普渡大学的Nictlolas J．Giordarlo和Hisao Nakarfistli具有多年的科研和教育经验，所著的本书是计算物理领域的一本优秀教材。它紧扣一些非常基本但难以解析求解的物理问题逐步展开，围绕各个物理学专题介绍了物理学研究中各种基本的计算机数值模拟方法，深入浅出地讨论其理论基础和实际应用，着重于解决实际物理问题的基本数值方法。这样可以使读者通过学习，对物理学中应用的主要计算技术有一个全面的了解，从而具有利用计算机进行数值计算解决复杂体系物理问题的能力。

本书包含了很多物理学专题，方便教师在教学内容及其深度的选择方面有较大的灵活性。

  Preface

About the Authors

1 A First Numerical Problem

1.1 Radioactive Decay

1.2 A Numerical Approach

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

1.4 Testing Your Program

1.5 Numerical Considerations

1.6 Programming Guidelines and Philosophy

Realistic Projectile Motion

2.1 Bicycle Racing: The Effect of Air Resistance

2.2 Projectile Motion: The Trajectory of a Cannon Shell

2.3 Baseball: Motion of a Batted Ball

2.4 Throwing a Baseball: The Effects of Spin

2.5 Golf

3 Oscillatory Motion and Chaos

3.1 Simple Harmonic Motion

3.2 Making the Pendulum More Interesting: Adding Dissipation, Non-

   linearity, and a Driving Force

3.3 Chaos in the Driven Nonlinear Pendulum

3.4 Routes to Chaos: Period Doubling

3.5 The Logistic Map: Why the Period Doubles

3.6 The Lorenz Model

3.7 The Billiard Problem

3.8 Behavior in the Frequency Domain: Chaos and Noise

4 The Solar System

4.1 Kepler's Laws

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

4.3 Precession of the Perihelion of Mercury

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

4.5 Resonances in the Solar System: Kirkwood Gaps and Planetary

   Rings

4.6 Chaotic Tumbling of Hyperion

Potentials and Fields

5.1 Electric Potentials and Fields: Laplace's Equation

5.2 Potentials and Fields Near Electric Charges

5.3 Magnetic Field Produced by a Current

5.4 Magnetic Field of a Solenoid: Inside and Out

Waves

6.1 Waves: The Ideal Case

6.2 Frequency Spectrum of Waves on a String

6.3 Motion of a (Somewhat) Realistic String

6.4 Waves on a String (Again): Spectral Methods

Random Systems

7.1 Why Perform Simulations of Random Processes?

7.2 Random Walks

7.3 Self-Avoiding Walks

7.4 Random Walks and Diffusion

7.5 Diffusion, Entropy, and the Arrow of Time

7.6 Cluster Growth Models .

7.7 Fractal Dimensionalities of Curves

7.8 Percolation

7.9 Diffusion on Fractals

8 Statistical Mechanics, Phase Transitions, and the Ising Model

8.1 The Ising Model and Statistical Mechanics

8.2 Mean Field Theory

8.3 The Monte Carlo Method

8.4 The Ising Model and Second-Order Phase Transitions

8.5 First-Order Phase Transitions

8.6 Scaling

9 Molecular Dynamics

9.1 Introduction to the Method: Properties of a Dilute Gas

9.2 The Melting Transition

9.3 Equipartition and the Fermi-Pasta-Ulam Problem

10 Quantum Mechanics

10.1 Time-Independent Schrodinger Equation: Some Preliminaries

10.2 One Dimension: Shooting and Matching Methods

10.3 A Matrix Approach

10.4 A Variational Approach

10.5 Time-Dependent SchrSdinger Equation: Direct Solutions

10.6 Time-Dependent SchrSdinger Equation in Two Dimensions

10.7 Spectral Methods

11 Vibrations, Waves, and the Physics of Musical Instruments

11.1 Plucking a String: Simulating a Guitar

11.2 Striking a String: Pianos and Hammers

11.3 Exciting a Vibrating System with Friction: Violins and Bows

11.4 Vibrations of a Membrane: Normal Modes and Eigenvalue Problems

11.5 Generation of Sound

12 Interdisciplinary Topics

12.1 Protein Folding

12.2 Earthquakes and Self-Organized Criticality

12.3 Neural Networks and the Brain

12.4 Real Neurons and Action Potentials

12.5 Cellular Automata

APPENDICES

A Ordinary Differential Equations with Initial Values

A.1 First-Order, Ordinary Differential Equations

A.2 Second-Order, Ordinary Differential Equations

A.3 Centered Difference Methods

A.4 Summary

B Root Finding and Optimization

B.1 Root Finding

B.2 Direct Optimization

B.3 Stochastic Optimization

C The Fourier Transform

C.1 Theoretical Background

C.2 Discrete Fourier Transform

C.3 Fast Fourier Transform (FFT)

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

C.5 Examples: Aliasing

C.6 Power Spectrum

D Fitting Data to a Function

D.1 Introduction

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

D.3 Method of Least Squares: More General Cases

E Numerical Integration

E.1 Motivation

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

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

E.4 Monte Carlo Integration

F Generation of Random Numbers

F.1 Linear Congruential Generators

F.2 Nonuniform Random Numbers

G Statistical Tests of Hypotheses

G.1 Central Limit Theorem and the X2 Distribution

G.2 X2 Test of a Hypothesis

H Solving Linear Systems

H.1 SolvingA.x=b,b≠0

   H.I.1 Gaussian Elimination

   H.1.2 Gauss-Jordan elimination

   H.1.3 LU decomposition

   H.1.4 Relaxational method

H.2 Eigenvalues and Eigenfunctions

   H.2.1 Approximate Solution of Eigensystems

Index