FYSP120 Fysiikan Numeeriset menetelmät / numerical methods in physics SYLLABUS ========= - GENERAL: Matlab and/or octave - Approximation of data : least squares fit - spline interpolation - Pade approximants - Fourier series and FFT - B-spline basis functions - Numerical Integration - Newton-Cotes quadratures - Simpson rules - derivation of quadratures - Adaptive integration routines - Gauss quadratures - derivation - Zeros of a real function - Newton bisection and Newton-Raphson methods - Optimization - downhill simplex emthod (Nelder and Mead) - Steepest descent - Newton's method - Levenberg-Marquardt method - Trust region algorithms (Dog Leg algorithm) - Differential equations - Coupled diff. equations - Stiff set of equations; implicit Euler method - 4th order Runge-Kutta method - Eigenvalue equations - Power method - Krylov subsspace: Arnoldi and Lanczos iterations - B-spline solution of Schrödinger equation - Simulations - Molecular dynamics - Variational Monte Carlo - Metropolis algorithm - detailed balance - Markov chains - Statistical independence and error estimation