Preface disclaimer of Warranties Acknowledgment 1 Introduction 1.1 Computations and science 1.2 The emergence of modern computers 1.3 Computer algorithms and languages 2 Basic numerical methods 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 3 Ordinary differential equations 3.1 initial-value problems 3.2 The Euler and Picard methods 3.3 Predictor-corrector methods 3.4 The Runge-kutta method 3.5 Chaotic dynamics of a driven pendulum 3.6 Boundary-value and eignevalue problems 3.7 The shooting method 3.8 Linear equations and the Sturm-Lioville problem 3.9 The on-dimensional Schordinger equation 4 Numerical methodes for matrices …… 5 Spectral analysis and Gaussian quadrature 6 Partial differential equations 7 Molecular dynamics simulations 8 Modeling continuous systems 9 Monte Carlo simulations 10 Numerical renormalization 11 Symbolic computing 12 High-performance computing References Index
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