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	4	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
Login	Name	Tuitor	Teacher giving lectures
KOL70	doc. Dr. Mgr. Ivan Kolomazník
PRA76	Ing. Pavel Praks, Ph.D.

Extent of instruction for forms of study
Form of study	Way 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.

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

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 name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Exercises evaluation and Examination	Credit and Examination	100 (100)	51	3
Exercises evaluation	Credit	20 (20)	0	3
Project	Project	5	0	3
Written exam	Written test	15	0	3
Examination	Examination	80 (80)	0	3
Written examination	Written examination	60	0	3
Oral	Oral examination	20	0	3

Mandatory attendence participation:

Show history

Conditions for subject completion and attendance at the exercises within ISP:

Show history

Occurrence in study plans

Academic year	Programme	Branch/spec.	Spec.	Form	Study language	Tut. centre	Year	Type 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

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner

Assessment of instruction

Předmět neobsahuje žádné hodnocení.