Gurantor department | Department of Mathematical Methods in Economics | Credits | 5 |

Subject guarantor | Mgr. Marian Genčev, Ph.D. | Subject version guarantor | Mgr. Marian Genčev, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | summer |

Study language | Czech | ||

Year of introduction | 2010/2011 | Year of cancellation | 2020/2021 |

Intended for the faculties | EKF | Intended for study types | Bachelor |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

ARE30 | Ing. Orlando Arencibia Montero, Ph.D. | ||

GEN02 | Mgr. Marian Genčev, Ph.D. | ||

KUB33 | Mgr. Aleš Kubíček | ||

S1A20 | prof. RNDr. Dana Šalounová, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Part-time | Examination | 6+8 |

The students will be able to master the basic techniques specified by the three main topics (see below, items 1-3). 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 introduced to the basics of linear algebra and its application possibilities in economics.
(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. The student will be able to discuss the relating application possibilities in economics.
(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. The student will be able to discuss the relating application possibilities and to mention appropriate generalizations for functions of 'n' real variables.

Lectures

Individual consultations

Tutorials

The course is 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.

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.

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

Written exam
- max. 100 pts,
- min. 51 pts

According to teacher's instructions.

Subject code | Abbreviation | Title | Requirement |
---|---|---|---|

151-0400 | MatKomb | Mathematics A | Compulsory |

Subject has no co-requisities.

I. Systems of linear equations and analytic geometry
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- basic concepts,
- Gaussian elimination, Frobenius' theorem,
- Cramer's rule,
- use of systems of linear equations for determining the mutual position of
- two planes in E3,
- two lines in E2 and E3,
- plane and a line in E3
- basic applications in economics
II. Integral calculus
---------------------
Indefinite integral
- definition and properties,
- basic integration formulas and rules,
- per partes, substitution,
- integration of rational functions (partial fractions),
- basic applications in economics
Definite integral
- the problem of calculating the area of a region bounded by continuous curves
- definitions a properties of the definite integral,
- Newton-Leibniz' formula,
- basic applications in economics
Generalized and improper integral
- improper integral of the first and second kind,
- Gaussian integral (for information only),
- calculating improper integrals by limits,
- generalized definite integrals (the case of discontinuous functions),
- basic applications in economics and connection with statistics
III. Functions of two real variables
------------------------------------
- definitions of basic concepts,
- domain and its visualization,
- homogeneous functions of order 's',
- partial derivatives and their geometric interpretation
- tangent plane,
- total differential, differentiable functions, approximations of number expressions,
- local extremes,
- constrained local extremes
- method of substitution,
- Lagrange's multiplier,
- basic applications in economics
IV. Ordinary differential equations (ODE)
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- definition of ODE,
- order of ODE,
- solution of ODE (general, particular, singular, extraordinary),
- basic types of first-order ODE's
- separated,
- separable,
- linear first-order DE (variation of constants),
- second-order linear DE with constant coefficients and special right-hand side (undetermined coefficients),
- basic applications in economics
V. Difference calculus and difference equations
-----------------------------------------------
Introduction to difference calculus
- difference of order 'k',
- basic formulas and rules for calculating the differences,
- the sign of the first-order difference as the indicator of the sequence monotonicity,
- the sign of the second-order difference as the indicator of the sequence monotonicity dynamics,
- relation of summation and difference
Ordinary difference equations (ODifE)
- definition of the ODifE
- order of the ODifE
- solution of the ODifE (general, particular)
- first- and second-order ODifE with constant coefficients and special right-hand side (undetermined coefficients)
- basic applications in economics

Conditions for completion are defined only for particular subject version and form of study

Academic year | Programme | Branch/spec. | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2020/2021 | (B6202) Economic Policy and Administration | (6202R055) Public Economics and Administration | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2018/2019 | (B6208) Economics and Management | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2018/2019 | (B6202) Economic Policy and Administration | K | Czech | Šumperk | 1 | Compulsory | study plan | |||||

2018/2019 | (B6202) Economic Policy and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2018/2019 | (B6202) Economic Policy and Administration | K | Czech | Valašské Meziříčí | 1 | Compulsory | study plan | |||||

2017/2018 | (B6202) Economic Policy and Administration | K | Czech | Valašské Meziříčí | 1 | Compulsory | study plan | |||||

2017/2018 | (B6202) Economic Policy and Administration | K | Czech | Šumperk | 1 | Compulsory | study plan | |||||

2017/2018 | (B6202) Economic Policy and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2017/2018 | (B6208) Economics and Management | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2016/2017 | (B6202) Economic Policy and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2016/2017 | (B6202) Economic Policy and Administration | K | Czech | Valašské Meziříčí | 1 | Compulsory | study plan | |||||

2016/2017 | (B6202) Economic Policy and Administration | K | Czech | Šumperk | 1 | Compulsory | study plan | |||||

2016/2017 | (B6208) Economics and Management | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2015/2016 | (B6202) Economic Policy and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2015/2016 | (B6208) Economics and Management | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2015/2016 | (B6202) Economic Policy and Administration | K | Czech | Šumperk | 1 | Compulsory | study plan | |||||

2015/2016 | (B6202) Economic Policy and Administration | K | Czech | Valašské Meziříčí | 1 | Compulsory | study plan | |||||

2014/2015 | (B6202) Economic Policy and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2014/2015 | (B6202) Economic Policy and Administration | K | Czech | Šumperk | 1 | Compulsory | study plan | |||||

2014/2015 | (B6208) Economics and Management | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2013/2014 | (B6202) Economic Policy and Administration | K | Czech | Šumperk | 1 | Compulsory | study plan | |||||

2013/2014 | (B6202) Economic Policy and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2013/2014 | (B6208) Economics and Management | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2012/2013 | (B6202) Economic Policy and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2012/2013 | (B6202) Economic Policy and Administration | K | Czech | Šumperk | 1 | Compulsory | study plan | |||||

2012/2013 | (B6208) Economics and Management | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2011/2012 | (B6202) Economic Policy and Administration | K | Czech | Šumperk | 1 | Compulsory | study plan | |||||

2011/2012 | (B6202) Economic Policy and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2011/2012 | (B6208) Economics and Management | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2010/2011 | (B6202) Economic Policy and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2010/2011 | (B6202) Economic Policy and Administration | K | Czech | Šumperk | 1 | Compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner | |
---|---|---|---|---|---|---|---|---|---|

Subject block without study plan - EKF - K - cs | 2020/2021 | Part-time | Czech | Optional | EKF - Faculty of Economics | stu. block | |||

Subject block without study plan - EKF - K - cs | 2019/2020 | Part-time | Czech | Optional | EKF - Faculty of Economics | stu. block |

2018/2019 Summer |

2017/2018 Summer |

2016/2017 Summer |

2015/2016 Summer |

2014/2015 Summer |

2013/2014 Summer |

2012/2013 Summer |

2011/2012 Summer |

2010/2011 Summer |