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Course detail

Mathematical Modelling by Differential Equations

Course unit code: FSI-SA0
Academic year: 2016/2017
Type of course unit: optional (voluntary)
Level of course unit: Bachelor's (1st cycle)
Year of study: 2
Semester: summer
Number of ECTS credits:
Learning outcomes of the course unit:
Students will acquire knowledge of basic methods of mathematical modelling by means of ordinary differential equations. They also will master solving obtained differential equations.
Mode of delivery:
90 % face-to-face, 10 % distance learning
Prerequisites:
Differential and integral calculus of functions in a single and more variables, theory of ordinary differential equations.
Co-requisites:
Not applicable.
Recommended optional programme components:
Not applicable.
Course contents (annotation):
The course provides basic applications of ordinary differential equations in technical and scientific branches. Various problems of mechanics, strength of materials, biology, chemistry and other areas are disussed in the framework of this course. Solvings of studied problems consist in forming of a differential equation as a corresponding mathematical model, finding its solution and analysis of this solution.
Recommended or required reading:
Fulford, G., Forrester, P., Jones, A.: Modelling with Differential and Difference Equations, New York, 2001.
Fulford, G., Forrester, P., Jones, A.: Modelling with Differential and Difference Equations, New York, 2001
Soare, M.V., Teodorescu, P.P., Toma, I.: Ordinary Differential Equations with Applications to Mechanics, Dordrecht, 2007.
Soare, M.V., Teodorescu, P.P., Toma, I.: Ordinary Differential Equations with Applications to Mechanics, Dordrecht, 2007.
Čermák, J., Ženíšek, A.: Matematika III, Brno, 2001.
Čermák, J., Ženíšek, A.: Matematika III, Brno, 2001.
Planned learning activities and teaching methods:
The course is taught through lectures explaining the basic principles and theory of the discipline.
Assesment methods and criteria linked to learning outcomes:
Course-unit credit is awarded on the following conditions: Active participation in lessons.
Language of instruction:
Czech
Work placements:
Not applicable.
Course curriculum:
Not applicable.
Aims:
The aim of the course is to explain basic applications of the theory of differential equations. The task of the course is to demonstrate elementary procedures in mathematical modelling by means of ordinary differential equations, including finding and discussion of their solutions.
Specification of controlled education, way of implementation and compensation for absences:
Attendance at lectures is recommended. Lessons are planned according to the week schedules. Absence from lessons may be compensated for by the agreement with the teacher.

Type of course unit:

Lecture: 26 hours, optionally
Teacher / Lecturer: doc. RNDr. Jan Čermák, CSc.
Syllabus: 1. Applications of ordinary differential equations (ODEs) in mechanics (basic problems).
2. Applications of ODEs in mechanics (linear oscillators).
3. Applications of ODEs in mechanics (special problems).
4. Applications of ODEs in flight dynamics (space velocities and related problems).
5. Applications of ODEs in flight dynamics (systems with a variable mass).
6. Geometric applications of ODEs (orthogonal trajectories).
7. Geometric applications of ODEs (some problems in optics).
8. Applications of ODEs in biology (logistic equation).
9. Applications of ODEs in biology (model predator-prey).
10. Applications of ODEs in chemistry.
11. Catenary curve problem.
12. Applications of ODEs in strength of materials.
13. Summary and completion.

The study programmes with the given course