Course detail
Discrete Methods in Civil Engineering II
FAST-DA59Acad. year: 2022/2023
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
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
of discrete and difference equations.
Solving problems in the areas cited in the annotation.
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
b)Stability of linear systems with the variable matrix.
c)Stability of nonlinear systems via linearization.
d)Ljapunov direct method of stability.
e)Phase analysis of two-dimensional linear discrete system with constant matrix, classification of equilibrium points.
f) Application of difference equations
g)Discrete equivalents of continuous systems.
h)Discrete control theory.
i)The controllability and the complete controllability.
j)Matrix of controllability, the canonical forms of controllability, controllable canonical form, construction of the control algorithm. k)Observability, complete observability, nononservability, principle of duality, the observability matrix, canonical forms of observability, relation of controllability and observability.
l)Stabilization of control by feedback.
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
J. Diblík. Diskrétní metody ve stavebnictví II, studijní materiál, 66 stran (EN)
Michael A. Radin. Difference Equations For Scientists And Engineering: Interdisciplinary Difference Equations, World Scientific, 2019 (EN)
Saber, Elaydi, N. An Introduction to Difference Equations. Springer-Verlag 2010 (EN)
Recommended reading
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 D-K-E-CE (N) Doctoral
branch FMI , 2 year of study, winter semester, compulsory-optional
branch KDS , 2 year of study, winter semester, compulsory-optional
branch MGS , 2 year of study, winter semester, compulsory-optional
branch VHS , 2 year of study, winter semester, compulsory-optional
branch PST , 2 year of study, winter semester, compulsory-optional - Programme D-K-C-SI (N) Doctoral
branch VHS , 2 year of study, winter semester, compulsory-optional
branch MGS , 2 year of study, winter semester, compulsory-optional
branch PST , 2 year of study, winter semester, compulsory-optional
branch FMI , 2 year of study, winter semester, compulsory-optional
branch KDS , 2 year of study, winter semester, compulsory-optional - Programme D-P-E-CE (N) Doctoral
branch PST , 2 year of study, winter semester, compulsory-optional
branch FMI , 2 year of study, winter semester, compulsory-optional
branch KDS , 2 year of study, winter semester, compulsory-optional
branch MGS , 2 year of study, winter semester, compulsory-optional
branch VHS , 2 year of study, winter semester, compulsory-optional - Programme D-P-C-SI (N) Doctoral
branch PST , 2 year of study, winter semester, compulsory-optional
branch FMI , 2 year of study, winter semester, compulsory-optional
branch KDS , 2 year of study, winter semester, compulsory-optional
branch MGS , 2 year of study, winter semester, compulsory-optional
branch VHS , 2 year of study, winter semester, compulsory-optional - Programme D-P-C-GK Doctoral
branch GAK , 2 year of study, winter semester, compulsory-optional
- Programme D-K-C-GK Doctoral
branch GAK , 2 year of study, winter semester, compulsory-optional
Type of course unit
Lecture
Teacher / Lecturer
Syllabus