Course detail

Mathematics 5 (E)

FAST-CA005Acad. year: 2022/2023

Parametric and non-parametric problems with one and two random samples, analysis of relationships, regression analysis, introduction to time series. Use of the EXCEL program.
Errors in numeric calculation. Solving the f(x)=0 equation by graphic and bisection methods. Contraction theorem and solving an f(x)=0 equation by the simple iteration and Newton methods. Iteration methods used to solve systems of linear equations. Interpolating functions by polynomials and cubic splines. Numeric differentiation. Numeric integration.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

prof. Ing. Jiří Vala, CSc.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Knowledge of using the statistical programs to apply statistics in regression, analysis of relationships and time series. Knowledge of numerical methods to solve non-linear equations, systems of linear equations, to interpolate functions by polynomials, to differentiate and integrate numerically.

Prerequisites

Elementary notions of the theory of one- and more-functions (derivative, partial derivative, limit, continuity, graphs of functions). Calculating integrals of one-functions, knowing about their basic applications. The basics of the theory of probability and statistics.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

1. Parametric problems with one random sample.
2. Parametric problems with two random samples.
3. Non-parametric tests. Goodness-of-fit tests.
4. Analysis of relationships.
5. Regression analysis.
6. Time series. Descriptive characteristics of a time series.
7. Estimating the trend and seasonal components of a time series.
8. Error in numeric calculation. Method of bisection. Contraction theorem.
9. Solving f(x)=0 by iteration methods. Norms of matrices and vectors.
10. Iteration methods used to solve systems of linear equations.
11. Interpolating functions by polynomials and cubic splines.
12. Numeric differentiating.
13. Numeric integration.

Work placements

Not applicable.

Aims

Students will learn how to use the EXCEL and STATISTICA programs to apply statistics, study the basic notions of regression, analysis of relationships, analysis of time series. Next they will acquaint themselves with the methods used to solve non-linear equations, iteration methods used to solve systems of linear and non-linear equations, to interpolate functions by polynomials and cubic splines, learning how to numerically differentiate, solve boundary problems in second order ordinary differential equations by the method of grids and by numeric integration.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

DALÍK, Josef. Numerická analýza. Brno: Akademické nakladatelství CERM, 2010. ISBN 978-80-7204-702-4
DALÍK, Josef. Numerická analýza. Brno: Akademické nakladatelství CERM, 2010. ISBN 978-80-7204-702-4
WONNACOTT, Thomas H a Ronald J WONNACOTT. Statistika pro obchod a hospodářství. Praha: Victoria Publishing, 1998.

Recommended reading

CYHELSKÝ, Lubomír, HUSTOPECKÝ, Jiří a ZÁVODSKÝ, Prokop. Příklady k teorii statistiky. Praha: SNTL, 1988.
DALÍK, Josef. Numerické metody. Brno: Akademické nakladatelství CERM, 1997. ISBN 80-214-0646-1¨
SCHEID, Francis. Numerical Analysis. New York: McGraw-Hill, 1988.
WALPOLE, R. E. et al. Probability and Statistics for Engineers and Scientists, 9th edition. Boston: Pearson Education, Inc., ISBN 978-0-321-62911-12011.

Classification of course in study plans

  • Programme N-P-C-SI Master's

    branch N , 1 year of study, winter semester, compulsory

  • Programme N-K-C-SI Master's

    branch N , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Jiří Vala, CSc.

Syllabus

1. Parametric problems with one random sample. 2. Parametric problems with two random samples. 3. Non-parametric tests. Goodness-of-fit tests. 4. Analysis of relationships. 5. Regression analysis. 6. Time series. Descriptive characteristics of a time series. 7. Estimating the trend and seasonal components of a time series. 8. Error in numeric calculation. Method of bisection. Contraction theorem. 9. Solving f(x)=0 by iteration methods. Norms of matrices and vectors. 10. Iteration methods used to solve systems of linear equations. 11. Interpolating functions by polynomials and cubic splines. 12. Numeric differentiating. 13. Numeric integration.

Exercise

13 hod., compulsory

Teacher / Lecturer

prof. Ing. Jiří Vala, CSc.

Syllabus

1. Graphical methods of data files representation I. 2. Graphical methods of data files representation II. 3. Computational methods of data processing I. 4. Computational methods of data processing II. 5. Summary of survey analysis of one-dimensional populations. 6. Two-dimensional data files. 7. Linear regression. 8. Nonlinear regression. 9. Linear forecasting. 10. Multiple correlation and regression. 11. Numerical solutions of nonlinear equations and systems of linear equations. 12. Interpolation. Numeric differentiating. 13. Numeric integration. Seminar evaluation.