714-0023/01 – Mathematics and Numerical Methods-PSP (MaNM)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits6
Subject guarantordoc. RNDr. Zdeněk Boháč, CSc.Subject version guarantordoc. RNDr. Zdeněk Boháč, CSc.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2002/2003Year of cancellation2006/2007
Intended for the facultiesFBIIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
BOH10 doc. RNDr. Zdeněk Boháč, CSc.
DOL30 doc. RNDr. Jarmila Doležalová, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Part-time Credit and Examination 24+0

Subject aims expressed by acquired skills and competences

This course is closed.

Teaching methods

Summary

Probability: probability of random events, independence of events, random variables, mean and variance, important distributions. Functions of several variables: partial differentiation, extremal values. Integral calculus of functions of two variables and its application. Line integral and its applications. 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: iterative methods. Interpolation and approximation of functions: Polynomial interpolation, least squares approximation. Numerical integration: Trapezoid rule, Simpson’s rule, Richardson extrapolation. Characteristics of population and sample, measures of central tendency, measures of dispersion and skewness, sampling distributions, point estimate, moment method, maximum likelihood Metod, confidence interval.

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:

Úvod do počtu pravděpodobnosti Základní pojmy z kombinatoriky, náhodný pokus a náhodný jev, definice pravděpodobnosti, nezávislé jevy a jejich pravděpodobnost, pojem náhodné veličiny, diskrétní náhodná veličina, pravděpodobnostní funkce a distribuční funkce diskrétní náhodné veličiny, spojitá náhodná veličina, hustota pravděpodobnosti a distribuční funkce, střední hodnota, rozptyl, rozdělení alternativní, binomické, Poissonovo, rovnoměrné, exponenciální, normální. Dvojrozměrné integrály Dvojrozměrný integrál v obdélníku, dvojrozměrný integrál v obecné uzavřené oblasti, transformace dvojrozměrných integrálů, použití dvojrozměrných integrálů. 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. Metoda prosté iterace, Seidelova iterační metoda, podmínky konvergence. Interpolace a aproximace funkcí Polynomiální interpolace, aproximace metodou nejmenších čtverců. Numerická kvadratura Lichoběžníková a Simpsonova metoda, Richardsonova extrapolace. Zpracování statistického souboru Určení empirických charakteristik statistického souboru s jedním argumentem, odhady parametrů, momentová metoda, metoda maximální věrohodnosti, intervaly spolehlivosti.

Conditions for subject completion

Part-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
                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.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2005/2006 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety (30) Fire Protection Engineering and Industrial Safety K Czech Ostrava 1 Compulsory study plan
2005/2006 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety (30) Fire Protection Engineering and Industrial Safety K Czech Praha 1 Compulsory study plan
2004/2005 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety (30) Fire Protection Engineering and Industrial Safety K Czech Ostrava 1 Compulsory study plan
2003/2004 (N3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety (30) Fire Protection Engineering and Industrial Safety K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner