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
there are 11 fields of study the course is directly associated with, display
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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