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
The subject knowledge in mathematics on the Bachelor´s and Magister´s degree level is requested.
Recommended optional programme components
Recommended or required reading
Saber, Elaydi, N.: An Introduction to Difference Equations. Springer-Verlag 2010
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Language of instruction
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.
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
39 hours, optionally
Teacher / Lecturer