230-0265/02 – Numerical Methods (NM)
| Gurantor department | Department of Mathematics | Credits | 10 |
| Subject guarantor | doc. Ing. Martin Čermák, Ph.D. | Subject version guarantor | doc. Ing. Martin Čermák, Ph.D. |
| Study level | postgraduate | Requirement | Compulsory |
| Year | | Semester | winter + summer |
| | Study language | English |
| Year of introduction | 2020/2021 | Year of cancellation | |
| Intended for the faculties | FAST | Intended for study types | Doctoral |
Subject aims expressed by acquired skills and competences
The course aims to acquaint students with basic numerical methods for solving engineering problems so that they can use a suitable numerical method for a given type of problem and decide on its suitability based on the theoretical foundations of the method. The theoretical foundations represented by the analysis of errors and stability should then serve students to choose a suitable method from some commercial and freely available numerical methods packages. Students will try to modify basic numerical methods and their implementation in a programming language in this course.
Teaching methods
Lectures
Individual consultations
Summary
Compulsory literature:
V. Vondrák, L. Pospíšil, Numerické metody 1. VŠB-TU Ostrava, http://mi21.vsb.cz/modul/numericke-metody-1
O. Steinbach, Numerische Mathematik 1. TU Graz, 2005.
Recommended literature:
L. Čermák, I. Růžičková, R. Hlavička, Numerické metody, VUT Brno, http://physics.ujep.cz/~jskvor/NME/DalsiSkripta/Numerika.pdf
A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematic, Springer-Verlag New Yourk, Inc. 2000.
Additional study materials
Way of continuous check of knowledge in the course of semester
E-learning
Other requirements
Tests, semester project, consultations for the subject of dissertation thesis and the publications of the student, oral exams.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
• Errors in numerical calculations
• Solution of systems of nonlinear equations - fixed point theorem, bisection, Newton's method
• Iterative solution of systems of linear equations - Jacobi, Gauss-Seidel, Richardson method and method of combined gradients, preconditions
• Find eigenvalues and eigenvectors of matrices
• Interpolation - polynomial, trigonometric, splines
• Approximation - least squares method, Chebyshev's approximation
• Numerical derivation and quadrature
• Numerical solution of initial value problems for ordinary differential equations.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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