714-0552/03 – Numerical Methods and Statistics (NMaS)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits3
Subject guarantorprof. RNDr. Radek Kučera, Ph.D.Subject version guarantordoc. Dr. Mgr. Ivan Kolomazník
Study levelundergraduate or graduateRequirementCompulsory
Year2Semestersummer
Study languageCzech
Year of introduction1999/2000Year of cancellation2005/2006
Intended for the facultiesHGFIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
KOL70 doc. Dr. Mgr. Ivan Kolomazník
POL12 RNDr. Jiří Poláček, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Combined Credit and Examination 14+0

Subject aims expressed by acquired skills and competences

The aim of this course is to acquaint students with the numerical solution of mathematical problems that arise in the other courses of their study and in the technical practice. The main accent lays in explanations of fundamental principles of numerical methods with emphases their general properties. It should lead to the ability in concrete situations to decide whether a numerical procedure is a suitable tool for solving a particular problem. An important ingredient of the course consists in the algorithmic implementation and in the utilization of existing computer programs specialized for numerical computations.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

Basic problems of the numerical mathematics, errors in computations. Solving of equation f(x)=0: bisection method, regula-falsi, iterative method, Newton´s iteration. Numerical solution of systems of linear algebraic equations: LU-factorization, iterative methods, condition number of matrix, ill-conditioned matrices. Interpolation and approximation of functions: polynomial interpolation, interpolation by spline functions, least squares approximation. Numerical integration: Trapezoid rule, Simpson’s rule, Richardson extrapolation. Statistical processing data with one or more arguments, empirical characteristics of statistical data, testing of hypotheses. Regression analysis.

Compulsory literature:

1. Boháč, Zdeněk: Numerical Methods and Statistics, VŠB – TUO, Ostrava 2005, ISBN 80-248-0803-X

Recommended literature:

1. Forsythe, G., E., Malcolm, M.,A., Moler, B., C.: Computer Methods for Mathematical Computations. Prentice –Hall, Inc., Englewood Clifs, N.J. 07632, 1977. 2. Buchanan, J., L., Turner, P., R.: Numerical Method and Analysis. McGraw-Hill, Inc., New York, 1992. 3. Stoer, J., Burlish, R.: Introduction to Numerical Analysis. Springer-Verlag, New York, Berlin, Heidelberg, 1992.

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Problematika numerických výpočtů Zdroje a typy chyb. Podmíněnost úloh a algoritmů. Metody řešení algebraických a transcendentních rovnic Metoda půlení intervalu, iterační metoda řešení rovnic.Metoda Newtonova, metoda regula-falsi, kombinovaná metoda. Řešení soustav lineárních rovnic Přímé metody řešení. Iterační metody (Jacobiova, Seidelova). Norma matice. Interpolace a aproximace funkcí Aproximace - metoda nejmenších čtverců. Lagrangeův interpolační polynom, Newtonův interpolační polynom. Interpolace spline-funkcemi. Numerický výpočet integrálu Newton-Cotesovy kvadraturní vzorce. Složené kvadraturní vzorce. Odhad chyby. Richardsonova extrapolace. Počáteční úlohy pro obyčejné diferenciální rovnice Jednokrokové metody. Eulerova metoda. Odhad chyby metodou polovičního kroku. Metody Rungova-Kuttova typu. Odhad chyby aproximace. Zpracování statistického souboru s jedním argumentem Charakteristiky statistického souboru, zpracování rozsáhlého statistického souboru. Odhady parametrů základního souboru. Základní soubor, náhodný výběr, bodové a intervalové odhady parametrů základního souboru. Testy dobré shody Pearsonův test chí-kvadrát dobré shody. Kolmogorovův-Smirnovův test pro jeden výběr. Kolmogorovův-Smirnovův test pro dva výběry.

Conditions for subject completion

Combined form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 20 (20) 0
                Other task type Other task type 20  0
        Examination Examination 80 (80) 0
                Written examination Written examination 60  0
                Oral Oral examination 20  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2004/2005 (M2111) Hornictví (2101T008) Mining Engineering K Czech Ostrava 2 Compulsory study plan
2003/2004 (M2111) Hornictví (2101T008) Mining Engineering K Czech Ostrava 2 Compulsory study plan
2002/2003 (M2111) Hornictví (2101T008) Mining Engineering K Czech Ostrava 2 Compulsory study plan
2001/2002 (M2111) Hornictví (2101T008) Mining Engineering K Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner