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
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