# 151-0300/01 – Mathematics A (Mat A)

 Gurantor department Department of Mathematical Methods in Economics Credits 4 Subject guarantor RNDr. Pavel Rucki, Ph.D. Subject version guarantor Ing. Orlando Arencibia Montero, Ph.D. Study level undergraduate or graduate 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.
CTV0004 RNDr. Eva Čtveráčková
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.
MIH22 RNDr. Šárka Michalcová, Ph.D.
POL95 RNDr. Alena Poloučková
SOB33 RNDr. Simona Pulcerová, Ph.D., MBA
REZ0011 RNDr. Lenka Řezníčková
RUC05 RNDr. Pavel Rucki, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit 1+2

### Subject aims expressed by acquired skills and competences

Knowledge • Define the function of one variable. • Find the domain and range and basic properties. • Draw graphs of elementary functions. • Compute limits and derivates of functions. • Find the properties of no elementary functions a draw theirs graphs. • Obtain easier imagine about economic functions. • Order knowledge about vectors in the plain. • Identify the types of matrices. • Solve the system of linear equations. Comprehension • Express economic dependences using a mathematical function. • Explain the slope of a function. • Restate the terms “concavity” and “convexity” into the “degressive” and “progressive”. • Generalise the functions on the dependences in the real live. • Express knowledge of vectors to the space. Applications • Relate economic and mathematical functions. • Discover the tools suitable for describing of dependences in economics and other sciences. • Develop the technique of graphs drawing. • Apply knowledge of linear algebra in economics, e.g. traffic problems, structural analysis. • Solve basic problems of linear programming.

### Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

### Summary

Taught in Czech. The subject continues fulfilling general methodical and professional goals of Mathematics, i.e. to train the rational thinking and the ability to conceive and work with quantitative information concerning the real world. This is being done especially by mathematization of the practical as well as theoretical economic problems. This subject supplies the students’ education with realms of higher Mathematics which is applicable namely to the creation and investigation of economic models.

### Compulsory literature:

[1] SYDSAETER, K., HAMMOND, P. J. Mathematics for Economics Analysis. Pearson, 2002, ISBN 978-81-7758104-1. [2] HOY, M., LIVERNOIS, J., MCKENNA, Ch., REES, R., STENGOS, T. Mathematics for Economics. The MIT Press, London, 3rd edition, 2011, ISBN 978-0-262-01507-3. [3] TAN, T.S. Single variable calculus: early transcendentals. Brooks/Cole Cengage Learning, Belmont, 2011, ISBN 978-1-4390-4600-5.

### Recommended literature:

[1] LARSON, R. Elementary Linear Algebra. Brooks/Cole Cengage Learning, Belmont, 8th edition, 2016, ISBN 978-1305658004. [2] LUDERER, B., NOLLAU, V., VETTERS, K. Mathematical Formulas for Economists. Springer Verlag, 3rd edition, 2006, ISBN 978-3540469018.

### Way of continuous check of knowledge in the course of semester

Požadavky na ukončení (zápočet): 1. Aktivní účast na cvičeních, maximálně tři absence bez omluvy, znalost látky z přednášky, schopnost řešit s porozuměním zadané příklady. 2. Splnění průběžných zápočtových prácí (minimálně dvě povinnosti, z toho alespoň jedna písemka). Z maximálního počtu bodů je nutno získat alespoň 50%. Úprava podmínek pro individuální studium: Aktivní účast na cvičeních je možno nahradit písemnými úkoly podle zadání pedagoga, ostatní podmínky zůstávají.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Obsah přednášek: 1. Funkce jedné reálné proměnné – definice, definiční obor, obor hodnot, graf funkce, vlastnosti funkcí: funkce monotónní, omezená, sudá, lichá, periodická, prostá, složená. 2. Funkce jedné reálné proměnné – elementární funkce, inverzní funkce, cyklometrické funkce. 3. Limita funkce a posloupnosti – pravidla pro výpočet limit, limita funkce v nevlastním bodě, nevlastní limita, jednostranné limity, spojitost funkce, posloupnosti, limita posloupnosti. 4. Derivace funkce – geometrický a obecný význam derivace, pravidla derivování, derivace vyšších řádů, diferenciál, rovnice tečny a normály, L’Hospitalovo pravidlo. 5. Průběh funkce – extrémy funkce, intervaly monotónnosti, inflexní body, konvexnost, konkávnost, asymptoty grafu funkce, lokální extrémy. 6. Lineární algebra – Euklidovský prostor, vektory, lineární závislost a nezávislost vektorů, lineární kombinace vektorů, matice, operace s maticemi, hodnost matice, determinanty. 7. Lineární algebra – inverzní matice, maticové rovnice, soustavy lineárních rovnic, Gaussova eliminační metoda. Obsah cvičení: 1. Definiční obor, obor hodnot, graf funkce. 2. Vlastnosti funkcí, inverzní funkce, cyklometrické funkce. 3. Výpočet limity funkce. 4. Limity v nevlastním bodě, nevlastní limity, jednostranné limity. 5. Posloupnosti, limita posloupnosti. 6. Výpočet derivací, derivace vyšších řádů, rovnice tečny a normály. 7. L’Hospitalovo pravidlo. 8. Průběh funkce – intervaly monotónnosti, lokální extrémy funkce. 9. Průběh funkce – konvexnost, konkávnost, inflexní body, asymptoty grafu funkce. 10. Zápočtová práce. 11. Lineární závislost a nezávislost vektorů, lineární kombinace vektorů, operace s maticemi. 12. Hodnost matice, výpočet determinantu. 13. Výpočet inverzní matice, maticové rovnice. 14. Řešení soustav lineárních rovnic.

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Min. number of points
Exercises evaluation Credit 85 (85) 0
Written exam Written test 85  85
Mandatory attendence parzicipation:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2009/2010 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2009/2010 (B6208) Economics and Management (6208R101) Sports Management (01) Sports Management P Czech Ostrava 1 Compulsory study plan
2009/2010 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2009/2010 (B6208) Economics and Management (6208R101) Sports Management (02) Sports Management P Czech Uherské Hradiště 1 Compulsory study plan
2009/2010 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2009/2010 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
2009/2010 (B6202) Economic Policy and Administration P Czech Ostrava 1 Compulsory study plan
2009/2010 (B6202) Economic Policy and Administration P Czech Valašské Meziříčí 1 Compulsory study plan
2009/2010 (B6209) Systems Engineering and Informatics P Czech Valašské Meziříčí 1 Compulsory study plan
2009/2010 (B6209) Systems Engineering and Informatics P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6202) Economic Policy and Administration (6202R010) Finance (00) Finance P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6202) Economic Policy and Administration (6202R027) National Economy P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6202) Economic Policy and Administration (6202R040) Regional Development P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6202) Economic Policy and Administration (6202R055) Public Economics and Administration (00) Public Economics and Administration P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6202) Economic Policy and Administration (6210R004) European Integration (00) European Integration P Czech Ostrava 1 Compulsory study plan
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
2008/2009 (B6208) Economics and Management (6208R020) Business Economics (00) Business Economics P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6208) Economics and Management (6208R037) Management (00) Management P Czech Ostrava 1 Compulsory study plan
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
2008/2009 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
2008/2009 (B6208) Economics and Management (6208R101) Sports Management (02) Sports Management P Czech Uherské Hradiště 1 Compulsory study plan
2008/2009 (B6208) Economics and Management P Czech Uherské Hradiště 1 Compulsory study plan
2008/2009 (B6208) Economics and Management (6208R020) Business Economics (01) Business Economics P Czech Valašské Meziříčí 1 Compulsory study plan
2008/2009 (B6208) Economics and Management P Czech Valašské Meziříčí 1 Compulsory study plan
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 (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
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

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner