M5858 Diffrential Equations and Their Applications

Faculty of Science
Autumn 2005
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. Jiří Tesař (seminar tutor)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Zdeněk Pospíšil, Dr.
Timetable
Mon 8:00–9:50 UP1
  • Timetable of Seminar Groups:
M5858/01: Mon 10:00–11:50 UP1, Z. Pospíšil
Prerequisites
M1110 Linear Algebra I && M1100 Mathematical Analysis I
Any course of calculus and linear algebra
Course Enrolment Limitations
The course is offered to students of any study field.
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. Structure of linear systems solutions. 5. Differential inequalities, estimation of 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
Assessment methods (in Czech)
Přednáška, ve cvičení řešení rovnic - aktivní účast studentů. Zkouška má část písemnou (elementární metody řešení) v průběhu semestru a ústní.
Language of instruction
Czech
Follow-Up Courses
Further Comments
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 2007, Autumn 2009, Autumn 2011, Autumn 2011 - acreditation, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2005, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2005/M5858