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PřF:M5858 Continuous determin. models I - Course Information

## 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:

*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**- Mathematical Biology (programme PřF, B-EXB)

**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

- KALAS, Josef and Miloš RÁB.
**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****Further Comments**- Study Materials

The course is taught once in two years.

- Enrolment Statistics (recent)

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