# 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 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
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.

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
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

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner