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Numerical Methods of Computational Physics I - NEVF523

Title:	Numerické metody počítačové fyziky I
Guaranteed by:	Department of Surface and Plasma Science (32-KFPP)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2021
Semester:	winter
E-Credits:	6
Hours per week, examination:	winter 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, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	RNDr. Ivan Barvík, Ph.D.
Class:	DS, matematické a počítačové modelování
Classification:	Physics > Surface Physics and P. of Ion.M.
Is interchangeable with:	NEVF512

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Annotation -

Last update: T_KEVF (16.05.2005)

Numerical methods - basic terminology, evaluation of functions, approximation, root finding, integration of functions, solution of linear algebraic equations, integration of ordinary differential equations, partial differential equations. Designated for doctoral and master study.

Aim of the course -

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

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

Course completion requirements -

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

Successful passing of the exam is a condition for completing the course.

Literature -

Last update: T_KEVF (05.05.2010)

Ralston A.: Základy numerické matematiky, Academia, Praha 1978.

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

Cambridge 1992.

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

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: doc. RNDr. Jiří Pavlů, Ph.D. (14.06.2019)

Zkouška je ústní a student dostává otázky dle sylabu předmětu v rozsahu, který byl prezentován na přednáškách.

Syllabus -

Last update: T_KEVF (16.05.2005)

1. Numerical mathematics
Representation of numbers, accuracy, errors.

2. Interpolation and approximation
Interpolation. Least square aproximation, Čebyšev aproximation, spline functions.

3. Numerical integration and differentiation
Formulae for equally spaced abscissas. Gaussian quadrature. Numerical differentiation.

4. Solution of linear algebraic equations
Gauss elimination and Gauss-Jordan elimination. Iterative methods. Matrix operations.

5. Root finding and solution of nenlinear sets of equations

6. Integration of ordinary differential equations
Euler method. Runge-Kutta methods. Predictor-corrector methods. Errors.

7. Solution of partial differential equations
Diference equations. Relaxation method. Over-relaxation methods and further techniques for the increase of convergency. Solution of hyperbolic equations.

8. Application of Monte Carlo method in numerical mathematics