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Course, academic year 2018/2019
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Fundamentals of computational physics II - NEVF138
Title in English: Základy počítačové fyziky II
Guaranteed by: Department of Surface and Plasma Science (32-KFPP)
Faculty: Faculty of Mathematics and Physics
Actual: from 2013 to 2018
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: RNDr. Štěpán Roučka, Ph.D.
prof. RNDr. Rudolf Hrach, DrSc.
Annotation -
Last update: RNDr. Štěpán Roučka, Ph.D. (28.01.2019)
Advanced algorithms of numerical mathematics. Basics of mathematical statistics and theory of probability. Selected parties of classical computational physics - hybrid particle modelling, basics of percolation theory and mathematical morphology, image processing, integral transform and Fourier optics, automatisation in physical laboratory.
Aim of the course -
Last update: IBARVIK/MFF.CUNI.CZ (16.05.2008)

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

Literature - Czech
Last update: T_KEVF (07.05.2005)

Vicher M.: Numerická matematika, PF UJEP, Ústí nad Labem 2003.

Press W.H. et al.: Numerical Recipes in FORTRAN (Pascal, C) Cambridge University Press, Cambridge 1992.

Hrach R.: Počítačová fyzika I, II, PF UJEP, Ústí nad Labem 2003.

Rapaport D.C.: The Art of Molecular Dynamics Simulation, Cambridge University Press, Cambridge 1995.

Teaching methods -
Last update: IBARVIK/MFF.CUNI.CZ (16.05.2008)

Lectures and practical exercises in computer lab

Requirements to the exam - Czech
Last update: RNDr. Štěpán Roučka, Ph.D. (27.02.2018)

Zkouška sestává pouze z ústní části. Okruhy otázek odpovídají látce který byla prezentován na přednášce a studenti jsou s nimi seznámeni na první přednášce.

Syllabus -
Last update: RNDr. Štěpán Roučka, Ph.D. (28.01.2019)
1. Advanced algorithms of numerical mathematics
Numerical mathematics - 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, application of Monte Carlo method.

2. 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. Entrophy.

3. 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. Software aspects of automatisation.

4. Main directions of modern computational physics
Evolutionary modelling. Application of neural networks and fuzzy logic. Wavelet transform.

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