M5858 Continuous deterministic models I

Faculty of Science
Spring 2022

The course is not taught in Spring 2022

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
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.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught: every week.
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, Autumn 2011 - acreditation, Autumn 2013, Autumn 2015, autumn 2017, Autumn 2019, autumn 2021, Autumn 2023.
  • Enrolment Statistics (Spring 2022, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2022/M5858