Course detail

Discrete Methods in Civil Engineering 1

FAST-DAB029Acad. year: 2022/2023

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

Mode of study

Not applicable.

Guarantor

prof. RNDr. Josef Diblík, DrSc.

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

Diblík, Diskrétní metody ve stavebnictví I, studijní materiál, 82 stran (CS)
Elaydi, Saber N., An Introduction to Diﬀerence Equations, Third Edition, Springer, 2005 (EN)
Michael A. Radin, Difference Equations For Scientists And Engineering: Interdisciplinary Difference Equations, ‎ World Scientific, 2019 (EN)

Type of course unit

Lecture

39 hod., optionally

Teacher / Lecturer

prof. RNDr. Josef Diblík, DrSc.

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.

VUT

Faculties

University Institutes

Parts

Discrete Methods in Civil Engineering 1

Type of course unit