151-0301/01 – Mathematics B (Mat B)

Gurantor departmentDepartment of Mathematical Methods in EconomicsCredits4
Subject guarantorMgr. Marian Genčev, Ph.D.Subject version guarantorIng. Orlando Arencibia Montero, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageCzech
Year of introduction1999/2000Year of cancellation2009/2010
Intended for the facultiesEKFIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
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
ZAH0001 Marek Zahradníček
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 by using the Gaussian elimination and Cramer's rule, - control basic terminology and related applications in economics, - write the systems of linear equations with the help of the matrix notation - explain the concept of the primitive function and the indefinite integral, - explain and to control the basic rules, formulas and techniques of integration - define and to calculate the definite integral with the help of the Newton-Leibniz formula, - explain the validity of the geometric application (quadrature only), - present at least one application of the definite integral in economics - define the real function of two real variables, - give examples of basic functions of two variables (especially the constant, linear and Cobb-Douglass function), - give examples of using the functions of two variables in economics, - find the domain of the functions of two variables and its graphical visualization, - find the level curves of basic functions of two variables and to know the economic interpretation, - explain the concept of the homogenous functions of order 's' and to present the geometric and economic interpretation - define and to calculate the partial derivatives with the help of rules and formulas, - define the local extremes of functions of two variables, - interpret the local extremes in economics, - apply the partial derivatives for determining the existence and the nature of local extremes, - discuss the existence and nature of local extremes by means of their definition, - find the constrained extremes (the method of substitution, Lagrange's multiplier) - recognize the type of a basic ordinary first-order differential equation, - explain the existence and the solution form of the first- and second-order differential equations, - solve basic types of first-order differential equations with the help of the direct integration, the constant variation and with the method of undetermined coefficients, - solve the basic second-order linear differential equations with the constant coefficients and with the special right-hand side by means of the method of undetermined coefficients, - outline at least one basic interpretation of the first- and second-order differential equations in economics - control and to explain the basic rules and formulas of the difference calculus, - explain the connection of the first- and second-order difference sign in connection with monotonicity and its dynamics, - determine the monotonicity of sequences with the help of the first- and second-order difference, - know the relationship between the summation and difference, - define the first- and second-order linear difference equations, - explain the existence of general first- and second-order linear difference equations with constant coefficients, - explain the solution form of homogeneous first- and second-order linear difference equations with constant coefficients, - solve the first- and second-order linear difference equations with constant coefficients and with the special right-hand side, - find the closed form of basic finite sums with the help of the first-order linear difference equations, - present basic applications of difference equations in economics

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

Aims of the subject are... - to get acquainted with further basic concepts of caluclus, - to develop the logical thinking and argumentation skills, - to point out the basic application context of mathematics and economics.

Compulsory literature:

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

Recommended literature:

Stewart J.S.: Calculus - Concepts and Contexts. Cengage Learning (2010) Canuto C., Tabacco A.: Mathematical Analysis I. Springer Verlag (2008) 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).

E-learning

Other requirements

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)
Task nameType of taskMax. number of points
(act. for subtasks)
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

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2009/2010 (B6208) Economics and Management P Czech Ostrava 1 Compulsory study plan
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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
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
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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
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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