Advanced algorithms of numerical mathematics

Numerical mathematics ? accuracy, errors, stability of algorithms.

Approximation ? interpolation, least square approximation, splines.

Numerical integration and differentiation ? integration with equally spaced basis,

Gaussian quadrature.

Solution of linear algebraic equations ? Gaussian and Gauss-Jordan elimination, iterative methods.

Root finding and solution of nonlinear sets of equations

Integration of ordinary differential equations

Euler method and its modifications, Runge-Kutta methods, predictor-corrector methods.

Solution of partial differential equations difference, relaxation and super-relaxation method.

Basics of theory of probability and mathematical statistics random variables and their description, moments of random variables, selected random variables, basic laws of the theory of probability and mathematical statistics, statistical testing of hypotheses.

Selected algorithms of classical computational physics

Advanced algorithms of computer particle modelling and fluid modelling

Visualisation of large sets of static and dynamic data

Image analysis low-level image processing, basics of percolation theory and basics of mathematical morphology, implementation of their algorithms in the image analysis.

Integral transforms fast Fourier transform and other integral transforms, application of integral transforms for the calculation of convolution and deconvolution, signal/noise reduction and solution of integral equations, basics of Fourier optics.

Main directions of modern computational physics

Main directions of computational physics. Hardware and software basis of computational physics.

Computer modelling, computer graphics, image processing, integral transforms. Basic numerical methods.

Introduction to mathematical statistics and theory of probability.