Course detail

Discrete Methods in Civil Engineering 2

FAST-DAB034Acad. year: 2026/2027

The discipline is devoted to description of processes via discrete equations. It consists of three parts:
a) Stability of solutions. Stability of numerical algorithms.
b) Application of difference equations.
c) Control of processes using difference equations.

Language of instruction

Czech

Number of ECTS credits

10

Assignment to study programme types

Doctoral

Mode of study

Not applicable.

Guarantor

prof. RNDr. Josef Diblík, DrSc.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Entry knowledge

The ability to orientate in the basic notions and problems
of discrete and difference equations.
Solving problems in the areas cited in the annotation.

Rules for evaluation and completion of the course

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Aims

The purpose of continuation of this course is analysis of stability of linear and non-linear discrete systems and methods of their applications.

Study aids

Prerequisites and corequisites

Not applicable.

Basic literature

Diblík. Diskrétní metody ve stavebnictví II, studijní materiál, 66 stran (EN)
Elaydi, Saber N. An Introduction to Difference Equations, Third Edition, Springer, 2005  (EN)
J. Diblík. Diskrétní metody ve stavebnictví I, studijní materiál, 82 stran (CS)
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)

Classification of course in study plans

  • Programme DPA-V Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPA-S Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPA-M Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPA-K Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPA-GK Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPA-E Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DKA-V Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DKA-S Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DKA-M Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DKA-K Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DKA-GK Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DKA-E Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-S Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-M Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-K Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-GK Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-E Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-V Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-S Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-M Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-K Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-GK Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-E Doctoral 2 year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

prof. RNDr. Josef Diblík, DrSc.

Syllabus

  • 1. Stability of equilibrium points. Kinds of stabily and instability.
  • 2. Stability of linear systems with the variable matrix.
  • 3. Stability of nonlinear systems via linearization.
  • 4. Ljapunov direct method of stability.
  • 5. Phase analysis of two-dimensional linear discrete system with constant matrix, classification of equilibrium points.
  • 6. Application of difference equations. Multiple-room heating problem. Newton law of cooling.
  • 7. Discrete equivalents of continuous systems.
  • 8. Discrete control theory.
  • 9. The controllability and the complete controllability.
  • 10. Matrix of controllability, the canonical forms of controllability, controllable canonical form, construction of the control algorithm.
  • 11. Observability, complete observability, nononservability, principle of duality, the observability matrix, canonical forms of observability, relation of controllability and observability.
  • 12.–13. Stabilization of control by feedback.