UFTF518 Numerical Methods I

Faculty of Philosophy and Science in Opava
Winter 2013
Extent and Intensity
3/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. Ing. Peter Lichard, DrSc. (lecturer)
prof. Ing. Peter Lichard, DrSc. (seminar tutor)
Guaranteed by
prof. Ing. Peter Lichard, DrSc.
Centrum interdisciplinárních studií – Faculty of Philosophy and Science in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
To prepare students for effective and correct numerical solution of physical problems and learn how to use computers for numerical calculations.
Syllabus
  • Accuracy of calculations. Rounding errors and numerical methods. Representation of numbers in a computer. Strategy for reducing errors.
    Computational aspects. Programming languages ??, libraries programs. Making graphs.
    Solution of algebraic equations. The system of linear algebraic equations, Gauss elimination method. General algebraic equations. The method of dividing interval, secant method, Newton's method iteration. Newton's method in case of multiple roots of a system of equations with more unknowns.
    Approximation of functions. Interpolation polynomials (Lagrange, Hermite). Instability extrapolation. Chebyshev approximation type (method of minimizing the maximum error). Definition and properties of Chebyshev polynomials. Chebyshev interpolation. Padeh approximation. Splines, natural splines. The method of least squares. Physical motivation, hypothesis testing. Linear case: the system of normal equations, determining the parameters of hypotheses and their errors.
    The numerical calculation of derivatives. Calculation of derivatives by Lagrange interpolation. Richardson extrapolation.
    Numerical quadrature. Closed formulas of Newton and Cotes, trapezoidal and Simpson's method. Orthogonal polynomials, Gauss integration and the specific types (Legendre, Laguerre, Hermite, Jacobi, Chebyshev). Calculation of core values ??integral.
Literature
    recommended literature
  • Lindebaum, R. Gnuplot Tutorial. http://physicspmb.ukzn.ac.za/index.php/Gnuplot_tutorial. info
  • Virius, M. Programování v C++. Vydavatelství ČVUT, 1999. info
  • Přikryl, P. Numerické metody matematické analýzy. SNTL, 1988. info
  • Segethová, J. Základy numerické matematiky. Karolinum, 1988. info
  • Marčuk, G.I. - Přikryl, P. - Segeth, K. Metody numerické matematiky. Academia, 1987. info
  • Riečanová, Z. Numerické metódy a matematická štatistika. SNTL, 1987. info
  • Sedláček, V. - Sapák, O. Základy programování a programovací jazyk FORTRAN. SPN, 1984. info
  • Ralston, A. Základy numerické matematiky. Academia, 1978. info
  • Nekvinda, M. - Šrubař, J. - Vild, J. Úvod to numerické matematiky. SNTL, 1976. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
Teacher's information
* 60% attendance in seminars.
The course is also listed under the following terms Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022, Winter 2023.
  • Enrolment Statistics (Winter 2013, recent)
  • Permalink: https://is.slu.cz/course/fpf/winter2013/UFTF518