计算物理学导论 第二版

计算物理学导论 第二版
出版时间：2011年版
内容简介
　　《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。
目录
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