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| Preface to first edition | |
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| Preface | |
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| Acknowledgments | |
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| Introduction | |
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| Computation and science | |
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| The emergence of modern computers | |
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| Computer algorithms and languages | |
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| Exercises | |
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| Approximation of a function | |
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| Interpolation | |
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| Least-squares approximation | |
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| The Millikan experiment | |
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| Spline approximation | |
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| Random-number generators | |
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| Exercises | |
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| Numerical calculus | |
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| Numerical differentiation | |
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| Numerical integration | |
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| Roots of an equation | |
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| Extremes of a function | |
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| Classical scattering | |
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| Exercises | |
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| Ordinary differential equations | |
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| Initial-value problems | |
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| The Euler and Picard methods | |
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| Predictor-corrector methods | |
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| The Runge-Kutta method | |
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| Chaotic dynamics of a driven pendulum | |
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| Boundary-value and eigenvalue problems | |
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| The shooting method | |
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| Linear equations and the Sturm-Liouville problem | |
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| The one-dimensional Schrodinger equation | |
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| Exercises | |
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| Numerical methods for matrices | |
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| Matrices in physics | |
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| Basic matrix operations | |
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| Linear equation systems | |
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| Zeros and extremes of multivariable functions | |
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| Eigenvalue problems | |
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| The Faddeev-Leverrier method | |
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| Complex zeros of a polynomial | |
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| Electronic structures of atoms | |
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| The Lanczos algorithm and the many-body problem | |
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| Random matrices | |
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| Exercises | |
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| Spectral analysis | |
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| Fourier analysis and orthogonal functions | |
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| Discrete Fourier transform | |
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| Fast Fourier transform | |
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| Power spectrum of a driven pendulum | |
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| Fourier transform in higher dimensions | |
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| Wavelet analysis | |
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| Discrete wavelet transform | |
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| Special functions | |
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| Gaussian quadratures | |
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| Exercises | |
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| Partial differential equations | |
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| Partial differential equations in physics | |
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| Separation of variables | |
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| Discretization of the equation | |
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| The matrix method for difference equations | |
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| The relaxation method | |
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| Groundwater dynamics | |
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| Initial-value problems | |
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| Temperature field of a nuclear waste rod | |
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| Exercises | |
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| Molecular dynamics simulations | |
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| General behavior of a classical system | |
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| Basic methods for many-body systems | |
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| The Verlet algorithm | |
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| Structure of atomic clusters | |
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| The Gear predictor-corrector method | |
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| Constant pressure, temperature, and bond length | |
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| Structure and dynamics of real materials | |
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| Ab initio molecular dynamics | |
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| Exercises | |
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| Modeling continuous systems | |
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| Hydrodynamic equations | |
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| The basic finite element method | |
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| The Ritz variational method | |
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| Higher-dimensional systems | |
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| The finite element method for nonlinear equations | |
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| The particle-in-cell method | |
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| Hydrodynamics and magnetohydrodynamics | |
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| The lattice Boltzmann method | |
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| Exercises | |
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| Monte Carlo simulations | |
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| Sampling and integration | |
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| The Metropolis algorithm | |
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| Applications in statistical physics | |
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| Critical slowing down and block algorithms | |
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| Variational quantum Monte Carlo simulations | |
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| Green's function Monte Carlo simulations | |
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| Two-dimensional electron gas | |
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| Path-integral Monte Carlo simulations | |
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| Quantum lattice models | |
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| Exercises | |
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| Genetic algorithm and programming | |
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| Basic elements of a genetic algorithm | |
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| The Thomson problem | |
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| Continuous genetic algorithm | |
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| Other applications | |
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| Genetic programming | |
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| Exercises | |
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| Numerical renormalization | |
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| The scaling concept | |
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| Renormalization transform | |
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| Critical phenomena: the Ising model | |
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| Renormalization with Monte Carlo simulation | |
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| Crossover: the Kondo problem | |
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| Quantum lattice renormalization | |
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| Density matrix renormalization | |
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| Exercises | |
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| References | |
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| Index | |