# 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

Knowledge, comprehension The student will be able... - to solve the systems of linear equations (including simple parameterized coefficients), to control basic terminology and related applications - to explain the concept of the primitive function and indefinite integral, to control the basic rules, formulas and techniques of integration - to define the definite integral, to compute the definite integral with the help of Newton-Leibniz formula, to outline the proof of Newton-Leibniz formula, to control the related basic geometric and economic applications - to define real functions of two real variables, to find the domain of functions of two variables and its visualization, to give the overview of basic functions of two variables used in economics (mainly constant, linear and Cobb-Douglass function), to explain the concept of homogenous functions of order 's', to present geometrical point of view and to give the connections to economics - to define and to compute the partial derivatives with the help of their definitions and with the help of rules and formulas, to apply the partial derivatives for determining of local extremes (Hessian matrix), to define and interpret local extrema in a correct way, to discuss local extrema by means of their definition (inequality-type conditions, i.e., without the Hessian matrix), to find constrained extremes (method of substitution, Lagrange's multiplier) - to distinguish and to solve the basic types of differential and difference equations of 1st and 2nd order, to state the basic application possibilities in economics - to control the principles of difference calculus in connection with the monotonicity and dynamics of real sequences, to explain the connection between summation and difference, to find closed form of basic sums by means of 1st order difference equations

### Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

### Summary

The aim of the subject is to get acquainted with the basic knowledge of advanced mathematics, which is necessary for further studies of quantitative methods in economics. The subject’s structure and nature themselves have their importance as they help to develop logical thinking as well as the ability to enunciate thoughts accurately and to give clear argumentation when solving various practical problems.

### Compulsory literature:

[1] Larson R., Falvo C.D. Elementary Linear Algebra. Houghton Mifflin, Boston, New York, 2008. [2] Tan T.S. Calculus: Multivariable Calculus. Brooks/Cole Cengage Learning, Belmont, 2010. [3] Hoy M., Livernois J., McKenna Ch., Rees R., Stengos T. Mathematics for Economics. The MIT Press, London, 2011.

### Recommended literature:

[1] Stewart J.S. Calculus - Concepts and Contexts. Cengage Learning, 2010. [2] Canuto C., Tabacco A. Mathematical Analysis I. Springer Verlag, 2008. [3] Luderer B., Nollau V., Vetters K. Mathematical Formulas for Economists. Springer Verlag, 3rd ed., 2007.

### 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
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
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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
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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 (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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