PřF:M5858 Continuous determin. models I - Course Information
M5858 Continuous deterministic models I
Faculty of ScienceAutumn 2011
- Extent and Intensity
- 2/2. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)
doc. RNDr. Lenka Přibylová, Ph.D. (seminar tutor)
Mgr. Vlastimil Severa (seminar tutor) - Guaranteed by
- prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Thu 16:00–17:50 M1,01017
- Timetable of Seminar Groups:
M5858/02: Mon 16:00–17:50 M4,01024, V. Severa
M5858/03: Mon 18:00–19:50 M2,01021, V. Severa - Prerequisites
- ( M1110 Linear Algebra I || M1111 Linear Algebra I ) && ( M1100 Mathematical Analysis I || M1101 Mathematical Analysis I || FI:MB000 Calculus I )
Any course of calculus and linear algebra - 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 Biology (programme PřF, B-BI)
- Mathematical Biology (programme PřF, B-EXB)
- Course objectives
- The aim of the course is to present a fundamentals of ODE theory, information on elementary solving methods and simple continuous deterministic models in biology.
- Syllabus
- 1. Fundamental concepts - equation, initial value problem, general and particular solution. 2. Elementary solving methods - linear, separable, exact equations, homogenous equations, Bernoulli equation, linear higher order equations with constant coefficients, systems of linear equations with constant coefficients. 3. Existence and uniqueness of solution, dependence on initial conditions and parameters. 4. Differential inequalities, estimation of solutions. 5. Structure of linear systems solutions. 6. Autonomous systems, orbits, stationary solutions, stability. 7. Population dynamics models. 8. Epidemiological models.
- Literature
- PLCH, Roman. Příklady z matematické analýzy, Diferenciální rovnice. 1. vydání. Brno: Masarykova univerzita, 2002, 31 pp. ISBN 80-210-2806-8. info
- KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii (Continuous models in biology). 1st ed. Brno: Masarykova univerzita v Brně, 2001, 256 pp. ISBN 80-210-2626-X. info
- RÁB, Miloš. Metody řešení obyčejných diferenciálních rovnic. 2. přeprac. vyd. Brno: Masarykova univerzita, 1998, 96 s. ISBN 8021018186. info
- KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 1. vyd. Brno: Masarykova univerzita, 1995, 207 s. ISBN 8021011300. info
- Teaching methods
- Two hours of theoretical lecture and two hours of class exercises weekly. The lecture during the last third of semester includes demonstration of selected applications. Seminary requires active participation of students.
- Assessment methods
- Written test on elementary methods during semester, final exam contains written test and subsequent oral part.
- Language of instruction
- Czech
- Follow-Up Courses
- Further Comments
- Study Materials
The course is taught once in two years.
- Enrolment Statistics (Autumn 2011, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2011/M5858