Course Details
Discrete Methods in Civil Engineering I
Academic Year 2024/25
DA58 course is part of 7 study plans
D-K-C-SI (N) / VHS Summer Semester 1st year
D-K-C-SI (N) / MGS Summer Semester 1st year
D-K-C-SI (N) / PST Summer Semester 1st year
D-K-C-SI (N) / FMI Summer Semester 1st year
D-K-C-SI (N) / KDS Summer Semester 1st year
D-K-C-GK / GAK Summer Semester 1st year
D-K-E-SI (N) / PST Summer Semester 1st year
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.
a)difference euquations of first-order,
b)diffeence equations of higher-order,
c)methods of solutions of difference equations.
Credits
4 credits
Language of instruction
Czech
Semester
summer
Course Guarantor
Institute
Forms and criteria of assessment
course-unit credit
Entry Knowledge
The subject knowledge in mathematics on the Bachelor´s and Magister´s degree level is requested.
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.
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)
Offered to foreign students
Not to offer
Course on BUT site
Lecture
13 weeks, 3 hours/week, elective
Syllabus
Basic notions and methods of investigation of discrete equations.
a) Discrete calculus (some difference relations based on corresponding continuous relations).
b)Difference equations and systems.
c)Basic notions used in difference equations.
d)Equilibrium points, periodic points, eventually equilibrium points and eventually periodic points.
e)Stability of solution, repelling and attracting points and their illustration on examples.
f)Algorithms of solutions of systems of discrete equations and equations of higher-order, the case of constant coefficients.
g)The method of variation of parameters.
h)The method of variation of constants.
i)Transformation of some nonlinear equations into linear equations. j)Difference equations modelled with the aid of sampling.