Course detail

# Discrete Methods in Civil Engineering I

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

Basic notions and methods of investigation of discrete equations.
a) Discrete calculus (some difference relations based on corresponding continuous relations).
b)Difference equations and systems.
c)Basic notions used in difference equations.
d)Equilibrium points, periodic points, eventually equilibrium points and eventually periodic points.
e)Stability of solution, repelling and attracting points and their illustration on examples.
f)Algorithms of solutions of systems of discrete equations and equations of higher-order, the case of constant coefficients.
g)The method of variation of parameters.
h)The method of variation of constants.
i)Transformation of some nonlinear equations into linear equations. j)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)

Farlow, S.J.: An Introduction to Diﬀerential Equations, Dover Publications, 2006 (EN)

Lakshmikantham, V., Trigiante, Donato: Theory of Diﬀerence Equations, Numerical Methods and Applications, Second Edition, Marcel Dekker, 2002

(EN)

Classification of course in study plans

• Programme D-P-C-SI (N) Doctoral

branch PST , 1. year of study, summer semester, compulsory-optional

• Programme D-K-E-SI (N) Doctoral

branch PST , 1. year of study, summer semester, compulsory-optional

• Programme D-P-E-SI (N) Doctoral

branch PST , 1. year of study, summer semester, compulsory-optional

• Programme D-K-C-SI (N) Doctoral

branch PST , 1. year of study, summer semester, compulsory-optional

• Programme D-K-E-SI (N) Doctoral

branch MGS , 1. year of study, summer semester, compulsory-optional

• Programme D-P-E-SI (N) Doctoral

branch MGS , 1. year of study, summer semester, compulsory-optional

• Programme D-K-C-SI (N) Doctoral

branch KDS , 1. year of study, summer semester, compulsory-optional

• Programme D-P-C-SI (N) Doctoral

branch KDS , 1. year of study, summer semester, compulsory-optional
branch MGS , 1. year of study, summer semester, compulsory-optional

• Programme D-K-C-SI (N) Doctoral

branch MGS , 1. year of study, summer semester, compulsory-optional

• Programme D-P-C-SI (N) Doctoral

branch FMI , 1. year of study, summer semester, compulsory-optional

• Programme D-P-E-SI (N) Doctoral

branch FMI , 1. year of study, summer semester, compulsory-optional

• Programme D-K-E-SI (N) Doctoral

branch FMI , 1. year of study, summer semester, compulsory-optional

• Programme D-K-C-SI (N) Doctoral

branch FMI , 1. year of study, summer semester, compulsory-optional

• Programme D-P-E-SI (N) Doctoral

branch KDS , 1. year of study, summer semester, compulsory-optional

• Programme D-K-E-SI (N) Doctoral

branch KDS , 1. year of study, summer semester, compulsory-optional

• Programme D-K-C-SI (N) Doctoral

branch VHS , 1. year of study, summer semester, compulsory-optional

• Programme D-K-E-SI (N) Doctoral

branch VHS , 1. year of study, summer semester, compulsory-optional

• Programme D-P-C-SI (N) Doctoral

branch VHS , 1. year of study, summer semester, compulsory-optional

• Programme D-P-E-SI (N) Doctoral

branch VHS , 1. year of study, summer semester, compulsory-optional

• Programme D-K-C-GK Doctoral

branch GAK , 1. year of study, summer semester, compulsory-optional

• Programme D-P-C-GK Doctoral

branch GAK , 1. year of study, summer semester, compulsory-optional

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer

Syllabus

Basic notions and methods of investigation of discrete equations. a) Discrete calculus (some difference relations based on corresponding continuous relations). b)Difference equations and systems. c)Basic notions used in difference equations. d)Equilibrium points, periodic points, eventually equilibrium points and eventually periodic points. e)Stability of solution, repelling and attracting points and their illustration on examples. f)Algorithms of solutions of systems of discrete equations and equations of higher-order, the case of constant coefficients. g)The method of variation of parameters. h)The method of variation of constants. i)Transformation of some nonlinear equations into linear equations. j)Difference equations modelled with the aid of sampling.