457-0515/02 – Ordinary Differential Equations (ODR)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorMgr. Bohumil Krajc, Ph.D.Subject version guarantorMgr. Bohumil Krajc, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year3Semesterwinter
Study languageCzech
Year of introduction2004/2005Year of cancellation2009/2010
Intended for the facultiesUSPIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRA04 Mgr. Bohumil Krajc, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined 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:

Reálné funkce několika reálných proměnných. Euklidovské prostory. Topologické vlastnosti podmnožin euklidovského metrického prostoru. Limita a spojitost. Parciální derivace funkce, pojem derivace ve směru. Totální diferenciál a gradient funkce. Aplikace. Geometrický význam gradientu, nástin metody metody největšího spádu. Diskuze souvislostí mezi základními pojmy diferenciálního počtu. Diferenciály vyšších řádů, Taylorův polynom, Taylorova věta. Věta o implicitně zadané funkci. Weierstrassova věta o globálních extrémech, lokální extrémy. Kritéria existence lokálních extrému. Vázané lokální extrémy, metoda Lagrangeových multiplikátorů. Hledání globálních extrémů - praktické postupy. Definice Riemannova dvojného integrálu, základní vlastnosti. Fubiniovy věty pro dvojný integrál. Věta o substituci pro dvojný integrál, aplikace dvojného integrálu Definice Riemannova trojného integrálu, základní vlastnosti. Fubiniovy věty pro trojný integrál. Věta o substituci pro trojný integrál. Aplikace. Diferenciální rovnice prvního řádu, věta o existenci a jednoznačnosti řešení Cauchyovy úlohy. Lineární diferenciální rovnice 1. řádu, rovnice se separovanými proměnnými. Lineární diferenciální rovnice vyšších řádů.

Conditions for subject completion

Full-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 (100) 51
        Examination Examination 70  0
        Exercises evaluation Credit 30 (30) 10
                1. test Written test 10  0
                2. test Written test 10  0
                Projekt Semestral project 10  0
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 3 Choice-compulsory study plan
2009/2010 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 3 Choice-compulsory study plan
2009/2010 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 3 Compulsory study plan
2009/2010 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 3 Compulsory study plan
2008/2009 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 3 Compulsory study plan
2008/2009 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 3 Choice-compulsory study plan
2008/2009 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 3 Choice-compulsory study plan
2007/2008 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 3 Compulsory study plan
2007/2008 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 3 Compulsory study plan
2007/2008 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 3 Choice-compulsory study plan
2007/2008 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 3 Choice-compulsory study plan
2006/2007 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 3 Compulsory study plan
2006/2007 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 3 Compulsory study plan
2006/2007 (B2647) Information and Communication Technology (1103R031) Computational Mathematics P Czech Ostrava 3 Choice-compulsory study plan
2006/2007 (B2647) Information and Communication Technology (1103R031) Computational Mathematics K Czech Ostrava 3 Choice-compulsory study plan
2005/2006 (B2646) Information Technology (1103R021) Computation Mathematics P Czech Ostrava 3 Compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2005/2006 (B2646) Information Technology (1103R021) Computation Mathematics K Czech Ostrava 3 Compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 1 Compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 1 Compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner