UIINK16 Numerical Methods

Faculty of Philosophy and Science in Opava
Summer 2021
Extent and Intensity
12/0/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Petra Nábělková, Ph.D. (lecturer)
Guaranteed by
RNDr. Petra Nábělková, Ph.D.
Institute of Computer Science – Faculty of Philosophy and Science in Opava
Prerequisites
TYP_STUDIA(B)
Mathematical Analysis II
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The aim of this course is to acquaint students with basic numerical approaches to solving problems they have already encountered in mathematical analysis and algebra.
Learning outcomes
Students should understand the numerical approaches discussed and recognize the suitability of their choice where appropriate problems cannot be solved analytically, or. obtaining a solution in this way is extremely difficult.
Syllabus
  • 1. Numerical representation: representation of numbers, origin, and classification of errors, errors of arithmetic operations, the conditionality of problems and numerical stability of algorithms. 2. Interpolation: interpolation by algebraic polynomials - existence and uniqueness of interpolation polynomial, estimation of interpolation error, Lagrange, Newton and Hermit interpolation polynomial, interpolation on equidistant nodes. Spline interpolation.
  • 3. Approximation: a selection of approximating function class, least-squares method.
  • 4. Numerical solution of nonlinear equations: root separation, simple iteration method, interval bisection method, tangent method, mowing method, falsi regulation method.
  • 5. Numerical solution of systems of equations: direct-LU-decomposition methods, Gaussian elimination method, a partial and complete selection of the main element.
  • 6. Numerical integration: Newton-Cotes quadrature formulas, composite quadrature formulas, error estimation.
Literature
    required literature
  • I. Horová. Numerické metody. Masarykova univerzita v Brně, Brno, 1999. ISBN 80-210-2202-7. info
  • R, Kučera. Numerické metody. Ostrava. ISBN 80-248-1198-7. info
  • J. Segethová. Základy numerické matematiky. Karolinum, Praha, 1998. ISBN 80-7184-596-5. info
    recommended literature
  • BURDEN, R. L. and J. D. FAIRES. Numerical analysis. Boston, USA, 2011. ISBN 978-0-538-73351-9. info
  • VITÁSEK, E. Numerické metody. SNTL, Praha, 1987. info
  • Z. Riečanová a kol. Numerické metody a matematická štatistika. Alfa, Bratislava, 1987. ISBN 063-559-87. info
Teaching methods
Interactive lectures
Tutorials
Assessment methods
The written part of the exam is focused on numerical mastering of the curriculum. The oral part of the exam examines the understanding of the basic concepts and theories of the theory and their interrelations. Students should understand the numerical approaches discussed and recognize the suitability of their choice where appropriate problems cannot be solved analytically, or. obtaining a solution in this way is extremely difficult.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Information on the extent and intensity of the course: Přednáška 12 HOD/SEM.
The course is also listed under the following terms Summer 2020, Summer 2022, Summer 2023, Summer 2024, Summer 2025.
  • Enrolment Statistics (Summer 2021, recent)
  • Permalink: https://is.slu.cz/course/fpf/summer2021/UIINK16