151-0086/02 – Mathematics B (Mat)

Gurantor departmentDepartment of Mathematical Methods in EconomicsCredits5
Subject guarantorprof. RNDr. Dana Šalounová, Ph.D.Subject version guarantorprof. RNDr. Dana Šalounová, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction1999/2000Year of cancellation2007/2008
Intended for the facultiesEKFIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
S1A20 prof. RNDr. Dana Šalounová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+3

Subject aims expressed by acquired skills and competences

Teaching methods

Summary

Taught only in Czech.

Compulsory literature:

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:

1. Primitivní funkce, neurčitý integrál. Základní vzorce. Integrační metody: per partes a substituční. 2. Integrace racionální lomené funkce, některých iracionálních a goniometrických funkcí. 3. Určitý integrál, motivace jeho zavedení. Vlastnosti určitého integrálu. Newton-Leibnizova formule, metody výpočtu. 4. Základní aplikace: obsah části roviny ohraničené křivkami, střední hodnota funkce. Nevlastní integrál. 5. Funkce více proměnných, základní pojmy (definiční obor, obor hodnot, graf, vrstevnice). Parciální derivace a jejich geometrický význam. 6. Totální diferenciál. Tečná rovina a normála plochy. Parciální derivace vyšších řádů. 7. Totální diferenciál druhého řádu (funkce dvou a tří proměnných). Lokální extrémy funkce dvou a tří proměnných, podmínky existence. 8. Vázané lokální extrémy. Lagrangeova funkce. 9. Diferenciální rovnice, základní pojmy (obecné, partikulární, singulární a výjimečné řešení). Separovatelná a homogenní diferenciální rovnice. 10. Lineární diferenciální rovnice, variace konstanty. Exaktní diferenciální rovnice. 11. Lineární diferenciální rovnice n-tého řádu s konstantními koeficienty homogenní, nehomogenní (se speciální pravou stranou). Obecné řešení. 12. Diference funkce a posloupnosti, diference vyšších řádů. 13. Diferenční rovnice. Lineární diferenční rovnice s konstantními koeficienty a speciální pravou stranou, obecné, partikulární řešení. 14. Číselné řady. Kritéria konvergence.

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:

Show history

Occurrence in study plans

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2005/2006 (B6202) Economic Policy and Administration (6210R004) European Integration (02) European Integration P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes (02) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6208) Economics and Management (6208R037) Management (02) Management P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6208) Economics and Management (6208R020) Business Economics (02) Business Economics P Czech Valašské Meziříčí 1 Compulsory study plan
2005/2006 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes (05) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6208) Economics and Management (6208R020) Business Economics (05) Business Economics P Czech Ostrava 1 Compulsory study plan
2004/2005 (M6208) Business and Management (6201T004) Economics P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6202) Economic Policy and Administration (6210R004) European Integration (02) European Integration P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes (02) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6208) Economics and Management (6208R037) Management (02) Management P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6208) Economics and Management (6208R020) Business Economics (02) Business Economics P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6208) Economics and Management (6208R062) Marketing and Business (02) Marketing and Business P Czech Ostrava 1 Compulsory study plan
2003/2004 (M6208) Business and Management (6201T004) Economics P Czech Ostrava 1 Compulsory study plan
2003/2004 (M6202) Economic Policy and Administration (6201T004) Economics P Czech Ostrava 1 Compulsory study plan
2003/2004 (M6209) Systems Engineering and Informatics (6201T004) Economics P Czech Ostrava 1 Compulsory study plan
2002/2003 (B6208) Economics and Management (6208R101) Sports Management (01) Sports Management P Czech Ostrava 1 Compulsory study plan
2002/2003 (M6208) Business and Management (6201T004) Economics P Czech Ostrava 1 Compulsory study plan
2002/2003 (M6202) Economic Policy and Administration (6201T004) Economics P Czech Ostrava 1 Compulsory study plan
2002/2003 (M6209) Systems Engineering and Informatics (6201T004) Economics P Czech Ostrava 1 Compulsory study plan
2002/2003 (B6202) Economic Policy and Administration (6210R004) European Integration (00) European Integration P Czech Ostrava 1 Compulsory study plan
2002/2003 (B6208) Economics and Management (6201R004) Economics P Czech Ostrava 1 Compulsory study plan
2001/2002 (B6208) Economics and Management (6208R101) Sports Management (01) Sports Management P Czech Ostrava 1 Compulsory study plan
2001/2002 (M6208) Business and Management (6201T004) Economics P Czech Ostrava 1 Compulsory study plan
2001/2002 (M6202) Economic Policy and Administration (6201T004) Economics P Czech Ostrava 1 Compulsory study plan
2001/2002 (M6209) Systems Engineering and Informatics (6201T004) Economics P Czech Ostrava 1 Compulsory study plan
2001/2002 (B6202) Economic Policy and Administration (6202R010) Finance (00) Finance P Czech Ostrava 1 Compulsory study plan
2001/2002 (B6208) Economics and Management (6201R004) Economics P Czech Ostrava 1 Compulsory study plan
2000/2001 (B6208) Economics and Management (6208R101) Sports Management (01) Sports Management P Czech Ostrava 1 Compulsory study plan
2000/2001 (M6208) Business and Management (6201T004) Economics P Czech Ostrava 1 Compulsory study plan
2000/2001 (M6202) Economic Policy and Administration (6201T004) Economics P Czech Ostrava 1 Compulsory study plan
2000/2001 (M6209) Systems Engineering and Informatics (6201T004) Economics P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner