470-6504/01 – Numerical Methods (NM)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantordoc. Ing. Dalibor Lukáš, Ph.D.Subject version guarantordoc. Ing. Dalibor Lukáš, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Web linkhttp://homel.vsb.cz/~luk76/Teaching/NM1Study languageCzech
Year of introduction2010/2011Year of cancellation
Intended for the facultiesFS, HGF, FEI, USP, FASTIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
HAS35 prof. RNDr. Jaroslav Haslinger, DrSc.
KOZ75 prof. Ing. Tomáš Kozubek, Ph.D.
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
VON15 doc. Mgr. Vít Vondrák, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 28+0
Combined Examination 28+0

Subject aims expressed by acquired skills and competences

The main aim of the course is to introduce the basic numerical algorithms to students. Students should be able to solve engineering problems using apropriate numerical method.Theoretical knowledge represented by error analysis and analysis of stability should help to select appropriate method from wide range of commercial and noncommercial libraries or to implement a new method.

Teaching methods

Lectures

Summary

Subject of lectures is description of basic numerical methods which are used for solution of problems in engineering.

Compulsory literature:

Quarteroni A., Sacco R., Saleri F.: Numerical mathematics, Springer, 2007 Press, W.H., Flannery, B.P., Teukolski, S.A., Vetterling, W.T.: Numerical Recipes in C. Cambridge University Press, Cambridge 1990.

Recommended literature:

Quarteroni A., Sacco R., Saleri F.: Numerical mathematics, Springer, 2007 Press, W.H., Flannery, B.P., Teukolski, S.A., Vetterling, W.T.: Numerical Recipes in C. Cambridge University Press, Cambridge 1990.

Way of continuous check of knowledge in the course of semester

E-learning

Another demands for student

There are no additional requirements.

Minimum knowledge requirements

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Topics: 1. Data fiting - Lagrange and Chebyshev interpolation, least-square method, polygonal regression, fast Fourier transform. 2. Numerical integration - Newton-Cotes, Gauss-Legendre, and Gauss-Hermite formula. 3. Iterative methods for linear systems - methods of Jacobi, Gauss-Seidel, Richardson, and the conjugate gradients method, preconditioning. 4. Iterative methods for nonlinear equations - bisection, fixed point iterations, Newton method. 5. Numerical solution of ordinary differential equations - one-step Euler and Crank-Nicholson methods, multi-step Runge-Kutta methods, predictor-corrector, Galerkin, and parareal methods.

Conditions for subject completion

Combined form (validity from: 2013/2014 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Scope of obligatory attendance:

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Occurrence in special blocks

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