714-0587/01 – Numerical Methods and Statistics (NMaS)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 5 Subject guarantor doc. Dr. Mgr. Ivan Kolomazník Subject version guarantor doc. Dr. Mgr. Ivan Kolomazník Study level undergraduate or graduate Requirement Choice-compulsory Year 1 Semester summer Study language Czech Year of introduction 1999/2000 Year of cancellation 2009/2010 Intended for the faculties HGF Intended for study types Bachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KOL70 doc. Dr. Mgr. Ivan Kolomazník
PRA76 Ing. Pavel Praks, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

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, roots of polynomials. Numerical solution of systems of linear algebraic equations: LU-factorization, iterative methods, condition number of matrix, ill-conditioned matrices. Numerical solution of systems of nonlinear equations: Fixed-point iteration, Newton’s method. Interpolation and approximation of functions: Polynomial interpolation, interpolation by cubic spline functions, least squares approximation. Numerical integration: Trapezoid rule, Simpson’s rule, Richardson extrapolation, Monte Carlo method. Characteristics of population and sample, measures of central tendency, measures of dispersion and skewness, sampling distributions, point estimate, confidence interval, moment method, maximum likelihood method, testing hypotheses.

Compulsory literature:

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

Recommended literature:

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

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

Full-time 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
Project Project 5  0
Written exam Written test 15  0
Examination Examination 80 (80) 0
Written examination Written examination 60  0
Oral Oral examination 20  0
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2006/2007 (M3646) Geodézie a kartografie (3602T002) Geoinformatics P Czech Ostrava 4 Choice-compulsory study plan
2006/2007 (N3646) Geodesy and Cartography (3602T002) Geoinformatics (10) P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2102) Mineral Raw Materials (2102T012) Management of Resource of Building Mineral Raw Materials P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2102) Mineral Raw Materials (3902R033) System Engineering in Raw Materials Industry P Czech Ostrava 2 Choice-compulsory study plan

Occurrence in special blocks

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