M5858 Diffrential Equations and Their Applications

Faculty of Science
Autumn 2009
Extent and Intensity
2/2. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)
Mgr. Jitka Kühnová, Ph.D. (seminar tutor)
Mgr. Václav Pink, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 13:00–14:50 M1,01017
  • Timetable of Seminar Groups:
M5858/01: Wed 12:00–13:50 M2,01021, V. Pink
M5858/02: Mon 16:00–17:50 M5,01013, J. Kühnová
M5858/03: Mon 18:00–19:50 M4,01024, J. Kühnová
M5858/04: Tue 12:00–13:50 M4,01024, V. Pink
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
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.
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 2011, Autumn 2011 - acreditation, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2009, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2009/M5858