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# Course detail

## Discrete Methods in Civil Engineering I

Course unit code: FAST-DA58
Type of course unit: optional
Level of course unit: Doctoral (3rd cycle)
Year of study: 1
Semester: summer
Number of ECTS credits:
 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.
 Course contents (annotation): 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.
 Recommended or required reading: 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 prof. RNDr. Josef Diblík, DrSc.

The study programmes with the given course