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

Gurantor department	Department of Applied Mathematics	Credits	4
Subject guarantor	Mgr. Bohumil Krajc, Ph.D.	Subject version guarantor	Mgr. Bohumil Krajc, Ph.D.
Study level	undergraduate or graduate	Requirement	Compulsory
Year	1	Semester	summer
		Study language	Czech
Year of introduction	2003/2004	Year of cancellation	2009/2010
Intended for the faculties	FEI	Intended for study types	Bachelor

Extent of instruction for forms of study
Form of study	Way 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

Other requirements

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

Full-time form (validity from: 1960/1961 Summer semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Exercises evaluation and Examination	Credit and Examination	100 (145)	51	3
Examination	Examination	100	0	3
Exercises evaluation	Credit	45	0	3

Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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Occurrence in study plans

Academic year	Programme	Branch/spec.	Form	Study language	Tut. centre	Year	Type 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

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner

Assessment of instruction

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