Course detail

# Discrete Methods in Civil Engineering 1

The discipline is devoted to description of processes via discrete equations. It consists of three parts:
a) difference euquations of first-order,
b) diffeence equations of higher-order,
c) methods of solutions of difference equations.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

The ability to orientate in the basic notions and problems
of discrete and difference equations.
Solving problems in the areas cited in the annotation.

Prerequisites

The subject knowledge in mathematics on the Bachelor´s and Magister´s degree level is requested.

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. Basic notions and methods of investigation of discrete equations.
2. Discrete calculus (some difference relations based on corresponding continuous relations).
3. Difference equations and systems.
4. Basic notions used in difference equations.
5. Equilibrium points, periodic points, eventually equilibrium points and eventually periodic points.
6. Stability of solution, repelling and attracting points and their illustration on examples.
7. Algorithms of solutions of systems of discrete equations and equations of higher-order, the case of constant coefficients.
8. The method of variation of parameters.
9. The method of variation of constants.
10. Rovnice průhybu nosníku, řešení metodou diskrétních rovnic. Okrajové a počáteční podmínky.
11. Průhyb nosníku, řešení metodou diskrétních rovnic.
12.–13. Difference equations modelled with the aid of sampling.

Work placements

Not applicable.

Aims

Discrete and difference equations are the mathematical base of many fields of engineering science. The purpose of this course is to develop the basic notions concerning the properties of solutions of such equations and to give methods of their applications.

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

Not applicable.

Not applicable.

Classification of course in study plans

• Programme DPA-S Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKA-S Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPC-S Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKC-S Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPA-E Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPC-E Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKA-E Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKC-E Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKA-GK Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKC-GK Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPA-GK Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPC-GK Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPA-M Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKC-M Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKA-M Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPC-M Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPA-K Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKC-K Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKA-K Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPC-K Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPA-V Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DPC-V Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKA-V Doctoral, 1. year of study, summer semester, compulsory-optional
• Programme DKC-V Doctoral, 1. year of study, summer semester, compulsory-optional

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

Syllabus

1. Basic notions and methods of investigation of discrete equations. 2. Discrete calculus (some difference relations based on corresponding continuous relations). 3. Difference equations and systems. 4. Basic notions used in difference equations. 5. Equilibrium points, periodic points, eventually equilibrium points and eventually periodic points. 6. Stability of solution, repelling and attracting points and their illustration on examples. 7. Algorithms of solutions of systems of discrete equations and equations of higher-order, the case of constant coefficients. 8. The method of variation of parameters. 9. The method of variation of constants. 10. Rovnice průhybu nosníku, řešení metodou diskrétních rovnic. Okrajové a počáteční podmínky. 11. Průhyb nosníku, řešení metodou diskrétních rovnic. 12.–13. Difference equations modelled with the aid of sampling.