Syllabus
1. Basic methods of numerical mathematics, accuracy of numerical solutions, error treatment in experimental data.
Introduction to Octave/Matlab. 2. Basics concept of programming in Octave/Matlab, linear algebra - basics command, loading a saving files, reading input from files and keyboard , graphical output, scripting, vectors and matrices. 3.
Matrices and system of linear equations - elemetal arithmetics with matrices, linear algebra. Calculation of trace of matrix, determinant, matrix inversion and transposition.
Solution of the system of linear equation, dense and sparse matrices. 4.Interpolation and extrapolation. Spline curves, roots of the polynom. 5.Numerical methods for nonlinear equations and system of nonlinear equations. 6.
Numerical integration - trapezoidal method, Simpson's rules, Romberg's methods. Gaussian quadrature, integration of complex functions. 7.
Numerical derivation, Golay-Savitzky filters. 8. Least square methods - Gauss's method, method Levenberg-Marquardt, simplex. 9.
Fourier transformation - frequence analysis, convolution/deconvolution using FT, low and highpass filters, numerical integration using FT 10. Numerical solution of ordinary differential equation (ODE), systems of ODE - Euler's method, Runge-Kutta methods. 11.
Numerical solution of partial diferential equation - Laplace's (Poisson's) equation, heat transfer equation, diffusion equation, wave equation. 12. Monte Carlo methods - (multidimensional) integration using MC, simulation of Brown motion, Ising model
Annotation
Basic methods of numerical mathematics, computation accurary on PC, basics of experimental data treatment
(with error analysis as well). Practical solutions of selected physical problems by using numerical methods in
Octave/Matlab. Exercises for practice linear/nonlinear regression, convolution, deconvolution, Fourier transformation and numerical method for ordinary and partial differential equations. Basic concept of Monte Carlo method (Metropolis Aplgorithm).