470-2501/02 – Numerical Methods (NM)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantordoc. Ing. Dalibor Lukáš, Ph.D.Subject version guarantordoc. Ing. Dalibor Lukáš, Ph.D.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year3Semesterwinter
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+10

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Lectures
Tutorials
Project work

Summary

In this course numerical methods for selected problems of mathematical analysis are tought. We shall also prove convergence rates and present efficient implementation.

Compulsory literature:

- O. Steinbach, Numerische Mathematik 1. TU Graz, 2005. - A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics. Springer, 2007.

Recommended literature:

- W.H. Press, B.P. Flannery, S.A. Teukolski, W.T. Vetterling, Numerical Recipes in C. Cambridge University Press, 1990.

Way of continuous check of knowledge in the course of semester

Průběžná kontrola studia: 2 průběžné písemné testy, každý za 0 - 10 bodů. Podmínky udělení zápočtu: Pro udělení zápočtu je zapotřebí 15 bodů.

E-learning

Další požadavky na studenta

Successful defense of semestral project of point value 0 - 20.

Prerequisities

Subject codeAbbreviationTitleRequirement
470-2102 MA 1 Mathematical Analysis I Recommended
470-2103 MA2 Mathematical Analysis II Recommended
470-2105 MAIT Mathematical Analysis for IT Recommended
470-2106 MA2PM Mathematical Analysis II Recommended
470-2201 LA1 Linear Algebra Recommended
470-2202 LA-IT Linear Algebra Recommended
470-2203 LAM Linear Algebra with Matlab Recommended

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lectures: Errors in numerical computations Solution of non-linear equations: fixed point theorem, Newton method Iterative solution of systems of linear equations Eigenvalues and eigenvectors Interpolation: polynomial, trigonometric, spline Approximation:least square method, Tchebyshev metod Numerical differentiation and quadrature Numerical solution of initial value problem for ordinary differential equations Projects: The aim of the projects is solution of practical problem using numerical methods and their comparison with exact solution. Project solution: Problem analysis and proposal of appropriate numerical solution Numerical solution Exact solution and comparison with numerical solution Discussion and conlusions Excercises: Introduction to Matlab Error estimation on examples, computing of computer epsilon Roots separation of nonlinear equations. Solution of nonlinear equations using bisection method, fixed point iterations and Newton method. Conditions of convergence. Solutions of systems of non-linear equations. Jacobi and Gauss-Seidel nad SOR methods for solution of systems of linear equations. Solution of systems of linear equations using steepest descent method and conjugate gradient method. Preconditioning. Methods for finding of characteristic polynomial. Power method for largest and smallest eigenvalues. Similarity transformations, Jacobi method, Givens, Housholder and Lanczos methods. Lagrange and Newton interpolating polynomial, piecewise linear and cubic spline functions. Least square method and normal equations. Systems of orthogonal functions. Numerical differentiations. Numerical quadrature: Newton-Cotes and Gauss formulae. Numerical solution of initial value problem for ordinary differntial equations: Euler method, Runge-Kutta method.

Conditions for subject completion

Combined form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 40  15
        Examination Examination 60  11
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P English Ostrava 3 Choice-compulsory study plan
2019/2020 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K English Ostrava 3 Choice-compulsory study plan
2018/2019 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P English Ostrava 3 Choice-compulsory study plan
2018/2019 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K English Ostrava 3 Choice-compulsory study plan
2017/2018 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P English Ostrava 3 Choice-compulsory study plan
2017/2018 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K English Ostrava 3 Choice-compulsory study plan
2016/2017 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P English Ostrava 3 Choice-compulsory study plan
2016/2017 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K English Ostrava 3 Choice-compulsory study plan
2015/2016 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P English Ostrava 3 Choice-compulsory study plan
2015/2016 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K English Ostrava 3 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner