Course detail

# Discrete Methods in Civil Engineering I

FAST-DA58OptionalDoctoral (3rd cycle)Acad. year: 2017/2018Summer semester1. year of study4  credits

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.

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.

Mode of delivery

20 % face-to-face, 80 % distance learning

Prerequisites

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

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Saber, Elaydi, N.: An Introduction to Difference Equations. Springer-Verlag 2010

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction

Czech

Work placements

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.

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.

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer