M6160 Differential Equations and Continuous Models

Faculty of Science
Spring 2001
Extent and Intensity
4/2/0. 9 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Josef Kalas, CSc.
Prerequisites (in Czech)
M3100 Mathematical Analysis III
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
Introduction to the theory of ordinary differential equations. Linear systems (existence and uniqueness of solutions, structure of the family of solutions, variation-of-constants method, linear systems with constant coefficients, connection of linear systems with higher-order linear differential equations). Local properties of solutions (existence and uniqueness of solutions of nonlinear initial value problems). Global properties of solutions (global existence and uniqueness, dependence on initial values and parameters). Introduction to the stability theory (Lyapunov concept of stability, uniform, asymptotic and exponential stability, stability of linear and perturbed linear systems, Hurwitz criterion, direct method of Lyapunov). Autonomous equations (basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R^2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions). Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. Masaryk University. ISBN 80-210-1130-0. info
  • KURZWEIL, Jaroslav. Obyčejné diferenciální rovnice : úvod do teorie obyčejných diferenciálních rovnic v reálném oboru. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1978, 418 s. info
  • GREGUŠ, Michal, Marko ŠVEC and Valter ŠEDA. Obyčajné diferenciálne rovnice. 1. vyd. Bratislava: Alfa, vydavateľstvo technickej a ekonomickej literatúry, 1985, 374 s. info
  • Hartman, Philip. Ordinary differential equations. Wiley, New York-London-Sydney, 1964.
  • Coppel, W. A. Stability and asymptotic behaviour of differential equations. D. C. Heath and company, Boston, 1965.
  • RÁB, Miloš. Metody řešení diferenciálních rovnic. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1989, 68 s. info
  • RÁB, Miloš. Metody řešení diferenciálních rovnic. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1989, 61 s. info
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
  • Mesterton-Gibbons, M. A. A concrete approach to mathematical modelling. Addison-Wesley Publishing Company, 1989.
  • Edelstein-Keshet, L. Mathematical models in biology. The Ramdom House/Birkhäuser Mathematics Series, New York, 1987.
  • Ponomarev, K. K. Sostavlenie differencial'nych uravnenij. Vyšejšaja škola, Minsk, 1973.
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
  • Enrolment Statistics (recent)
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