Course detail
Mathematical Modelling by Differential Equations
FSI-SA0 Acad. year: 2019/2020 Summer semester
The course provides basic applications of ordinary differential equations in technical and scientific branches. Various problems of mechanics, hydromechanics, flight dynamics, 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.
Language of instruction
Czech
Number of ECTS credits
2
Supervisor
Department
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.
Prerequisites
Differential and integral calculus of functions in a single and more variables, theory of ordinary differential equations.
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.
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.
The study programmes with the given course
Programme B3A-P: Applied Sciences in Engineering, Bachelor's
branch B-MAI: Mathematical Engineering, elective (voluntary)
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
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. Chaotic systems and their applications.