ETFNSP0006 Numerical Methods in Physics

Institute of physics in Opava
summer 2024
Extent and Intensity
1/4/0. 7 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Stanislav Hledík, Ph.D. (lecturer)
doc. RNDr. Jan Schee, Ph.D. (lecturer)
doc. RNDr. Stanislav Hledík, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jan Schee, Ph.D.
Institute of physics in Opava
Prerequisites (in Czech)
(FAKULTA(FU)&&SOUHLAS)
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Students will learn fundamental numerical methods generally used in physics.
Learning outcomes
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.
Syllabus
  • 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.
Literature
    recommended literature
  • 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
Teaching methods
Lectures. Exercises. Working out given project.
Assessment methods
oral exam, defense of final project
Language of instruction
English
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Information on course enrolment limitations: Erasmus
  • Enrolment Statistics (recent)
  • Permalink: https://is.slu.cz/course/fu/summer2024/ETFNSP0006