AN INTRODUCTION TO COMPUTATIONAL PHYSICS

By V. GIERO

CONTENTS 1 INTRODUCTION COMPUTATION AND SCIENCE THE EMERGENCE OF MODERN COMPUTERS COMPUTER ALGORITHMS AND LANGUAGES EXERCISES 2 APPROXIMATION OF A FUNCTION INTERPOLATION LEAST-SQUARES APPROXIMATION THE MILLIKAN EXPERIMENT SPLINE APPROXIMATION RANDOM-NUMBER GENERATORS 3 NUMERICAL CALCULUS NUMERICAL DIFFERENTIATION NUMERICAL INTEGRATION ROOTS OF AN EQUATION EXTREMES OF A FUNCTION CLASSICAL SCATTERING 4 ORDINARY DIFFERENTIAL EQUATIONS INITIAL-VALUE PROBLEMS THE EULER AND PICARD METHODS PREDICTOR–CORRECTOR METHODS THE RUNGE–KUTTA METHOD CHAOTIC DYNAMICS OF A DRIVEN PENDULUM BOUNDARY-VALUE AND EIGENVALUE PROBLEMS THE SHOOTING METHOD LINEAR EQUATIONS AND THE STURM–LIOUVILLE PROBLEM THE ONE-DIMENSIONAL SCHR¨ODINGER EQUATION 5 NUMERICAL METHODS FOR MATRICES MATRICES IN PHYSICS BASIC MATRIX OPERATIONS LINEAR EQUATION SYSTEMS ZEROS AND EXTREMES OF MULTIVARIABLE FUNCTIONS EIGENVALUE PROBLEMS THE FADDEEV–LEVERRIER METHOD COMPLEX ZEROS OF A POLYNOMIAL ELECTRONIC STRUCTURES OF ATOMS THE LANCZOS ALGORITHM AND THE MANY-BODY PROBLEM 5 10 RANDOM MATRICES 6 SPECTRAL ANALYSIS FOURIER ANALYSIS AND ORTHOGONAL FUNCTIONS DISCRETE FOURIER TRANSFORM FAST FOURIER TRANSFORM POWER SPECTRUM OF A DRIVEN PENDULUM FOURIER TRANSFORM IN HIGHER DIMENSIONS WAVELET ANALYSIS DISCRETE WAVELET TRANSFORM SPECIAL FUNCTIONS GAUSSIAN QUADRATURES 7 PARTIAL DIFFERENTIAL EQUATIONS PARTIAL DIFFERENTIAL EQUATIONS IN PHYSICS SEPARATION OF VARIABLES DISCRETIZATION OF THE EQUATION THE MATRIX METHOD FOR DIFFERENCE EQUATIONS THE RELAXATION METHOD GROUNDWATER DYNAMICS TEMPERATURE ?ELD OF A NUCLEAR WASTE ROD 8 MOLECULAR DYNAMICS SIMULATIONS GENERAL BEHAVIOR OF A CLASSICAL SYSTEM BASIC METHODS FOR MANY-BODY SYSTEMS THE VERLET ALGORITHM STRUCTURE OF ATOMIC CLUSTERS THE GEAR PREDICTOR–CORRECTOR METHOD CONSTANT PRESSURE, TEMPERATURE, AND BOND LENGTH STRUCTURE AND DYNAMICS OF REAL MATERIALS AB INITIO MOLECULAR DYNAMICS 9 MODELING CONTINUOUS SYSTEMS HYDRODYNAMIC EQUATIONS THE BASIC ?NITE ELEMENT METHOD THE RITZ VARIATIONAL METHOD HIGHER-DIMENSIONAL SYSTEMS THE ?NITE ELEMENT METHOD FOR NONLINEAR EQUATIONS THE PARTICLE-IN-CELL METHOD HYDRODYNAMICS AND MAGNETOHYDRODYNAMICS THE LATTICE BOLTZMANN METHOD 10 MONTE CARLO SIMULATIONS 10 1 SAMPLING AND INTEGRATION 10 2 THE METROPOLIS ALGORITHM 10 3 APPLICATIONS IN STATISTICAL PHYSICS 10 4 CRITICAL SLOWING DOWN AND BLOCK ALGORITHMS 10 5 VARIATIONAL QUANTUM MONTE CARLO SIMULATIONS 10 6 GREEN’S FUNCTION MONTE CARLO SIMULATIONS 10 7 TWO-DIMENSIONAL ELECTRON GAS 10 8 PATH-INTEGRAL MONTE CARLO SIMULATIONS 10 9 QUANTUM LATTICE MODELS 11 GENETIC ALGORITHM AND PROGRAMMING 11 1 BASIC ELEMENTS OF A GENETIC ALGORITHM 11 2 THE THOMSON PROBLEM 11 3 CONTINUOUS GENETIC ALGORITHM 11 4 OTHER APPLICATIONS 11 5 GENETIC PROGRAMMING 12 NUMERICAL RENORMALIZATION 12 1 THE SCALING CONCEPT 12 2 RENORMALIZATION TRANSFORM 12 3 CRITICAL PHENOMENA: THE ISING MODEL 12 4 RENORMALIZATION WITH MONTE CARLO SIMULATION 12 5 CROSSOVER: THE KONDO PROBLEM 12 6 QUANTUM LATTICE RENORMALIZATION 12 7 DENSITY MATRIX RENORMALIZATION