MU01136 Numerical Methods

Mathematical Institute in Opava
Summer 2022
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Petra Nábělková, Ph.D. (lecturer)
Guaranteed by
RNDr. Petra Nábělková, Ph.D.
Mathematical Institute in Opava
Timetable
Tue 13:05–14:40 R2
Prerequisites (in Czech)
MU01002 Mathematical Analysis II && NOW( MU01936 Numerical Methods - Exercises ) && ! MU10136 Numerical Methods && !NOW( MU10136 Numerical Methods ) && TYP_STUDIA(B)
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 (in Czech)
Cílem výuky tohoto předmětu je seznámit studenty se základními numerickými přístupy k řešení problémů, se kterými se již dříve setkali v matematické analýze a algebře.
Syllabus
  • 1. Numerical representation: representation of numbers, origin and classification of errors, errors of arithmetic operations, conditionality of tasks and numerical stability of algorithms.
    2. Interpolation: Algebraic polynomial interpolation-existence and uniqueness of polynomial interpolation, estimation of interpolation error, Lagrange, Newton and Hermit interpolating polynomials, interpolation on equidistant nodes. Spline interpolation.
    3. Approximation: choosing the class of approximating functions, least squares method.
    4. Numerical solution of nonlinear equations: roots separation, simple iteration method, bisection method, tangent method, secant methods, regula falsi.
    5. Numerical solution of systems of equations: Gauss elimination with control column, LU-decomposition, Jacobi method, Gauss-Seidel method.
    6. Numerical integration: Newton-Cotes quadrature formulas, error estimates.
Literature
    recommended literature
  • I. Horová. Numerické metody. Masarykova univerzita v Brně, Brno, 1999. ISBN 80-210-2202-7. info
  • J. Segethová. Základy numerické matematiky. Karolinum, Praha, 1998. ISBN 80-7184-596-5. 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
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020, Summer 2021.
  • Enrolment Statistics (recent)
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