230-0265/01 – Numerical Methods (NM)

Gurantor departmentDepartment of MathematicsCredits10
Subject guarantordoc. Ing. Martin Čermák, Ph.D.Subject version guarantordoc. Ing. Martin Čermák, Ph.D.
Study levelpostgraduateRequirementCompulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction2020/2021Year of cancellation
Intended for the facultiesFASTIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
CER365 doc. Ing. Martin Čermák, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 28+0
Part-time Examination 28+0

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.

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

Part-time form (validity from: 2020/2021 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (P0732D260004) Civil Engineering P Czech Ostrava Compulsory study plan
2021/2022 (P0732D260004) Civil Engineering K Czech Ostrava Compulsory study plan
2020/2021 (P0732D260004) Civil Engineering K Czech Ostrava Compulsory study plan
2020/2021 (P0732D260004) Civil Engineering P Czech Ostrava Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner