M8230 Discrete deterministic models

Faculty of Science
Autumn 2018
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. Jan Böhm (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
Mon 17. 9. to Fri 14. 12. Fri 10:00–11:50 M6,01011
  • Timetable of Seminar Groups:
M8230/01: Mon 17. 9. to Fri 14. 12. Thu 18:00–19:50 M5,01013, J. Böhm
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
Course objectives
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.
Learning outcomes
Passing the course, student will be able:
- to construct a simple model of processes in discrete time;
- to solve explicitely linear and particular nonlinear difference equations;
- to analyse a non-linear autonomous model (to find equilibria and examine their stability)
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
  • SEDEGHAT, Hassan. Nonlinear difference equations : theory with applications to social science models. Dordrecht: Kluwer Academic Publishers, 2003, xv, 388. ISBN 1402011164. info
  • BRITTON, N. F. Essential mathematical biology. London: Springer, 2003, xv, 335. ISBN 185233536X. info
Teaching methods
lectures followed by class discussion and homework.
Assessment methods
Written exam followed by an oral one.
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 2020, Autumn 2022, Autumn 2024.
  • Enrolment Statistics (Autumn 2018, recent)
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