PřF:M7960 Dynamical Systems - Course Information
M7960 Dynamical Systems
Faculty of ScienceSpring 2011
- Extent and Intensity
- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). 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 - Timetable
- Thu 8:00–9:50 M6,01011
- Timetable of Seminar Groups:
- Prerequisites
- Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix. - 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
- Mathematical Analysis (programme PřF, N-MA)
- Course objectives
- The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling. After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
- Syllabus
- 1. Survey of selected resuts from the theory of ordinary differential equations.
- 2. 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 R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
- 3. General concept of a dynamical system, continuous and discrete dynamical systems.
- 4. 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
- VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
- PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
- KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
- 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
- Teaching methods
- lectures and class exercises
- Assessment methods
- Teaching: lecture 2 hours a week, class exercises 2 hours a week. Examination: written and oral.
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course is taught annually.
- Enrolment Statistics (Spring 2011, recent)
- Permalink: https://is.muni.cz/course/sci/spring2011/M7960