FU:ETFNSP0006 Numerical Methods in Physics - Informace o předmětu
ETFNSP0006 Numerical Methods in Physics
Fyzikální ústav v Opavěléto 2024
- Rozsah
- 1/4/0. 7 kr. Ukončení: zk.
- Vyučující
- doc. RNDr. Stanislav Hledík, Ph.D. (přednášející)
doc. RNDr. Jan Schee, Ph.D. (přednášející)
doc. RNDr. Stanislav Hledík, Ph.D. (cvičící) - Garance
- doc. RNDr. Jan Schee, Ph.D.
Fyzikální ústav v Opavě - Předpoklady
- (FAKULTA(FU)&&SOUHLAS)
- Omezení zápisu do předmětu
- Předmět je otevřen studentům libovolného oboru.
Jiné omezení: Erasmus - Cíle předmětu
- Students will learn fundamental numerical methods generally used in physics.
- Výstupy z učení
- Passing the course a student acquires following skills:
- to apply learned numerical methods on specific physical problem,
- to analyze stability and frame of usability of chosen method,
- to determine error of given problem discretization and use of proper method to solve the problem. - Osnova
- The key topics of the course:
• Learning development environment, compilator, linker. Fundamentals of C/C++ usefull for numerical calculations. Program organization and control structures.
• Machine number representation and finite precision arithmetic: binary and hexadecimal representation, floating point representation. Machine precision. Errors: roundoff and truncation. Error propagation. Stability of calculations.
• Number series and their convergence. Polynomials and Rational functions.
• Linear algebraic equations solvers: Gauss-Jordan elimination. Gauss elimination with back-substitution. LU dekomposition.
• Interpolation and extrapolation: Polynomial interpolation and extrapolation. Rational function interpolation and extrapolation.
• Nonlinear algebraic equations solvers, extremum determination: bracketing, bisection method, regula-falsi method, Brent's method, Newton-Raphson method.
• Methods to determine minimum of 1-D functions using 1st derivative and multidimensional functions using „Downhill Simplex“ method.
• Methods to determine roots of polynomial equations of n-th order in both Real and Complex domains.
• Random numbers: uniform distribution generators, linear congruential generator, Schrange's method,Schranges's algorithm,subtractive method. Transformation and rejection methods for generation other than uniform distributions. Exponential and normal distributions.
• Numerical integration: Classical formulae (open, closed, semiopen) and algorithms (trapezoidal, Simpson's rules). Romberg integration.
• Gauss quadrature and orthogonal polynomials.
• Ordinary differential equations: initial value problem, boundary value problem. Euler method with fixed and adaptive integration step.
• Runge-Kutta scheme, method derivation, stability analysis.
- The key topics of the course:
- Literatura
- doporučená literatura
- Vetterling, W. T., Teukolsky, S. A., Press, W. H., Flannery, B. Numerical Recipes Example Book (C). Cambridge University Press, Cambridge, 1993. ISBN 0-521-43720-2. URL info
- Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, Cambridge, 1997. ISBN 0-521-43108-5. URL info
- A. Ralston. Základy numerické matematiky. Praha, 1978. info
- Výukové metody
- Lectures. Exercises. Working out given project.
- Metody hodnocení
- oral exam, defense of final project
- Vyučovací jazyk
- Angličtina
- Další komentáře
- Předmět je dovoleno ukončit i mimo zkouškové období.
- Statistika zápisu (nejnovější)
- Permalink: https://is.slu.cz/predmet/fu/leto2024/ETFNSP0006