714-0403/01 – Mathematical Analysis III (MA III)

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 introduction1999/2000Year of cancellation2005/2006
Intended for the facultiesFEIIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRA37 Mgr. Ilona Hummelová
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 course is closed.

Teaching methods

Summary

The first part - principles of vector analysis - uses curviliner and surface integrals to study of field theory. Systems of differential equations is the second part proceeding on ordinary diffrential equations in previous semester. The basic methods to study of dynamical systems are presented. The short final part - number series - is introducing to the following semester.

Compulsory literature:

Základní literatura Bouchala, J.: Matematická analýza III. VŠB-TU Ostrava, 2000 Burda, P. - Doležalová, J.: Cvičení z matematiky IV. Skriptum VŠB-TU Brabec, J. a kol.: Matematická analýza II. SNTL Praha, 1985 Častová, N. a kol.: Cvičení z matematiky III. Skriptum VŠB-TU Eliaš, J. a kol.: Zbierka úloh z vyššej matematiky, diel 4. ALFA, Bratislava 1970 Holenda, J.: Řady. SNTL (MVŠT XII), Praha 1990 Škrášek, J. - Tichý, Z.: Základy aplikované matematiky I. SNTL Praha,1986 Vlček, J. - Vrbický, J.: Diferenciální rovnice (Matematika IV). VŠB-TU,1998 Vlček, J. - Vrbický, J.: Řady (Matematika VI). VŠB-TU, 2000

Recommended literature:

*

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Osnova předmětu Základy vektorové analýzy Klasifikace a znázornění polí, křivky a jejich parametrizace, vektorové funkce, diferenciální operátory, křivkové integrály, Greenova věta, potenciálové pole, plošné integrály, Stokesova věta, Gaussova-Ostrogradského věta, harmonické pole. Soustavy diferenciálních rovnic Základní pojmy, klasifikace, existence a jednoznačnost řešení; soustavy lineárních rovnic - homogenní (Eulerova metoda řešení), nehomogenní; stabilita řešení diferenciálních rovnic a jejich soustav, klasifikace bodů rovnováhy autonomních soustav. Číselné řady Základní pojmy, řady s kladnými členy - kriteria konvergence, alternující řady a řady s obecnými členy, číselné řady v komplexním oboru.

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 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2005/2006 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2002/2003 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava 2 Compulsory study plan
2001/2002 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2612) Electrical Engineering and Computer Science (2612T999) Common Base for FEI P Czech Ostrava 2 Compulsory study plan
2000/2001 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner