Course detail

Discrete Methods in Civil Engineering I

FAST-DA58Acad. year: 2024/2025

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.

Guarantor

prof. RNDr. Josef Diblík, DrSc.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Entry knowledge

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

Rules for evaluation and completion of the course

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

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

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

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

Recommended reading

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-K-C-SI (N) Doctoral

    branch VHS , 1 year of study, summer semester, compulsory-optional
    branch MGS , 1 year of study, summer semester, compulsory-optional
    branch PST , 1 year of study, summer semester, compulsory-optional
    branch FMI , 1 year of study, summer semester, compulsory-optional
    branch KDS , 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-K-E-CE (N) Doctoral

    branch FMI , 1 year of study, summer semester, compulsory-optional
    branch KDS , 1 year of study, summer semester, compulsory-optional
    branch MGS , 1 year of study, summer semester, compulsory-optional
    branch VHS , 1 year of study, summer semester, compulsory-optional
    branch PST , 1 year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

prof. RNDr. Josef Diblík, DrSc.

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.