| Preface to first edition | p. xi |
| Preface | p. xiii |
| Acknowledgments | p. xv |
| Introduction | p. 1 |
| Computation and science | p. 1 |
| The emergence of modern computers | p. 4 |
| Computer algorithms and languages | p. 7 |
| Exercises | p. 14 |
| Approximation of a function | p. 16 |
| Interpolation | p. 16 |
| Least-squares approximation | p. 24 |
| The Millikan experiment | p. 27 |
| Spline approximation | p. 30 |
| Random-number generators | p. 37 |
| Exercises | p. 44 |
| Numerical calculus | p. 49 |
| Numerical differentiation | p. 49 |
| Numerical integration | p. 56 |
| Roots of an equation | p. 62 |
| Extremes of a function | p. 66 |
| Classical scattering | p. 70 |
| Exercises | p. 76 |
| Ordinary differential equations | p. 80 |
| Initial-value problems | p. 81 |
| The Euler and Picard methods | p. 81 |
| Predictor-corrector methods | p. 83 |
| The Runge-Kutta method | p. 88 |
| Chaotic dynamics of a driven pendulum | p. 90 |
| Boundary-value and eigenvalue problems | p. 94 |
| The shooting method | p. 96 |
| Linear equations and the Sturm-Liouville problem | p. 99 |
| The one-dimensional Schrodinger equation | p. 105 |
| Exercises | p. 115 |
| Numerical methods for matrices | p. 119 |
| Matrices in physics | p. 119 |
| Basic matrix operations | p. 123 |
| Linear equation systems | p. 125 |
| Zeros and extremes of multivariable functions | p. 133 |
| Eigenvalue problems | p. 138 |
| The Faddeev-Leverrier method | p. 147 |
| Complex zeros of a polynomial | p. 149 |
| Electronic structures of atoms | p. 153 |
| The Lanczos algorithm and the many-body problem | p. 156 |
| Random matrices | p. 158 |
| Exercises | p. 160 |
| Spectral analysis | p. 164 |
| Fourier analysis and orthogonal functions | p. 165 |
| Discrete Fourier transform | p. 166 |
| Fast Fourier transform | p. 169 |
| Power spectrum of a driven pendulum | p. 173 |
| Fourier transform in higher dimensions | p. 174 |
| Wavelet analysis | p. 175 |
| Discrete wavelet transform | p. 180 |
| Special functions | p. 187 |
| Gaussian quadratures | p. 191 |
| Exercises | p. 193 |
| Partial differential equations | p. 197 |
| Partial differential equations in physics | p. 197 |
| Separation of variables | p. 198 |
| Discretization of the equation | p. 204 |
| The matrix method for difference equations | p. 206 |
| The relaxation method | p. 209 |
| Groundwater dynamics | p. 213 |
| Initial-value problems | p. 216 |
| Temperature field of a nuclear waste rod | p. 219 |
| Exercises | p. 222 |
| Molecular dynamics simulations | p. 226 |
| General behavior of a classical system | p. 226 |
| Basic methods for many-body systems | p. 228 |
| The Verlet algorithm | p. 232 |
| Structure of atomic clusters | p. 236 |
| The Gear predictor-corrector method | p. 239 |
| Constant pressure, temperature, and bond length | p. 241 |
| Structure and dynamics of real materials | p. 246 |
| Ab initio molecular dynamics | p. 250 |
| Exercises | p. 254 |
| Modeling continuous systems | p. 256 |
| Hydrodynamic equations | p. 256 |
| The basic finite element method | p. 258 |
| The Ritz variational method | p. 262 |
| Higher-dimensional systems | p. 266 |
| The finite element method for nonlinear equations | p. 269 |
| The particle-in-cell method | p. 271 |
| Hydrodynamics and magnetohydrodynamics | p. 276 |
| The lattice Boltzmann method | p. 279 |
| Exercises | p. 282 |
| Monte Carlo simulations | p. 285 |
| Sampling and integration | p. 285 |
| The Metropolis algorithm | p. 287 |
| Applications in statistical physics | p. 292 |
| Critical slowing down and block algorithms | p. 297 |
| Variational quantum Monte Carlo simulations | p. 299 |
| Green's function Monte Carlo simulations | p. 303 |
| Two-dimensional electron gas | p. 307 |
| Path-integral Monte Carlo simulations | p. 313 |
| Quantum lattice models | p. 315 |
| Exercises | p. 320 |
| Genetic algorithm and programming | p. 323 |
| Basic elements of a genetic algorithm | p. 324 |
| The Thomson problem | p. 332 |
| Continuous genetic algorithm | p. 335 |
| Other applications | p. 338 |
| Genetic programming | p. 342 |
| Exercises | p. 345 |
| Numerical renormalization | p. 347 |
| The scaling concept | p. 347 |
| Renormalization transform | p. 350 |
| Critical phenomena: the Ising model | p. 352 |
| Renormalization with Monte Carlo simulation | p. 355 |
| Crossover: the Kondo problem | p. 357 |
| Quantum lattice renormalization | p. 360 |
| Density matrix renormalization | p. 364 |
| Exercises | p. 367 |
| References | p. 369 |
| Index | p. 381 |
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