Course Details

Discrete Methods in Civil Engineering I

Academic Year 2023/24

DA58 course is part of 12 study plans

​ D-P-C-SI (N) / PST Summer Semester 1st year

​ D-P-C-SI (N) / FMI Summer Semester 1st year

​ D-P-C-SI (N) / KDS Summer Semester 1st year

​ D-P-C-SI (N) / MGS Summer Semester 1st year

​ D-P-C-SI (N) / VHS Summer Semester 1st year

​ D-K-C-SI (N) / VHS Summer Semester 1st year

​ D-K-C-SI (N) / MGS Summer Semester 1st year

​ D-K-C-SI (N) / PST Summer Semester 1st year

​ D-K-C-SI (N) / FMI Summer Semester 1st year

​ D-K-C-SI (N) / KDS Summer Semester 1st year

​ D-K-C-GK / GAK Summer Semester 1st year

​ D-K-E-SI (N) / PST Summer Semester 1st year

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.

Credits

4 credits

Language of instruction

Czech

Semester

summer

Course Guarantor

prof. RNDr. Josef Diblík, DrSc.

Institute

Institute of Mathematics and Descriptive Geometry

Forms and criteria of assessment

course-unit credit

Entry Knowledge

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

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.

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)

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)

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.

Prerequisites

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

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

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

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/272121

Lecture

13 weeks, 3 hours/week, elective

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.