Course: Numerical Methods I

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Course title Numerical Methods I
Course code UF/TF518
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • LICHARD Peter, prof. Ing. DrSc.
  • ADÁMEK Karel, Mgr.
Course content
Accuracy. Rounding errors and numerical methods. Representation of numbers in a computer. Strategy of reducing errors. Computational aspects. Programming languages, program libraries. Making graphs. Solution of algebraic equations. The system of linear algebraic equations, Gauss elimination method. General algebraic equation. The method of dividing interval, secant method, Newton's method, iteration. Newton's method in case of multiple roots and of a system of equations with more unknowns. Approximation of functions. Interpolation polynomials (Lagrange, Hermite). Instability of extrapolation. Aproximations of the Chebyshev type (method of minimizing the maximum error). Definition and properties of Chebyshev polynomials. Chebyshev interpolation. Padé approximation. Splines in general, 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 using Lagrange interpolation and Taylor expansion. 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). Evaluation of the main-value integral.

Learning activities and teaching methods
Students' self-study, Lectures, tutorial sessions, regularly assigned and evaluated home tasks.
Recommended literature
  • Marčuk, G.I. - Přikryl, P. - Segeth, K. Metody numerické matematiky. Academia, 1987.
  • Nekvinda, M. - Šrubař, J. - Vild, J. Úvod to numerické matematiky. SNTL, 1976.
  • Přikryl, P. Numerické metody matematické analýzy. SNTL, 1988.
  • Ralston, A. Základy numerické matematiky. Academia, 1978.
  • Riečanová, Z. Numerické metódy a matematická štatistika. SNTL, 1987.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Philosophy and Science in Opava Theoretical Physics (2) Physics courses - Winter