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

- 2.1 Interpolations and approximations
- 2.2 Differentiation and integration
- 2.3 Zeros and extremes of a single-variable function
- 2.4 Classical scattering
- 2.5 Random number generators
- Exercises

- 3.1 Initial-value problems
- 3.2 The Euler and Picard methods
- 3.3 The Runge-Kutta method
- 3.4 Chaotic dynamics of a driven pendulum
- 3.5 Boundary-value and eigenvalue problems
- 3.6 The shooting method
- 3.7 Linear equations and Sturm-Liouville problem
- 3.8 The one-dimensional Schroedinger equation
- Exercises

- 4.1 Matrices in physics
- 4.2 Basic Matrix operations
- 4.3 Linear equation systems
- 4.4 Zeros and extremes of a multivariable function
- 4.5 Eigenvalue problem
- 4.6 The Faddeev-Leverrier method
- 4.7 Electronic structure of atoms
- 4.8 The Lanczos algorithm and the many-body problem
- 4.9 Random matrix
- Exercises

- 5.1 The Fourier transform and orthogonal functions
- 5.2 The discrete Fourier transform
- 5.3 The fast Fourier transform
- 5.4 The power spectrum of a driven pendulum
- 5.5 Wavelet analysis
- 5.6 Special functions
- 5.7 Gaussian quadrature
- Exercises

- 6.1 Partial differential equations in physics
- 6.2 Separation of variables
- 6.3 Discretization of the equation
- 6.4 The matrix method for differential equations
- 6.5 The relaxation method
- 6.6 Groundwater dynamics
- 6.7 Initial-value problems
- 6.8 Temperature field of nuclear waste storage facilities
- Exercises

- 7.1 General behavior of a classical system
- 7.2 Basic methods for many-body systems
- 7.3 The Verlet algorithm
- 7.4 Structure of atomic clusters
- 7.5 The Gear predictor-corrector method
- 7.6 Constant pressure, temperature, and bond length
- 7.7 Structure and dynamics of real materials
- 7.8 Ab initio molecular dynamics
- Exercises

- 8.1 Hydrodynamic equations
- 8.2 The basic finite element method
- 8.3 The Ritz variational method
- 8.4 Higher-dimensional systems
- 8.5 The finite element method for nonlinear equations
- 8.6 The particle-in-cell method
- 8.7 Hydrodynamics and magnetohydrodynamics
- 8.8 The Boltzmann lattice-gas method
- Exercises

- 9.1 Sampling and integration
- 9.2 The Metropolis algorithm
- 9.3 Applications in statistical physics
- 9.4 Critical slowing down and block algorithms
- 9.5 Variational quantum Monte Carlo simulations
- 9.6 Green's function Monte Carlo simulations
- 9.7 Path-integral Monte Carlo simulations
- 9.8 Quantum lattice models
- Exercises

- 10.1 The scaling concept
- 10.2 Renormalization transform
- 10.3 Critical phenomena: The Ising model
- 10.4 Renormalization with Monte Carlo simulation
- 10.5 Crossover: The Kondo problem
- 10.6 Quantum lattice renormalization
- 10.7 Density matrix renormalization
- Exercises

- 11.1 Symbolic computing systems
- 11.2 Basic symbolic mathematics
- 11.3 Computer calculus
- 11.4 Linear systems
- 11.5 Nonlinear systems
- 11.6 Differential equations
- 11.7 Computer graphics
- 11.8 Dynamics of a flying sphere
- Exercises

- 12.1 The basic concept
- 12.2 High-performance computer systems
- 12.3 Parallelism and parallel computing
- 12.4 Data parallel programming
- 12.5 Distributed computing and message passing
- 12.6 Some current applications
- Exercises