Course Details

Discrete Methods in Civil Engineering I

DA58 course is part of 22 study plans

Ph.D. full-t. program nD > PST compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nD > FMI compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nD > MGS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nD > VHS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nD > KDS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDK > PST compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDK > KDS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDK > VHS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDK > FMI compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDK > MGS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nDA > PST compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nDA > FMI compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nDA > MGS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nDA > VHS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program nDA > KDS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDKA > PST compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDKA > FMI compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDKA > MGS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDKA > VHS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program nDKA > KDS compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program I > GAK compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program IK > GAK compulsory-elective Summer Semester 1st year 4 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.

Course Guarantor

prof. RNDr. Josef Diblík, DrSc.

Institute

Institute of Mathematics and Descriptive Geometry

Learning outcomes

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.

Prerequisites

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

Planned educational activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Objective

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

Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.

Lecture

3 hours/week, 13 weeks, elective

Syllabus of lectures

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.