714-0762/01 – Differential equations (DR)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantordoc. RNDr. Jaroslav Vlček, CSc.Subject version guarantordoc. RNDr. Jaroslav Vlček, CSc.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semesterwinter
Study languageCzech
Year of introduction2015/2016Year of cancellation2018/2019
Intended for the facultiesFS, USPIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KUC14 prof. RNDr. Radek Kučera, Ph.D.
VLC20 doc. RNDr. Jaroslav Vlček, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

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:

VLČEK, J., Mathematical modeling - http://homen.vsb.cz/~vlc20 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)

E-learning

Další požadavky na studenta

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

Full-time form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  15
        Examination Examination 70  21
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2018/2019 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 2 Compulsory study plan
2017/2018 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 2 Compulsory study plan
2016/2017 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 2 Compulsory study plan
2015/2016 (B3968) Applied Sciences and Technologies (3901R076) Applied Sciences and Technologies P Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner