Skip to main content
Skip header

Numerical methods and statistics

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code310-2220/01
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *Second Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
KUC14prof. RNDr. Radek Kučera, Ph.D.
KRC76Mgr. Jiří Krček
Summary
The course is devoted to basic numerical methods of the linear algebra and mathematical analysis and to basic methods of analysing statistical data. The following themes will be presented: iterative methods for solving of nonlinear equations, direct and iterative methods for solving of linear systems, eigenvalue problems, interpolation and approximation of functions, numerical computation of derivatives and integrals, solving of ordinary differential equations, estimations of statistical parameters and
testing of hypotheses. The programming system Matlab is used during the course.
Learning Outcomes of the Course Unit
The aim of this course is to acquaint students with the numerical solution of mathematical problems and with the basic methods of analysing statistical data. The main accent lays in explanations of fundamental principles of methods so that the students should know to choose appropriate methods for problems arising in the other courses of the study or in the technical practice. An important ingredient of the course consists in the algorithmic implementation of methods and in the utilization of existing computer programms for numerical computations and statistical analyses.

The graduate of this course should know:

• to recognize problems suitable for solving by numerical procedures and to find an appropriate numerical method;
• to decide whether the computed solution is sufficiently accurate and, in case of need, to assess reasons of inaccuracies;
• to propose an algorithmic procedure for solving the problem and to choice a suitable computer environment for its realization.
Course Contents
1st Course contents, the issue of errors, stability of calculations.
2nd Solution of nonlinear equations, separation of roots, the simplest methods.
3rd Newton's method and fixed-point iterations.
4th Direct methods for solving linear equations, Gaussian elimination and LU-decomposition.
5th Eigenvalues and eigenvectors, numerical calculation.
6th Iterative methods for solving linear equations.
7th Interpolation by polynomials and splines.
8th Least squares approximation.
9th Numerical differentiation and integration.
10th Extrapolation in the calculation of integrals. Gaussian integration formulas.
11th One-step methods for solving initial value problems for ordinary differential equations.
12th Multi-step methods.
13th Statistical data processing, empirical characteristics.
14th Parameter estimation and testing of hypotheses.
Recommended or Required Reading
Required Reading:
1. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007.
1. Kučera, R.: Numerické metody, Skriptum VŠB-TU Ostrava, 2007. (na http://mdg.vsb.cz/M/)
2. Otipka, P., Šmajstrla, V.: Pravděpodobnost a statistika. Skriptum VŠB-TU Ostrava, 2007. (na http://mdg.vsb.cz/M/)
3. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007.
Recommended Reading:
1. Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003.
2. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper
Saddle River, NJ 07459, 1999.
1. Kubíček, M., Dubcová, M., Janovská, D.: Numerické metody a algoritmy. 2. vyd., VŠCHT Praha 2005.
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit20 5
        ExaminationExamination80 (80)30
                Písemná zkouškaWritten examination60 25
                Ústní zkouškaOral examination20 5