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Fundamentals of Computer Physics II - NBCM322

Title:	Základy počítačové fyziky II
Guaranteed by:	Institute of Physics of Charles University (32-FUUK)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2022
Semester:	summer
E-Credits:	6
Hours per week, examination:	summer s.:2/2, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Note:	enabled for web enrollment

Guarantor:	RNDr. Ivan Barvík, Ph.D.
Classification:	Mathematics > Mathematical Modeling in Physics Physics > Mathematical and Computing Modelling in Physics, Surface Physics and P. of Ion.M.

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Annotation -

Last update: T_FUUK (14.05.2009)

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.

Aim of the course -

Last update: T_FUUK (14.05.2009)

Students will learn basic numerical algorithms (see annotation and syllabus).

Course completion requirements -

Last update: RNDr. Ivan Barvík, Ph.D. (30.10.2019)

The exam is awarded on condition of at least 70% attendance.

In case of non-fulfillment, it is necessary to elaborate and present tasks from topics where absences occurred.

Another condition for passing the exam is the elaboration of assigned project.

Teaching methods -

Last update: T_FUUK (14.05.2009)

Lectures and practical exercises in computer lab

Syllabus -

Last update: T_FUUK (14.05.2009)

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