Course Details

Discrete Methods in Civil Engineering 1

DAB029 course is part of 24 study plans

Ph.D. full-t. program DPC-S compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPC-M compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPC-K compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPC-V compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPC-E compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPC-GK compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKC-S compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPA-S compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKC-V compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPA-V compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKC-M compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPA-M compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKC-K compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPA-K compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKC-E compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPA-E compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKC-GK compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPA-GK compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKA-GK compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKA-S compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKA-M compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKA-K compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKA-V compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKA-E 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.

Corequisites

Not required.

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.

Forms and criteria of assessment

A student will only receive credit if he will solve individual problems assigned by the teacher. The examination will be only a written one lasting 90 minutes and consisting of 4 problems to calculate.

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

1. Basic notions and methods of investigation of discrete equations.
2. Discrete calculus (some difference relations based on corresponding continuous relations).
3. Difference equations and systems.
4. Basic notions used in difference equations.
5. Equilibrium points, periodic points, eventually equilibrium points and eventually periodic points.
6. Stability of solution, repelling and attracting points and their illustration on examples.
7. Algorithms of solutions of systems of discrete equations and equations of higher-order, the case of constant coefficients.
8. The method of variation of parameters.
9. The method of variation of constants.
10. Rovnice průhybu nosníku, řešení metodou diskrétních rovnic. Okrajové a počáteční podmínky.
11. Průhyb nosníku, řešení metodou diskrétních rovnic.
12.–13. Difference equations modelled with the aid of sampling.