470-2501/03 – 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 graduateRequirementCompulsory
Year3Semesterwinter
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFEIIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
STR0159 Ing. Erika Straková
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time 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

Test (10 pts.) Project (20 pts.)

E-learning

Other requirements

Successful defense of a semestral project. Students are familiar with fundamentals of differential and integral calculus in 1 dimension.

Prerequisities

Subject codeAbbreviationTitleRequirement
470-2203 LAM Linear Algebra with Matlab Recommended

Co-requisities

Subject has no co-requisities.

Subject syllabus:

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.

Conditions for subject completion

Part-time form (validity from: 2019/2020 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 30  15
        Examination Examination 70  21
Mandatory attendence parzicipation: bude doplněno

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (B0713A060005) Electrical Power Engineering P Czech Ostrava 3 Optional study plan
2020/2021 (B0541A170008) Computational and Applied Mathematics VMI P Czech Ostrava 3 Compulsory study plan
2020/2021 (B0541A170008) Computational and Applied Mathematics VMI K Czech Ostrava 3 Compulsory study plan
2019/2020 (B0541A170008) Computational and Applied Mathematics VMI P Czech Ostrava 3 Compulsory study plan
2019/2020 (B0541A170008) Computational and Applied Mathematics VMI K Czech Ostrava 3 Compulsory study plan
2019/2020 (B0713A060005) Electrical Power Engineering P Czech Ostrava 3 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner