M8230 Discrete deterministic models

Faculty of Science
Autumn 2022
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)
Mgr. Pavel Morcinek (seminar tutor)
Guaranteed by
prof. RNDr. Zdeněk Pospíšil, Dr.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 14:00–15:50 M1,01017
  • Timetable of Seminar Groups:
M8230/01: Mon 18:00–19:50 M1,01017, P. Morcinek
M8230/02: Thu 8:00–9:50 M2,01021, P. Morcinek
Prerequisites
Any course of calculus and linear algebra
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 11 fields of study the course is directly associated with, display
Course objectives
The aim of the subject is to present elements of theory of difference equations. Student will be able to find explicite solution of linear equation, of autonomous linear system and of equation transformable to a linear one. She/he will be informed on basic qualitative methods dealing with autonomous equations and systems and she/he will be familiar with standard discrete dynamical models in life science and economy.
Learning outcomes
At the end of the course students should be able to: construct a mathematical model of a real phenomenon evolving in a "naturally" non-continuous time; to write down difference equations as an approximation of continuous proces described by differential equations; to interpret difference equations as models of real processes; to investigate basic qualitative properties of difference equation solutions.
Illustrating examples are taken from population dynamics and macroeconomy.
Syllabus
  • Elements of difference and summation calculus.
  • Difference equations of the first and second kinds.
  • Linear equations and their explicit solutions.
  • Equations transformable to the linear ones.
  • Nonlinear equations, "cod-web" procedure.
  • Stability of equilibria.
  • Autonomous systems
  • Z-transform method
Literature
    recommended literature
  • An introduction to difference equations. Edited by Saber N. Elaydi. 3rd ed. New York: Springer, 2005, xxii, 539. ISBN 0387230599. info
    not specified
  • BRITTON, N. F. Essential mathematical biology. London: Springer, 2003, xv, 335. ISBN 185233536X. info
  • SEDEGHAT, Hassan. Nonlinear difference equations : theory with applications to social science models. Dordrecht: Kluwer Academic Publishers, 2003, xv, 388. ISBN 1402011164. info
  • MURRAY, J. D. Mathematical biology. 3rd ed. New York: Springer, 2002, xxiii, 551. ISBN 0387224378. info
Teaching methods
Lectures and seminars followed by class discussion and homework.
Assessment methods
Written exam followed by an oral one. The oral exem can be replaced by a distant form in the case of forbiddance of the direct teaching.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught once in two years.
The course is also listed under the following terms Spring 2011, spring 2012 - acreditation, Spring 2013, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020, Autumn 2024.
  • Enrolment Statistics (Autumn 2022, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2022/M8230