MU10136 Numerical Methods

Mathematical Institute in Opava
Summer 2015
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
Prerequisites (in Czech)
MU10130 Mathematical Analysis II && MU10936 Numerical Methods - Exercises
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, absolute and relative error, cumulative error, errors of arithmetic operations).
    2. Approximation (choosing the class of approximating functions, least squares method).
    3. Interpolation (estimating interpolation error, iterated interpolation, Lagrange, Hermite and Newton polynomials, interpolation on equidistant nodes, Fraser diagram, inverse interpolation, splines).
    4. Numerical solution of nonlinear equations (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, Gauss-Seidl and Newton-Raphson methods, convergence of methods).
    6. Sturm sequence (localization of real roots of a polynomial, Sturm sequence).
    7. Numerical integration (numerical quadratire of definite integrals, rectangle, trapezoid and Simpson methods, error estimates).
    8. Numerical methods for differential equations (solving initial value problems for ordinary differential equations, power series solutions, Picard approcimations, Euler polygon, Runge-Kutta methods, order of a method).
    9. Mesh method for solution of boundary value problems for partial differential equations.
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 1998, Summer 1999, Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020, Summer 2021, Summer 2022.
  • Enrolment Statistics (Summer 2015, recent)
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