Table of Contents

• 1.1 Computation and science
• 1.2 The emergence of modern computers
• 1.3 Computer algorithms and languages
• Exercises

• 2.1 Interpolation
• 2.2 Least-squares approximation
• 2.3 The Millikan experiment
• 2.4 Spline approximation
• 2.5 Random-number generators
• Exercises

• 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

• 4.1 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 Sturm-Liouville problem
• 4.9 The one-dimensional Schroedinger equation
• Exercises

• 5.1 Matrices in physics
• 5.2 Basic matrix operations
• 5.3 Linear equation systems
• 5.4 Zeros and extremes of a multivariable function
• 5.5 Eigenvalue problems
• 5.6 The Faddeev-Leverrier method
• 5.7 Complex zeros of a polynomial
• 5.8 Electronic structure of atoms
• 5.9 The Lanczos algorithm and the many-body problem
• 5.10 Random matrices
• Exercises

• 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

• 7.1 Partial differential equations in physics
• 7.2 Separation of variables
• 7.3 Discretization of the equation
• 7.4 The matrix method for differential equations
• 7.5 The relaxation method
• 7.6 Groundwater dynamics
• 7.7 Initial-value problems
• 7.8 Temperature field of nuclear waste storage facilities
• Exercises

• 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

• 9.1 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 Boltzmann lattice-gas method
• Exercises

• 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

• 11.1 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

• 12.1 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