计算物理 英文版·第2版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

计算物理 英文版·第2版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

1 A First Numerical Problem1

1.1 Radioactive Decay1

1.2 A Numerical Approach2

1.3 Design and Construction of a Working Program：Codes and Pseu-docodes3

1.4 Testing Your Program11

1.5 Numerical Considerations12

1.6 Programming Guidelines and Philosophy14

2 Realistic Projectile Motion18

2.1 Bicycle Racing：The Effect of Air Resistance18

2.2 Projectile Motion：The Trajectory of a Cannon Shell25

2.3 Baseball：Motion of a Batted Ball31

2.4 Throwing a Baseball：The Effects of Spin36

2.5 Golf44

3 Oscillatory Motion and Chaos48

3.1 Simple Harmonic Motion48

3.2 Making the Pendulum More Interesting：Adding Dissipation,Non-linearity and a Driving Force54

3.3 Chaos in the Driven Nonlinear Pendulum58

3.4 Routes to Chaos：Period Doubling66

3.5 The Logistic Map：Why the Period Doubles70

3.6 The Lorenz Model75

3.7 The Billiard Problem82

3.8 Behavior in the Frequency Domain：Chaos and Noise88

4 The Solar System94

4.1 Kepler's Laws94

4.2 The Inverse-Square Law and the Stability of Planetary Orbits101

4.3 Precession of the Perihelion of Mercury107

4.4 The Three-Body Problem and the Effect of Jupiter on Earth113

4.5 Resonances in the Solar System：Kirkwood Gaps and Planetary Rings118

4.6 Chaotic Tumbling of Hyperion123

5 Potentials and Fields129

5.1 Electric Potentials and Fields：Laplace's Equation129

5.2 Potentials and Fields Near Electric Charges143

5.3 Magnetic Field Produced by a Current148

5.4 Magnetic Field of a Solenoid：Inside and Out151

6 Waves156

6.1 Waves：The Ideal Case156

6.2 Frequency Spectrum of Waves on a String165

6.3 Motion of a (Somewhat)Realistic String169

6.4 Waves on a String(Again)：Spectral Methods174

7 Random Systems181

7.1 Why Perform Simulations of Random Processes?181

7.2 Random Walks183

7.3 Self-Avoiding Walks188

7.4 Random Walks and Diffusion195

7.5 Diffusion,Entropy,and the Arrow of Time201

7.6 Cluster Growth Models206

7.7 Fractal Dimensionalities of Curves212

7.8 Percolation218

7.9 Diffusion on Fractals229

8 Statistical Mechanics,Phase Transitions,and the Ising Model235

8.1 The Ising Model and Statistical Mechanics235

8.2 Mean Field Theory239

8.3 The Monte Carlo Method244

8.4 The Ising Model and Second-Order Phase Transitions246

8.5 First-Order Phase Transitions259

8.6 Scaling264

9 Molecular Dynamics270

9.1 Introduction to the Method：Properties of a Dilute Gas270

9.2 The Melting Transition285

9.3 Equipartition and the Fermi-Pasta-Ulam Problem294

10 Quantum Mechanics303

10.1 Time-Independent Schr？dinger Equation：Some Preliminaries303

10.2 One Dimension：Shooting and Matching Methods307

10.3 A Matrix Approach323

10.4 A Variational Approach326

10.5 Time-Dependent Schr？dinger Equation：Direct Solutions333

10.6 Time-Dependent Schr？dinger Equation in Two Dimensions345

10.7 Spectral Methods349

11 Vibrations,Waves,and the Physics of Musical Instruments357

11.1 Plucking a String：Simulating a Guitar357

11.2 Striking a String：Pianos and Hammers362

11.3 Exciting a Vibrating System with Friction：Violins and Bows367

11.4 Vibrations of a Membrane：Normal Modes and Eigenvalue Problems372

11.5 Generation of Sound382

12 Interdisciplinary Topics389

12.1 Protein Folding389

12.2 Earthquakes and Self-Organized Criticality405

12.3 Neural Networks and the Brain418

12.4 Real Neurons and Action Potentials436

12.5 Cellular Automata445

APPENDICES456

A Ordinary Differential Equations with Initial Values456

A.1 First-Order,Ordinary Differential Equations456

A.2 Second-Order,Ordinary Differential Equations460

A.3 Centered Difference Methods464

A.4 Summary467

B Root Finding and Optimization469

B.1 Root Finding469

B.2 Direct Optimization472

B.3 Stochastic Optimization473

C The Fourier Transform479

C.1 Theoretical Background479

C.2 Discrete Fourier Transform481

C.3 Fast Fourier Transform (FFT)483

C.4 Examples：Sampling Interval and Number of Data Points486

C.5 Examples：Aliasing488

C.6 Power Spectrum490

D Fitting Data to a Function493

D.1 Introduction493

D.2 Method of Least Squares：Linear Regression for Two Variables494

D.3 Method of Least Squares：More General Cases497

E Numerical Integration500

E.1 Motivation500

E.2 Newton-Cotes Methods：Using Discrete Panels to Approximate an Integral500

E.3 Gaussian Quadrature：Beyond Classic Methods of Numerical Inte-gration504

E.4 Monte Carlo Integration506

F Generation of Random Numbers512

F.1 Linear Congruential Generators512

F.2 Nonuniform Random Numbers516

G Statistical Tests of Hypotheses520

G.1 Central Limit Theorem and the x2 Distribution521

G.2 x2 Test of a Hypothesis523

H Solving Linear Systems527

H.1 Solving Ax=b,b≠O528

H.1.1 Gaussian Elimination528

H.1.2 Gauss-Jordan elimination530

H.1.3 LU decomposition531

H.1.4 Relaxational method533

H.2 Eigenvalues and Eigenfunctions535

H.2.1 Approximate Solution of Eigensystems537

Index541