計算物理學(xué)導(dǎo)論

內(nèi)容概要

　　《計算物理學(xué)導(dǎo)論(第2版)》是一部本科生和低年級研究生學(xué)習計算物理的教程。這是第二版，將第一版做了全面的更新和修訂，改進后的課程不僅提供了學(xué)習計算物理學(xué)的基本方法，也全面介紹了計算科學(xué)領(lǐng)域的最新進展。書中講述了許多具體例子，包括現(xiàn)代物理和相關(guān)領(lǐng)域的數(shù)值方法實踐計算。每章末有練習題。本書不僅是一部教程，更是相關(guān)計算領(lǐng)域的的一本很好的參考書。
目次：緒論；函數(shù)逼近；數(shù)值微積分；基礎(chǔ)數(shù)值法；常微分方程；矩陣數(shù)值法；光譜分析法；偏微分方程；分子動力學(xué)模擬；模擬連續(xù)系統(tǒng)；蒙特卡羅模擬；遺傳算法和程序；數(shù)值重正化。
　　

作者簡介

作者：(美國)龐濤 (Tao Pang)

書籍目錄

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

章節(jié)摘錄

版權(quán)頁：插圖：The basic idea behind a genetic algorithm is to follow the biological processof evolution in selecting the path to reach an optimal configuration of a givencomplex system. For exampie, for an interacting many-body system, the equilib-rium is reached by moving the system to the configuration that is at the globalminimum on its potential energy surface. This is single-objective optimization,which can be described mathematically as searching for the global minimum ofa multivariable function. Multiobjective optimization involvesmore than one equation, for example, a search for the minima of gk Both types ofoptimization can involve some constraints.We limit ourselves to single-objective optimization here. For a detailed dis-cussion on multi-objective optimization using the genetic algorithm, see Deb.

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