UFTF518 Numerical Methods I

Faculty of Philosophy and Science in Opava
Winter 2022
Extent and Intensity
3/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jan Schee, Ph.D. (lecturer)
doc. RNDr. Jan Schee, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jan Schee, Ph.D.
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
The aim of the course is to acquaint students with the numerical methods used in physics calculations as well as in the processing of experimental and observational data. Acquired knowledge is exercised by individual solving the problems on the computer, which includes the use of existing program libraries in more complex cases.
Syllabus
  • 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.
Literature
    recommended literature
  • Přikryl, P. Numerické metody matematické analýzy. SNTL, 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
  • Ralston, A. Základy numerické matematiky. Academia, 1978. info
  • Nekvinda, M. - Šrubař, J. - Vild, J. Úvod to numerické matematiky. SNTL, 1976. info
Teaching methods
Students' self-study
Lectures, tutorial sessions, regularly assigned and evaluated home tasks.
Assessment methods
Credit
Active participation on tutorial sessions and the timely completion of home tasks is required. Detailed criteria will be announced by the tutorial lecturer. The exam consists of the main written part and a supplemental oral part.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
The attending of lectures is recommended, that of tutorial sessions is compulsory. If a student was absent for serious reasons, the teacher may prescribe him/her an alternative way of fulfilling the duties.
The course is also listed under the following terms Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2023.
  • Enrolment Statistics (Winter 2022, recent)
  • Permalink: https://is.slu.cz/course/fpf/winter2022/UFTF518