310-2421/01 – Differential equations (DR)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits6
Subject guarantorMgr. Zuzana Morávková, Ph.D.Subject version guarantorMgr. Zuzana Morávková, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KUC14 prof. RNDr. Radek Kučera, Ph.D.
MOR74 Mgr. Zuzana Morávková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+3

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



This objective presents the part of basic mathematical course in the bachelor degree.

Compulsory literature:

VLČEK, J., Mathematical modeling - http://mdg.vsb.cz/portal/dr/U18Mod.pdf AHMAD, S., AMBROSETTI, A.: A Textbook of Ordinary Differential Equations. Springer, 2014. ISBN 978-3-319-02129-4

Recommended literature:

LOGAN, J. D. A First Course in Differential Equations, Springer, 2011, 386 pp., ISBN 978-1-4419-7592-8

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)



Other requirements

No special requirements.


Subject has no prerequisities.


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

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  15
        Examination Examination 70  21 3
Mandatory attendence participation: 80 %

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Conditions for subject completion and attendance at the exercises within ISP: In order to complete credit, students submit homework and pass two tests. Participation in the exercises is not required. Based on a successfully completed credit, they can pass the exam.

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2023/2024 (B0588A170003) Applied Sciences and Technologies MAT P Czech Ostrava 2 Compulsory study plan
2022/2023 (B0588A170003) Applied Sciences and Technologies MAT P Czech Ostrava 2 Compulsory study plan
2021/2022 (B0588A170003) Applied Sciences and Technologies MAT P Czech Ostrava 2 Compulsory study plan
2020/2021 (B0588A170003) Applied Sciences and Technologies MAT P Czech Ostrava 2 Compulsory study plan
2019/2020 (B0588A170003) Applied Sciences and Technologies MAT P Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

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