310-2421/02 – Differential equations (DR)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 6 |
| Subject guarantor | RNDr. Martin Swaczyna, Ph.D. | Subject version guarantor | Mgr. Jiří Krček |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 2 | Semester | winter |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FS | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
This subject offers integrated view on mathematical methods and tools needed to a solution practical problems described by differential equations. The applications are oriented to the problem solving of engineering practice with regard to prevailing speciality of students. Established goals tend namely to following knowledges:
- an orientation in typology of ordianary and partial differential equations;
- acquirement of basic analytical methods for solving of ordinary DE;
- an use of selected numerical methods;
- an ability to perform adequate mathematical model of real problem.
Teaching methods
Lectures
Tutorials
Summary
This objective presents the part of basic mathematical course in the bachelor degree.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
pass two written test (2 x 10 points)
elaboration of semestral project (10 points)
E-learning
Other requirements
participation on tutorials is obligatory, 20% of absence can be apologized
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Introduction: basic notions, solution of DE, Cauchy problem, exitence and uniqueness of solution.
2. Solving methods of ordinary first-order DE: separation of variables, linear and Bernoulli DE, direction field and othogonal trajectories; special types of 1st order ODE.
3.Simple numerical methods: Picard approximation, Euler method.
4. Applications: kinematic equations, evolution an logistic models.
5. Linear ODE of higher order I - homogeneous equations: structure and properties of solution, equations with constant coefficients.
6. Linear ODE of higher order II: complete equation with constant coefficients, equation with special right side; selected applications: mechanical vibrations, electrical circuits.
7. Systems of DE: linear systems, homogeneous systems with constant coefficients.
8. Non-homogeneous linear systems: structure of solution, analytical methods for solving.
9. Phase-mapping of solution of homogeneous 2nd order system, introduction to the stability theory.
10. The backgrounds of partial DE: basic notions, method of characteristics for the 1st order PDE.
11. Second order PDE: typology, important equations in mathematical physics.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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