M5858 Continuous deterministic models I

Faculty of Science
Autumn 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:
M5858/01: Fri 8:00–9:50 M5,01013, L. Přibylová
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 and Geometry I || M1111 Linear Algebra and Geometry 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
Abstract
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.
Key topics
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.
Study resources and 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
Approaches, practices, and methods used in teaching
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.
Method of verifying learning outcomes and course completion requirements
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.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2002, Autumn 2003, Autumn 2005, Autumn 2007, Autumn 2009, Autumn 2011 - acreditation, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023, Autumn 2024, Autumn 2025.
  • Enrolment Statistics (Autumn 2011, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2011/M5858