计算物理学导论 : 第2版

preface to first edition

preface

acknowledgments

1 introduction

1.1 computation and science

1.2 the emergence of modem computers

1.3 computer algorithms and languages

exercises

2 approximation of a function

2.1 interpolation

2.2 least-squares approximation

2.3 the millikan experiment

2.4 spline approximation

2.5 random-number generators

exercises

3 numerical calculus

3.1 numerical differentiation

3.2 numerical integration

3.3 roots of an equation

3.4 extremes of a function

3.5 classical scattering

exercises

4 ordinary differential equations

4.1 initial-value problems

4.2 the euler and picard methods

4.3 predictor-corrector methods

4.4 the runge-kutta method

4.5 chaotic dynamics of a driven pendulum

4.6 boundary-value and eigenvalue problems

4.7 the shooting method

4.8 linear equations and the sturm-liouville problem

4.9 the one-dimensional schr6dinger equation

exercises

5 numerical methods for matrices

5.1 matrices in physics

5.2 basic matrix operations

5.3 linear equation systems

5.4 zeros and extremes of multivariable functions

5.5 eigenvalue problems

5.6 the faddeev-leverrier method

5.7 complex zeros of a polynomial

5.8 electronic structures of atoms

5.9 the lanczos algorithm and the many-body problem

5.10 random matrices

exercises

6 spectral analysis

6.1 fourier analysis and orthogonal functions

6.2 discrete fourier transform

6.3 fast fourier transform

6.4 power spectrum of a driven pendulum

6.5 fourier transform in higher dimensions

6.6 wavelet analysis

6.7 discrete wavelet transform

6.8 special functions

6.9 gaussian quadratures

exercises

7 partial differential equations

7.1 partial differential equations in physics

7.2 separation of variables

7.3 discretization of the equation

7.4 the matrix method for difference equations

7.5 the relaxation method

7.6 groundwater dynamics

7.7 initial-value problems

7.8 temperature field of a nuclear waste rod

exercises

8 molecular dynamics simulations

8.1 general behavior of a classical system

8.2 basic methods for many-body systems

8.3 the verlet algorithm

8.4 structure of atomic clusters

8.5 the gear predictor-corrector method

8.6 constant pressure, temperature, and bond length

8.7 structure and dynamics of real materials

8.8 ab initio molecular dynamics

exercises

9 modeling continuous systems

9.1 hydrodynamic equations

9.2 the basic finite element method

9.3 the ritz variational method

9.4 higher-dimensional systems

9.5 the finite element method for nonlinear equations

9.6 the particle-in-cell method

9.7 hydrodynamics and magnetohydrodynamics

9.8 the lattice boltzmann method

exercises

10 monte carlo simulations

10.1 sampling and integration

10.2 the metropolis algorithm

10.3 applications in statistical physics

10.4 critical slowing down and block algorithms

10.5 variational quantum monte carlo simulations

10.6 green's function monte carlo simulations

10.7 two-dimensional electron gas

10.8 path-integral monte carlo simulations

10.9 quantum lattice models

exercises

11 genetic algorithm and programming

11.1 basic elements of a genetic algorithm

11.2 the thomson problem

11.3 continuous genetic algorithm

11.4 other applications

11.5 genetic programming

exercises

12 numerical renormalization

12.1 the scaling concept

12.2 renormalization transform

12.3 critical phenomena: the ising model

12.4 renormalization with monte carlo simulation

12.5 crossover: the kondo problem

12.6 quantum lattice renormalization

12.7 density matrix renormalization

exercises

references

index

《计算物理学导论（第2版）》是一部本科生和低年级研究生学习计算物理的教程。这是第二版，将第一版做了全面的更新和修订，改进后的课程不仅提供了学习计算物理学的基本方法，也全面介绍了计算科学领域的最新进展。书中讲述了许多具体例子，包括现代物理和相关领域的数值方法实践计算。每章末有练习题。《计算物理学导论（第2版）》不仅是一部教程，更是相关计算领域的一本很好的参考书。目次：绪论；函数逼近；数值微积分；基础数值法；常微分方程；矩阵数值法；光谱分析法；偏微分方程；分子动力学模拟；模拟连续系统；蒙特卡罗模拟；遗传算法和程序；数值重正化。