfrog Methods131

5.3.1 Stability Analysis132

5.3.2 Generalization to Multi-step Scheme133

5.4 Implicit Methods135

5.4.1 The Most Fundamental Scheme135

5.4.2 Implicit Scheme of Second Order——Improved Euler Method138

5.5 The Runge-Kutta Method140

5.5.1 The Basic Idea of Runge-Kutta Method140

5.5.2 Stability Analysis143

5.5.3 Adaptive RK Method146

5.6 Predictor-Corrector（PC）Method149

5.7 Boundary Value Problems and Initial Value Problems of Second Order156

5.7.1 Shooting Method158

5.7.2 Numerov’s Method164

5.8 Problems for Chapter 5166

5.9 Computer Work for Chapter 5167

6 Partial Differential Equations168

6.1 Types of Equations168

6.2 Elliptic Equations170

6.2.1 Two or More Dimensions172

6.2.2 ADI（alternating direction implicit）Method177

6.3 Hyperbolic Equations181

6.3.1 The FTCS Scheme184

6.3.2 The Lax Scheme186

6.3.3 Leapfrog Scheme189

6.4 Parabolic Equations191

6.4.1 A Simple Method——FTCS Scheme192

6.4.2 Implicit Scheme of First Order195

6.4.3 Crank-Nicholson（CN）Scheme197

6.5 Five-point Stencil for 2D Poisson Equation in Electromagnetic Field200

6.6 Problems for Chapter 6206

6.7 Computer Work for Chapter 6207

7 Monte Carlo Methods and Simulation208

7.1 Probability210

7.1.1 Chance and Probability210

7.1.2 A One-dimensional Random Walk211

7.1.3 Probability Distribution213

7.1.4 Random Variables215

7.2 Random Number Generators217

7.2.1 Linear Gongruential Generators218

7.2.2 Shift Register Generators220

7.3 Non-uniform Probability Distribution222

7.3.1 Inverse Transform Method222

7.3.2 Generalized Transformation Method——Box-Muller Technique225

7.4 Monte Carlo Integration227

7.4.1 Splash Method（Hit or Miss Method）227

7.4.2 Sample Mean Method229

7.4.3 Two Theorems in Probability Theory230

7.4.4 MC Error Analysis231

7.4.5 Importance Sampling Technique236

7.5 Stochastic Dynamics239

7.5.1 Random Sequences239

7.5.2 Stochastic Dynamics242

7.6 Monte Carlo Simulation and Ising Model246

7.6.1 Simulation Methods246

7.6.2 Random Walk Methods248

7.6.3 The Ising Model249

7.6.4 The Metropolis Algorithm252

7.7 Problems for Chapter 7256

7.8 Computer Work for Chapter 7257

Bibliography259