457-0515/01 – Ordinary Differential Equations (ODR)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantorMgr. Bohumil Krajc, Ph.D.Subject version guarantorMgr. Bohumil Krajc, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year3Semesterwinter
Study languageCzech
Year of introduction2003/2004Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesBachelor
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

Succesful student will gain deep and wide knowledge of the subject of ordinary differential equations and their systems. Special attention will devoted to the applications in electricity and physics.

Teaching methods

Lectures
Tutorials
Project work

Summary

The subject consists of the basic parts of the ODE-s theory and practice in the following sequence: Fundamental notions of the theory of ordinary differential equations. Elementary methods of integration of ODE' s. Existence and uniqueness of solutions of the Cauchy problems. Linear equations. Boundary value problems. Stability approach.

Compulsory literature:

W. E. Boyce, R. C. DiPrima: Elementary differential equations. Wiley, New York 1992

Recommended literature:

M. Braun: Differential Equations and Their Applications. Springer, Berlin 1978.

Way of continuous check of knowledge in the course of semester

The control of students' corresponding home and school activities in the various forms.

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Klasická řešení systémů obyčejných diferenciálních rovnic (ODR), řešení Cauchyovy úlohy. Věty o existenci, o existenci a jednoznačnosti. Vztah mezi systémem ODR a rovnicí n-tého řádu. Geometrické interpretace. Eulerova metoda. Transformace proměnných v ODR. Elementární způsoby integrace (lineární ODR 1. řádu, metoda separace, homogenní ODR, Bernoulliova rovnice, exaktní rovnice,integrační faktor). Soustavy lineárních diferenciálních rovnic (LDR) (lineární prostor řešení homogenní soustavy LDR, prostor řešení nehomogenní soustavy LDR, soustavy s konstantními koeficienty, výpočet fundamentálního systému řešení soustavy LDR s konstantními koeficienty). Lineární ODR n-tého řádu. Druhy stabilit. Ljapunovská stabilita řešení ODR. Stabilita řešení soustav LDR. Metoda linearizace nelineárních soustav. Dvojbodové okrajové úlohy pro ODR.

Conditions for subject completion

Part-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2004/2005 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 3 Compulsory study plan
2004/2005 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 3 Compulsory study plan
2003/2004 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 3 Compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2003/2004 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 3 Compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

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