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Numerical Methods

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code470-2501/03
Number of ECTS Credits Allocated6 ECTS credits
Type of Course Unit *Optional
Level of Course Unit *First Cycle
Year of Study *Third Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites
PrerequisitiesCourse Unit CodeCourse Unit Title
470-2210Numerical Linear Algebra 1
Name of Lecturer(s)Personal IDName
LUK76doc. Ing. Dalibor Lukáš, Ph.D.
In this course numerical methods for selected problems of mathematical analysis are tought. We shall also prove convergence rates and present efficient implementation.
Learning Outcomes of the Course Unit
Numerical methods stands behind computer solutions to complex engineering problems. The course Numerical Methods 1 aims at helping students to choose a proper algorithm for the solution of selected problems of Calculus and analyze the solution regarding stability (sensitivity of the output data on the inputs) and computational complexity.
Course Contents
I. Data fitting: Lagrange interpolation, Chebyshev interpolation, least squares approximation, polynomial regression, orthogonal systems of polynomials (Legendre, Laguerre, Hermite), fast Fourier transform.

II. Numerical integration: Newton-Cotes quadrature, Gauss quadrature (Gauss-Legendre, Gauss-Laguerre, Gauss-Hermite).

III. Iterative methods for solution of nonlinear equations: bisection, fixed-point iterations, Newton method.

IV. Numerical solution to ordinary differential equations: one-step Euler, Crank-Nicholson, and Runge-Kutta methods, multi-step methods, predictor-corrector methods, Galerkin methods, parareal methods.
Recommended or Required Reading
Required Reading:
- O. Steinbach, Numerische Mathematik 1. TU Graz, 2005.
- A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics. Springer, 2007.
- D. Lukáš, Numerické metody 1 - zápisky a programy z přednášek. VŠB-TU Ostrava,
- A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics. Springer, 2007.
Recommended Reading:
- W.H. Press, B.P. Flannery, S.A. Teukolski, W.T. Vetterling, Numerical Recipes in C. Cambridge University Press, 1990.
- V. Vondrák, L. Pospíšil, Numerické metody 1. VŠB-TU Ostrava,
- O. Steinbach, Numerische Mathematik 1. TU Graz, 2005.
Planned learning activities and teaching methods
Lectures, Tutorials, Project work
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit30 15
        ExaminationExamination70 21