Course detail
Mathematical Modelling by Differential Equations
FSI-SA0 Acad. year: 2022/2023 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 B-MAI-P: Mathematical Engineering, Bachelor's, elective
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
1. Applications of ordinary differential equations (ODEs) in mechanics (basic problems).
2. Basic pursuit problems and their ODEs models.
3. Calculations of escape velocities via ODEs.
4. The first Kepler's problem and its solving.
5. Geometric applications of ODEs (constructions of curves with special properties).
6. Applications of ODEs in hydromechanics.
7. Applications of ODEs in hydromechanics. (continuation).
8. Two special pursuit problems.
9. Basic models of systems with a variable mass.
10. Applications of ODEs in biology ( predator-prey model).
11. ODEs on graphs and their use.
12. Catenary curve problem.
13. Chaotic systems and their applications.