Course: Numerical Methods

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Course title Numerical Methods
Course code MU/10136
Organizational form of instruction Lecture
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • BLASCHKE Petr, Mgr. Ph.D.
Course content
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.

Learning activities and teaching methods
Recommended literature
  • E. Vitásek. Numerické metody. SNTL, Praha, 1987.
  • I. Horová. Numerické metody. Masarykova univerzita v Brně, Brno, 1999. ISBN 80-210-2202-7.
  • J. Segethová. Základy numerické matematiky. Karolinum, Praha, 1998. ISBN 80-7184-596-5.
  • Z. Riečanová a kol. Numerické metody a matematická štatistika. Alfa, Bratislava, 1987. ISBN 063-559-87.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Philosophy and Science in Opava Computer Science and Technology (1) Electrical engineering, telecommunication and IT - Summer
Mathematical Institute in Opava Mathematical Methods in Economics (2) Economy 2 Summer
Mathematical Institute in Opava Applied Mathematics in Risk Management (3) Mathematics courses 2 Summer
Mathematical Institute in Opava Mathematical Methods in Economics (3) Economy 2 Summer