M6VM06 Deterministic models

Faculty of Science
spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Lenka Přibylová, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Lenka Přibylová, Ph.D.
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Any course of calculus, linear algebra and computer work is expected.
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
The aim of the course is to present basics of deterministic models (continuous and discrete), introduce fundamental methods and demonstrate usage of mathematical modelling on a wide area of science (biology, biochemistry, physics, ecology, economy, medicine, genetics, epidemiology etc.).
Syllabus
  • Basic concepts: object, system, model, conections; state variables, statický a dynamický model. Software tools: Maple, MATLAB, XppAut, table processors. Contents: static models, comparative statics, static models of interactions and game theory, dynamical models, basic continuous and discrete growth models, structured continuous and discrete models (Leslie-Lefkovitch population models, epidemiologic models), models of interactions - prey-predator models, Samuelson's model of economic cycles, dynamical Cournot's model of duopol, Goodwin's macroeconomic model, evolutionary games - conflicts models, game theory and dynamics, diffusion model and spreading - chemical, biological (gene spreading in population, Fisher's equation) and economic applications (Bass model of innovations), Turing mechanism, pattern formation.
Literature
  • Studijní materiál v e-learningové podobě vytvoření pro předmět přednášející.
  • KULENOVIĆ, Mustafa R. S. and Orlando MERINO. Discrete dynamical systems and difference equations with Mathematica. Boca Raton, Fla.: Chapman & Hall/CRC, 2002, xv, 344 s. ISBN 1-58488-287-5. info
  • LYNCH, Stephen. Dynamical systems with applications using MAPLE. Boston: Birkhäuser, 2000, xiii, 398. ISBN 0-8176-4150-5. info
Teaching methods
Two hours of theoretical lecture and one hour of computer exercises weekly. Seminary requires active participation of students and computer work.
Assessment methods
final project and oral exam
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2013, Spring 2015, Spring 2017, Spring 2019, Spring 2021.