ETFNSP0006 Numerical Methods in Physics

Fyzikální ústav v Opavě
léto 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.
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
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  • Statistika zápisu (nejnovější)
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