M5858 Continuous deterministic models I

Faculty of Science
Autumn 2019
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
prof. RNDr. Zdeněk Pospíšil, Dr. (lecturer)
Mgr. Jan Böhm (seminar tutor)
Guaranteed by
prof. RNDr. Zdeněk Pospíšil, Dr.
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Fri 8:00–9:50 M2,01021
• Timetable of Seminar Groups:
M5858/01: Fri 10:00–11:50 M2,01021, J. Böhm
Prerequisites
( M1110 Linear Algebra I || M1111 Linear Algebra I ) && ( M1100 Mathematical Analysis I || M1101 Mathematical Analysis I || FI:MB000 Calculus I || M1100F Mathematical Analysis I )|| FI:MB103 Cont. models and statistics || FI:MB203 Cont. models, statistics B || MB103v Mathematics III || FI:MB102 Calculus || M2B02 Calculus II
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 fundamentals of ODE theory. Student will be able to use elementary solving methods and understand simple continuous deterministic models in biology and economy.
Learning outcomes
Successful getting through the course allows a student:
- to express a real-world process going in a continuous time by means of (system of) ordinary differential equation;
- to analyze this model, in particular from the point of view of asymptotic properties;
- to interpret obtained results.
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. 9. Models in economy.
Literature
• KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 1. vyd. Brno: Masarykova univerzita, 1995. 207 s. ISBN 8021011300. info
• KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii (Continuous models in biology). 1. vyd. Brno: Masarykova univerzita v Brně, 2001. 256 pp. ISBN 80-210-2626-X. info
• DIBLÍK, Josef a RǓŽIČKOVÁ, Miroslava. Obyčajné diferenciálne rovnice, EDIS 2008
• RÁB, Miloš. Metody řešení obyčejných diferenciálních rovnic. 2. přeprac. vyd. Brno: Masarykova univerzita, 1998. 96 s. ISBN 8021018186. info
• PLCH, Roman. Příklady z matematické analýzy, Diferenciální rovnice. 1. vydání. Brno: Masarykova univerzita, 2002. 31 pp. ISBN 80-210-2806-8. 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. Typical tests with evaluation are disclosed in learning materials of the course.
Language of instruction
Czech
Follow-Up Courses