# 714-0552/04 – Numerical Methods and Statistics (NMaS)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 Subject guarantor prof. RNDr. Radek Kučera, Ph.D. Subject version guarantor doc. Dr. Mgr. Ivan Kolomazník Study level undergraduate or graduate Requirement Compulsory Year 2 Semester winter Study language Czech Year of introduction 1999/2000 Year of cancellation 2005/2006 Intended for the faculties HGF Intended for study types Master
Instruction secured by
KOL70 doc. Dr. Mgr. Ivan Kolomazník
POL12 RNDr. Jiří Poláček, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Combined Credit and Examination 14+0

### 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. Numerical solution of systems of linear algebraic equations: LU-factorization, iterative methods, condition number of matrix, ill-conditioned matrices. Interpolation and approximation of functions: polynomial interpolation, interpolation by spline functions, least squares approximation. Numerical integration: Trapezoid rule, Simpson’s rule, Richardson extrapolation. Statistical processing data with one or more arguments, empirical characteristics of statistical data, testing of hypotheses. Regression analysis.

### Compulsory literature:

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

### Recommended 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. 3. 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

Combined 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
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.FormStudy language Tut. centreYearWSType of duty
2004/2005 (M2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry K Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry K Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry K Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry K Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry K Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry K Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal K Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry K Czech Ostrava 2 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner