Course Details
Discrete Methods in Civil Engineering II
Academic Year 2024/25
DA59 course is part of 7 study plans
D-K-C-SI (N) / VHS Winter Semester 2nd year
D-K-C-SI (N) / MGS Winter Semester 2nd year
D-K-C-SI (N) / PST Winter Semester 2nd year
D-K-C-SI (N) / FMI Winter Semester 2nd year
D-K-C-SI (N) / KDS Winter Semester 2nd year
D-K-C-GK / GAK Winter Semester 2nd year
D-K-E-SI (N) / PST Winter Semester 2nd year
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.
a) Stability of solutions. Stability of numerical algorithms.
b) Application of difference equations.
c) Control of processes using difference equations.
Credits
10 credits
Language of instruction
Czech
Semester
winter
Course Guarantor
Institute
Forms and criteria of assessment
examination
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.
of discrete and difference equations.
Solving problems in the areas cited in the annotation.
Aims
The purpose of continuation of this course is analysis of stability of linear and non-linear discrete systems and methods of their applications.
Basic Literature
J. Diblík. Diskrétní metody ve stavebnictví I, studijní materiál, 82 stran (cs)
J. Diblík. Diskrétní metody ve stavebnictví II, studijní materiál, 66 stran (en)
Saber, Elaydi, N. An Introduction to Difference Equations. Springer-Verlag 2010 (en)
Michael A. Radin. Difference Equations For Scientists And Engineering: Interdisciplinary Difference Equations, World Scientific, 2019 (en)
J. Diblík. Diskrétní metody ve stavebnictví II, studijní materiál, 66 stran (en)
Saber, Elaydi, N. An Introduction to Difference Equations. Springer-Verlag 2010 (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)
Offered to foreign students
Not to offer
Course on BUT site
Lecture
13 weeks, 3 hours/week, elective
Syllabus
a)Stability of equilibrium points. Kinds of stabily and instability.
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.