# 714-0552/01 – 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
PRA76 Ing. Pavel Praks, Ph.D.
VLC20 doc. RNDr. Jaroslav Vlček, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 0+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

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.FormStudy language Tut. centreYearWSType of duty
2005/2006 (M2110) Geological Engineering (2101T003) Geological Engineering P Czech Ostrava 3 Compulsory study plan
2004/2005 (M2111) Hornictví (2101T008) Mining Engineering P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2110) Geological Engineering (2101T003) Geological Engineering P Czech Ostrava 3 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (3904T005) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (2102T006) Water Technology and Management P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2004/2005 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (3902T033) systems Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2004/2005 (M3646) Geodézie a kartografie (3602T002) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2004/2005 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (3902T006) Automation and Computers in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2102) Mineral Raw Materials (2102T012) Utilization of building raw-materials resources P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2111) Hornictví (2101T008) Mining Engineering P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2110) Geological Engineering (2101T003) Geological Engineering P Czech Ostrava 3 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (3904T005) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (2102T012) Utilization of building raw-materials resources P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (2102T009) Industrial treatment technologies P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (2102T006) Water Technology and Management P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2003/2004 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Compulsory study plan
2003/2004 (M3646) Geodézie a kartografie (3646T001) Mine Surveying P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (3902T006) Automation and Computers in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2102) Mineral Raw Materials (3902T033) systems Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2003/2004 (M3646) Geodézie a kartografie (3602T002) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2003/2004 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2111) Hornictví (2101T008) Mining Engineering P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (3904T005) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (2102T012) Utilization of building raw-materials resources P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (2102T009) Industrial treatment technologies P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (3902T006) Automation and Computers in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (2102T006) Water Technology and Management P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (3902T033) systems Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2002/2003 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2002/2003 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Compulsory study plan
2002/2003 (M3646) Geodézie a kartografie (3602T002) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2002/2003 (M3646) Geodézie a kartografie (3646T001) Mine Surveying P Czech Ostrava 2 Compulsory study plan
2002/2003 (M3908) Fire Protection and Industrial Safety (3908T002) Safety Engineering P Czech Ostrava 2 Compulsory study plan
2002/2003 (M3908) Fire Protection and Industrial Safety (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2111) Hornictví (2101T008) Mining Engineering P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (3904T005) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (2102T012) Utilization of building raw-materials resources P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (3902T006) Automation and Computers in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (2102T006) Water Technology and Management P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (3902T033) systems Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2001/2002 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2001/2002 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Compulsory study plan
2001/2002 (M3646) Geodézie a kartografie (3602T002) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2001/2002 (M3908) Požární ochrana a průmyslová bezpečnost (3908T002) Industrial Safety Engineering P Czech Ostrava 2 Compulsory study plan
2001/2002 (M3908) Požární ochrana a průmyslová bezpečnost (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2111) Hornictví (2101T008) Mining Engineering P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2110) Geological Engineering (2101T003) Geological Engineering P Czech Ostrava 3 Compulsory study plan
2000/2001 (M2102) Mineral Raw Materials (3904T005) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2102) Mineral Raw Materials (3904T022) Waste Treatment and Disposal P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2102) Mineral Raw Materials (2102T012) Utilization of building raw-materials resources P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2102) Mineral Raw Materials (2102T009) Industrial treatment technologies P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2102) Mineral Raw Materials (3902T006) Automation and Computers in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry K Czech Ostrava 2 Compulsory study plan
2000/2001 (M2102) Mineral Raw Materials (2102T001) Economics Management in Raw Materials treatment Industry P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2102) Mineral Raw Materials (2102T006) Water Technology and Management P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2102) Mineral Raw Materials (3902T033) systems Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2102) Mineral Raw Materials (3911T001) Applied Physics of Materials P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2102) Mineral Raw Materials (2102T003) Commerce Engineering in Raw Materials Treatment Industry P Czech Ostrava 2 Compulsory study plan
2000/2001 (B3646) Geodesy and Cartography (3646R006) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2000/2001 (M3646) Geodézie a kartografie (3646T001) Mine Surveying P Czech Ostrava 2 Compulsory study plan
2000/2001 (M3646) Geodézie a kartografie (3646T007) Geodesy Engineering P Czech Ostrava 2 Compulsory study plan
2000/2001 (M3646) Geodézie a kartografie (3602T002) Geoinformatics P Czech Ostrava 2 Compulsory study plan
2000/2001 (M3908) Požární ochrana a průmyslová bezpečnost (3908T002) Industrial Safety Engineering P Czech Ostrava 2 Compulsory study plan
2000/2001 (M3908) Požární ochrana a průmyslová bezpečnost (3908T006) Fire Protection Engineering and Industrial Safety P Czech Ostrava 2 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner