## An Introduction to Computational PhysicsThoroughly revised for its second edition, this advanced textbook provides an introduction to the basic methods of computational physics, and an overview of progress in several areas of scientific computing by relying on free software available from CERN. The book begins by dealing with basic computational tools and routines, covering approximating functions, differential equations, spectral analysis, and matrix operations. Important concepts are illustrated by relevant examples at each stage. The author also discusses more advanced topics, such as molecular dynamics, modeling continuous systems, Monte Carlo methods, genetic algorithm and programming, and numerical renormalization. It includes many more exercises. This can be used as a textbook for either undergraduate or first-year graduate courses on computational physics or scientific computation. It will also be a useful reference for anyone involved in computational research. |

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### Contents

Introduction i | 1 |

Approximation of a function | 16 |

Numerical calculus | 49 |

Ordinary differential equations | 80 |

Numerical methods for matrices | 119 |

Spectral analysis | 164 |

Partial differential equations | 197 |

Molecular dynamics simulations | 226 |

Modeling continuous systems | 256 |

Monte Carlo simulations | 285 |

Genetic algorithm and programming | 323 |

Numerical renormalization | 347 |

369 | |

381 | |

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### Common terms and phrases

accuracy approximation average binary boundary condition calculated Chapter chromosomes clusters coefficient matrix configuration coordinates data points density matrix differential equation diffusion equation discrete discussed distribution double[n+1 eigenvalue problem eigenvectors electron elements energy evaluation example fast Fourier transform finite first-order derivative function Gaussian Gaussian elimination genetic algorithm given Green's function Hamiltonian implementation import java.lang initial int i=0 integral interpolation introduced inverse Ising model iteration Java lattice linear equation set liquid LU decomposition many-body method molecular dynamics Monte Carlo simulations obtain one-dimensional optimization orthogonal parameters particle Poisson equation polynomial public class public static double public static void quantum Monte Carlo random number random-number recursion region renormalization result scheme Schrodinger equation secant method second-order derivative solution solve specific spin static void main(String step structure Taylor expansion temperature total number tridiagonal two-dimensional update variables vector velocity void main(String argv wavefunction wavelet zero