714-0052/02 – Numerical Methods and Statistics (NMaS)

Gurantor department	Department of Mathematics and Descriptive Geometry	Credits	3
Subject guarantor	doc. RNDr. Zdeněk Boháč, CSc.	Subject version guarantor	doc. RNDr. Zdeněk Boháč, CSc.
Study level	undergraduate or graduate	Requirement	Compulsory
Year	2	Semester	winter
		Study language	Czech
Year of introduction	1999/2000	Year of cancellation	2004/2005
Intended for the faculties	FBI	Intended for study types	Master

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
BOH10	doc. RNDr. Zdeněk Boháč, CSc.

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Part-time	Credit and Examination	14+0

Subject aims expressed by acquired skills and competences

This course is closed.

Teaching methods

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:

[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. ISBN 0-07-112922-7 [3] Stoer, J., Burlish, R.: Introduction to Numerical Analysis. Springer-Verlag, New York, Berlin, Heidelberg 1992. ISBN 0-387-97878-X [4] Triola, Mario, F.: Elementary Statistics. Benjamin/Cummings Publ. Comp., Inc., Redwood City, California 1989.

Recommended literature:

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 úlohy, numerická stabilita algoritmu. Metody řešení algebraických a transcendentních rovnic Separace kořenů, metoda půlení intervalu, metoda regula - falsi, Newtonova metoda, iterační metoda. Podmínky konvergence. Řešení soustav lineárních rovnic Normy matic, podmíněnost matic. LU rozklad. Metoda prosté iterace, Seidelova iterační metoda, podmínky konvergence. Interpolace a aproximace funkcí Polynomiální interpolace, interpolace pomocí spline funkcí. Aproximace metodou nejmenších čtverců. Numerická kvadratura Lichoběžníková a Simpsonova metoda, Rombergova integrace, Richardsonova extrapolace. Zpracování statistického souboru s jedním a více argumenty Určení empirických charakteristik statistického souboru s jedním a více argumenty, korelační a regresní analýza. Odhady parametrů a testování hypotéz Momentová metoda, metoda maximální věrohodnosti, intervaly spolehlivosti.

Conditions for subject completion

Part-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
Other task type	Other task type	20	0	3
Examination	Examination	80 (80)	0	3
Written examination	Written examination	60	0	3
Oral	Oral examination	20	0	3

Mandatory attendence participation:

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

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Occurrence in study plans

Academic year	Programme	Branch/spec.	Spec.	Zaměření	Form	Study language	Tut. centre	Year	W	S	Type of duty
2004/2005	(M3908) Fire Protection and Industrial Safety	(3908T006) Fire Protection Engineering and Industrial Safety			K	Czech	Ostrava	2			Compulsory	study plan
2003/2004	(M3908) Fire Protection and Industrial Safety	(3908T006) Fire Protection Engineering and Industrial Safety			K	Czech	Ostrava	2			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

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