151-0301/01 – Mathematics B (Mat B)

 Gurantor department Department of Mathematical Methods in Economics Credits 4 Subject guarantor Mgr. Marian Genčev, Ph.D. Subject version guarantor Ing. Orlando Arencibia Montero, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 1 Semester summer Study language Czech Year of introduction 1999/2000 Year of cancellation 2009/2010 Intended for the faculties EKF Intended for study types Bachelor
Instruction secured by
ARE30 Ing. Orlando Arencibia Montero, Ph.D.
FRI02 doc. Ing. Václav Friedrich, Ph.D.
GEN02 Mgr. Marian Genčev, Ph.D.
HRD0001 Mgr. Zdeněk Hrdina
HRU61 RNDr. Jana Hrubá, Ph.D.
LOR21 Mgr. Kristina Lorencová
MAJ40 PaedDr. Renata Majovská, PhD.
CTV0004 Anonymizovaná Osoba
REZ0011 Anonymizovaná Osoba
POL95 RNDr. Alena Poloučková
SOB33 RNDr. Simona Pulcerová, Ph.D., MBA
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 1+2

Subject aims expressed by acquired skills and competences

The students will be able to master the basic techniques specified by the five main topics listed in the syllabus. Also, they will be able to freely, but logically correct, discuss selected theoretical units that will allow talented individuals to excel. The student will also have an overview of basic application possibilities of the discussed apparatus in the field of economics. (1) The student will be able to solve systems of linear equations and apply them to describe the basic problems of network analysis. (2) The student will be able to apply the basic rules and formulas for the calculation of integrals, use them to calculate the area of planar regions, and for calculating of improper integrals and integrals of discontinuous functions. (3) The student will be able to find local extrema of functions of two variables without/with constraints, level curves and total differential, will be able to decide whether the given function is homogeneous. (4) The student will be able to solve selected ordinary differential equations of the 1st and 2nd order. (5) The student will be able to use basic rules and formulas to calculate the difference of the sequence and to assess the dynamic of monotonic sequences, will be able to solve linear difference equations of the 1st and 2nd order.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

The course is primarily focused on the practical mastery of selected mathematical methods in the field of linear algebra and calculus, which form the basis for further quantitative considerations in related subjects. The student will also be acquainted with the derivation of basic theoretical findings. This enables the development of logical skills, which form the basis for analytical and critical thinking. For better motivation of students, the presentation in lectures is always connected with appropriate economic problems.

Compulsory literature:

LARSON, Ron a David C. FALVO. Elementary linear algebra. 6th ed. Belmont: Brooks/Cole Cengage Lerning, 2010. ISBN 978-0-495-82923-2. TAN, Soo Tang. Multivariable calculus. International ed. Belmont: Brooks/Cole Cengage Learning, 2010. ISBN 978-0-495-83150-1. HOY, Michael, LIVERNOIS, John Richard and MCKENNA, C. J. Mathematics for economics. Cambridge: The MIT Press, 2022. ISBN 9780262046626.

Recommended literature:

STEWART, James. Calculus: metric version. Eighth edition. [Boston]: Cengage Learning, [2016]. ISBN 978-1-305-26672-8.

Way of continuous check of knowledge in the course of semester

Požadavky na ukončení (100 bodů, minimum 51 bodů): Zápočet (40 bodů, minimum 20 bodů) 1. Aktivní účast na cvičeních, maximálně tři absence bez omluvy, znalost látky z přednášky, schopnost řešit s porozuměním zadané příklady. 2. Splnění průběžných domácích úloh. 3. Alespoň na 50% vyřešené kontrolní testy zadávané v průběhu semestru. Zkouška (60 bodů, min. 31 bodů) Kombinovaná, tvořená částí písemnou (55 bodů, min. 28 bodů) a ústní (5 bodů, min. 3 body).

Prerequisities

Subject codeAbbreviationTitleRequirement
151-0300 Mat A Mathematics A Compulsory

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Obsah přednášek: 1. Neurčitý integrál – definice a vlastnosti, základní vzorce, pravidla integrování, metody integrace: substituční metoda, metoda per partes. 2. Neurčitý integrál – integrace racionální lomené funkce, rozklad na parciální zlomky, integrace některých iracionálních funkcí, integrace některých goniometrických funkcí. 3. Určitý integrál – definice a vlastnosti, Newton-Leibnizova formule, obsah rovinného obrazce, nevlastní integrál. 4. Funkce dvou proměnných – úvod a základní pojmy, definiční obor, obor hodnot, graf, parciální derivace prvního řádu, parciální derivace vyšších řádů. 5. Funkce dvou proměnných – tečná rovina k ploše, extrémy funkce dvou proměnných: lokální extrémy, vázané extrémy. 6. Obyčejné diferenciální rovnice 1. řádu – úvod a základní pojmy, obecné řešení, partikulární řešení, separovatelná diferenciální rovnice, homogenní diferenciální rovnice, lineární diferenciální rovnice homogenní a nehomogenní (metoda variace konstanty). Obsah cvičení: 1. Základní integrační pravidla. 2. Integrace substitucí, integrace metodou per partes. 3. Integrace racionální funkce, rozklad na parciální zlomky. 4. Integrace některých iracionálních funkcí, integrace některých goniometrických funkcí. 5. Určitý integrál. 6. Nevlastní integrál. 7. Definiční obor funkce dvou proměnných. 8. Parciální derivace prvního řádu, parciální derivace vyšších řádů. 9. Tečná rovina k ploše. 10. Lokální extrémy funkce dvou proměnných, vázané extrémy funkce dvou proměnných. 11. Separovatelná diferenciální rovnice, homogenní diferenciální rovnice. 12. Lineární diferenciální rovnice homogenní a nehomogenní (metoda variace konstanty). 13. Opakování. 14. Závěrečný test.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 40 (40) 20
Written exam Written test 40  20
Examination Examination 60 (60) 31
Written examination Written examination 55  0
Oral Oral examination 5  0
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2009/2010 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
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2009/2010 (B6209) Systems Engineering and Informatics P Czech Valašské Meziříčí 1 Compulsory study plan
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2008/2009 (B6202) Economic Policy and Administration (6202R040) Regional Development P Czech Ostrava 1 Compulsory study plan
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2008/2009 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6208) Economics and Management (6501R006) Tourism Economics (02) Tourism Economics P Czech Uherské Hradiště 1 Compulsory study plan
2008/2009 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2008/2009 (B6209) Systems Engineering and Informatics (6209R001) Applied Informatics (00) Applied Informatics P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6209) Systems Engineering and Informatics (6209R025) System Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6208) Economics and Management (6202R049) Accounting and Taxes (00) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
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2008/2009 (B6208) Economics and Management (6208R062) Marketing and Business (01) Marketing and Business P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes (00) Účetnictví a daně P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6208) Economics and Management (6208R101) Sports Management (01) Sports Management P Czech Ostrava 1 Compulsory study plan
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2008/2009 (B6202) Economic Policy and Administration (6210R004) European Integration (01) European Integration P Czech Valašské Meziříčí 1 Compulsory study plan
2008/2009 (B6202) Economic Policy and Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2008/2009 (B6209) Systems Engineering and Informatics (6209R001) Applied Informatics (01) Applied Infomatics P Czech Valašské Meziříčí 1 Compulsory study plan
2008/2009 (B6209) Systems Engineering and Informatics (6209R014) Information and Knowledge Management (00) Informační a znalostní management P Czech Valašské Meziříčí 1 Compulsory study plan
2008/2009 (B6209) Systems Engineering and Informatics P Czech Valašské Meziříčí 1 Compulsory study plan
2007/2008 (B6202) Economic Policy and Administration (6202R010) Finance (00) Finance P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6202) Economic Policy and Administration (6202R027) National Economy P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6202) Economic Policy and Administration (6202R040) Regional Development P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (00) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6202) Economic Policy and Administration (6210R004) European Integration (00) European Integration P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6202) Economic Policy and Administration (6210R004) European Integration (01) European Integration P Czech Valašské Meziříčí 1 Compulsory study plan
2007/2008 (B6208) Economics and Management (6501R006) Tourism Economics (02) Tourism Economics P Czech Uherské Hradiště 1 Compulsory study plan
2007/2008 (B6209) Systems Engineering and Informatics (6209R001) Applied Informatics (00) Applied Informatics P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6209) Systems Engineering and Informatics (6209R025) System Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6209) Systems Engineering and Informatics (6209R001) Applied Informatics (01) Applied Infomatics P Czech Valašské Meziříčí 1 Compulsory study plan
2007/2008 (B6209) Systems Engineering and Informatics (6209R014) Information and Knowledge Management (00) Informační a znalostní management P Czech Valašské Meziříčí 1 Compulsory study plan
2007/2008 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes (00) Účetnictví a daně P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6208) Economics and Management (6208R020) Business Economics (00) Business Economics P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6208) Economics and Management (6208R037) Management (00) Management P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6208) Economics and Management (6208R062) Marketing and Business (01) Marketing and Business P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6208) Economics and Management (6202R049) Accounting and Taxes (00) Accounting and Taxes P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6208) Economics and Management (6208R101) Sports Management (01) Sports Management P Czech Ostrava 1 Compulsory study plan
2007/2008 (B6208) Economics and Management (6208R101) Sports Management (02) Sports Management P Czech Uherské Hradiště 1 Compulsory study plan
2007/2008 (B6208) Economics and Management (6208R020) Business Economics (01) Business Economics P Czech Valašské Meziříčí 1 Compulsory study plan
2006/2007 (B6202) Economic Policy and Administration (6202R010) Finance (00) Finance P Czech Ostrava 1 Compulsory study plan
2006/2007 (B6202) Economic Policy and Administration (6202R027) National Economy P Czech Ostrava 1 Compulsory study plan
2006/2007 (B6202) Economic Policy and Administration (6202R040) Regional Development P Czech Ostrava 1 Compulsory study plan
2006/2007 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (00) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2006/2007 (B6208) Economics and Management (6208R101) Sports Management (01) Sports Management P Czech Ostrava 1 Compulsory study plan
2006/2007 (B6209) Systems Engineering and Informatics (6209R014) Information and Knowledge Management (00) Informační a znalostní management P Czech Valašské Meziříčí 1 Compulsory study plan
2006/2007 (B6208) Economics and Management (6501R006) Tourism Economics (02) Tourism Economics P Czech Uherské Hradiště 1 Compulsory study plan
2006/2007 (B6209) Systems Engineering and Informatics (6209R025) System Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2006/2007 (B6208) Economics and Management (6208R020) Business Economics (00) Business Economics P Czech Ostrava 1 Compulsory study plan
2006/2007 (B6209) Systems Engineering and Informatics (6209R001) Applied Informatics (00) Applied Informatics P Czech Ostrava 1 Compulsory study plan
2006/2007 (B6208) Economics and Management (6208R020) Business Economics (01) Business Economics P Czech Valašské Meziříčí 1 Compulsory study plan
2006/2007 (B6208) Economics and Management (6208R062) Marketing and Business (01) Marketing and Business P Czech Ostrava 1 Compulsory study plan
2006/2007 (B6209) Systems Engineering and Informatics (6209R001) Applied Informatics (01) Applied Infomatics P Czech Valašské Meziříčí 1 Compulsory study plan
2006/2007 (B6208) Economics and Management (6208R037) Management (00) Management P Czech Ostrava 1 Compulsory study plan
2006/2007 (B6208) Economics and Management (6208R101) Sports Management (02) Sports Management P Czech Uherské Hradiště 1 Compulsory study plan
2006/2007 (B6202) Economic Policy and Administration (6210R004) European Integration (00) European Integration P Czech Ostrava 1 Compulsory study plan
2006/2007 (B6202) Economic Policy and Administration (6210R004) European Integration (01) European Integration P Czech Valašské Meziříčí 1 Compulsory study plan
2006/2007 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes (00) Účetnictví a daně P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6202) Economic Policy and Administration (6202R010) Finance (00) Finance P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6202) Economic Policy and Administration (6202R027) National Economy P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6202) Economic Policy and Administration (6202R040) Regional Development P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes (00) Účetnictví a daně P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (00) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6202) Economic Policy and Administration (6210R004) European Integration (00) European Integration P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6208) Economics and Management (6208R020) Business Economics (00) Business Economics P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6208) Economics and Management (6208R037) Management (00) Management P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6208) Economics and Management (6208R101) Sports Management (01) Sports Management P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6208) Economics and Management (6208R062) Marketing and Business (01) Marketing and Business P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6202) Economic Policy and Administration (6210R004) European Integration (01) European Integration P Czech Valašské Meziříčí 1 Compulsory study plan
2005/2006 (B6209) Systems Engineering and Informatics (6209R001) Applied Informatics (00) Applied Informatics P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6209) Systems Engineering and Informatics (6209R001) Applied Informatics (01) Applied Infomatics P Czech Valašské Meziříčí 1 Compulsory study plan
2005/2006 (B6209) Systems Engineering and Informatics (6209R001) Applied Informatics (01) Applied Infomatics P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6209) Systems Engineering and Informatics (6209R014) Information and Knowledge Management (00) Informační a znalostní management P Czech Valašské Meziříčí 1 Compulsory study plan
2005/2006 (B6209) Systems Engineering and Informatics (6209R014) Information and Knowledge Management (00) Informační a znalostní management P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6208) Economics and Management (6208R020) Business Economics (01) Business Economics P Czech Valašské Meziříčí 1 Compulsory study plan
2005/2006 (B6202) Economic Policy and Administration (6210R004) European Integration (05) European Integration P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6208) Economics and Management (6208R037) Management (05) Management P Czech Ostrava 1 Compulsory study plan
2005/2006 (B6209) Systems Engineering and Informatics (6209R025) System Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6208) Economics and Management (6208R062) Marketing and Business (01) Marketing and Business P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (00) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6208) Economics and Management (6208R101) Sports Management (01) Sports Management P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6202) Economic Policy and Administration (6202R010) Finance (00) Finance P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes (00) Účetnictví a daně P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6202) Economic Policy and Administration (6210R004) European Integration (00) European Integration P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6208) Economics and Management (6208R086) Enterprise Economics and Management P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6208) Economics and Management (6208R037) Management (00) Management P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6202) Economic Policy and Administration (6202R027) National Economy P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6202) Economic Policy and Administration (6202R040) Regional Development P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6208) Economics and Management (6208R020) Business Economics (00) Business Economics P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6207) Quantitative Methods in Economics (6207R015) Managerial and Decision Making Methods in Economics P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6209) Systems Engineering and Informatics (6209R001) Applied Informatics (00) Applied Informatics P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6209) Systems Engineering and Informatics (6209R001) Applied Informatics (01) Applied Infomatics P Czech Ostrava 1 Compulsory study plan
2004/2005 (B6202) Economic Policy and Administration (6210R004) European Integration (01) European Integration P Czech Ostrava 1 Compulsory study plan
2003/2004 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (00) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2003/2004 (B6208) Economics and Management (6208R101) Sports Management (01) Sports Management P Czech Ostrava 1 Compulsory study plan
2003/2004 (B6209) Systems Engineering and Informatics (6209R001) Applied Informatics (01) Applied Infomatics P Czech Ostrava 1 Compulsory study plan
2003/2004 (B6208) Economics and Management (6201R004) Economics P Czech Ostrava 1 Compulsory study plan
2003/2004 (B6202) Economic Policy and Administration (6202R010) Finance (00) Finance P Czech Ostrava 1 Compulsory study plan
2003/2004 (B6202) Economic Policy and Administration (6202R049) Accounting and Taxes (00) Účetnictví a daně P Czech Ostrava 1 Compulsory study plan
2003/2004 (B6202) Economic Policy and Administration (6210R004) European Integration (00) European Integration P Czech Ostrava 1 Compulsory study plan
2003/2004 (B6202) Economic Policy and Administration (6201R004) Economics P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

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