UIINP16 Numerical Methods

Faculty of Philosophy and Science in Opava
Summer 2024
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Petra Nábělková, Ph.D. (lecturer)
RNDr. Lenka Rucká, Ph.D. (seminar tutor)
RNDr. Šárka Vavrečková, Ph.D. (assistant)
Guaranteed by
RNDr. Petra Nábělková, Ph.D.
Institute of Computer Science – Faculty of Philosophy and Science in Opava
Timetable
Tue 8:05–9:40 R2
  • Timetable of Seminar Groups:
UIINP16/A: Wed 9:45–11:20 R2, L. Rucká
Prerequisites
Mathematical Analysis II
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 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. ISBN 80-210-2202-7. 1999. info
  • R, Kučera. Numerické metody. Ostrava. ISBN 80-248-1198-7. info
  • J. Segethová. Základy numerické matematiky. Karolinum, Praha. ISBN 80-7184-596-5. 1998. info
    recommended literature
  • BURDEN, R. L. and J. D. FAIRES. Numerical analysis. Boston, USA. ISBN 978-0-538-73351-9. 2011. info
  • VITÁSEK, E. Numerické metody. SNTL, Praha, 1987. info
  • Z. Riečanová a kol. Numerické metody a matematická štatistika. Alfa, Bratislava. ISBN 063-559-87. 1987. 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)
Study Materials
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 2020, Summer 2021, Summer 2022, Summer 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.slu.cz/course/fpf/summer2024/UIINP16