Course detail
Discrete Methods in Civil Engineering 1
FAST-DAB029Acad. year: 2025/2026
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.
Language of instruction
Czech
Number of ECTS credits
4
Mode of study
Not applicable.
Guarantor
Department
Institute of Mathematics and Descriptive Geometry (MAT)
Entry knowledge
The subject knowledge in mathematics on the Bachelor´s and Magister´s degree level is requested.
Rules for evaluation and completion of the course
Extent and forms are specified by guarantor’s regulation updated for every academic year.
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.
The ability to orientate in the basic notions and problems
of discrete and difference equations.
Solving problems in the areas cited in the annotation.
The ability to orientate in the basic notions and problems
of discrete and difference equations.
Solving problems in the areas cited in the annotation.
Study aids
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic literature
Diblík, Diskrétní metody ve stavebnictví I, studijní materiál, 82 stran (CS)
Elaydi, Saber N., An Introduction to Difference Equations, Third Edition, Springer, 2005 (EN)
Michael A. Radin, Difference Equations For Scientists And Engineering: Interdisciplinary Difference Equations, World Scientific, 2019 (EN)
Elaydi, Saber N., An Introduction to Difference Equations, Third Edition, Springer, 2005 (EN)
Michael A. Radin, Difference Equations For Scientists And Engineering: Interdisciplinary Difference Equations, World Scientific, 2019 (EN)
Recommended reading
Farlow, S.J.: An Introduction to Differential Equations, Dover Publications, 2006 (EN)
Lakshmikantham, V., Trigiante, Donato: Theory of Difference Equations, Numerical Methods and Applications, Second Edition, Marcel Dekker, 2002 (EN)
Lakshmikantham, V., Trigiante, Donato: Theory of Difference Equations, Numerical Methods and Applications, Second Edition, Marcel Dekker, 2002 (EN)
Classification of course in study plans
- Programme DKA-E Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-E Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPA-E Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-E Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKA-K Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-K Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPA-K Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-K Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKA-M Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-M Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPA-M Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-M Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-S Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPA-S Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-S Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKA-S Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-GK Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPA-GK Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-GK Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKA-GK Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKA-V Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-V Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPA-V Doctoral 1 year of study, summer semester, compulsory-optional
Type of course unit
Lecture
39 hod., optionally
Teacher / Lecturer
Syllabus
- 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.