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 | English | ||

Year of introduction | 2015/2016 | Year of cancellation | |

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

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

Login | Name | Tuitor | Teacher giving lectures |

GEN02 | Mgr. Marian Genčev, Ph.D. |

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

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

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

Lectures

Individual consultations

Tutorials

Other activities

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.

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)

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)
Tan T.S.: Calculus: Early Transcendentals. Brooks/Cole Cengage Learning, Belmont (2011)

Credit (written form - test)
- max. 40 pts,
- min. 20 pts
Examination (written and oral)
- written exam (written test)
- max. 42 pts,
- min. 22 pts
- oral exam (open-book)
- max. 18 pts,
- min. 9 pts

http://lms.vsb.cz/

- active participation on seminars,
- maximal one unexcused absence,
- understanding the basic concepts and methods presented at the lecture,
- completion of all tasks assigned by the lecturer

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

151-0500 | Math A | Mathematics A | Compulsory |

Subject has no co-requisities.

I. Systems of linear equations and analytic geometry
----------------------------------------------------
- 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)
-----------------------------------------
- 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

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Credit and Examination | Credit and Examination | 100 (100) | 51 |

Credit | Credit | 40 (40) | 20 |

Písemka | Written test | 40 | 20 |

Examination | Examination | 60 (60) | 31 |

Písemná zkouška | Written examination | 42 | 22 |

Ústní zkouška | Oral examination | 18 | 9 |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2021/2022 | (B0311A050005) Applied Economics | (S01) Economic Development | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (B0311A050005) Applied Economics | (S02) International Economic Relations | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (B0412A050006) Finance | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2020/2021 | (B0311A050005) Applied Economics | (S02) International Economic Relations | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (B0311A050005) Applied Economics | (S01) Economic Development | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (B0412A050006) Finance | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2019/2020 | (B0311A050005) Applied Economics | (S02) International Economic Relations | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (B0311A050005) Applied Economics | (S01) Economic Development | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (B0412A050006) Finance | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2018/2019 | (B6202) Economic Policy and Administration | (6202R010) Finance | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (B6202) Economic Policy and Administration | (6202R010) Finance | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2016/2017 | (B6202) Economic Policy and Administration | (6202R010) Finance | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2015/2016 | (B6202) Economic Policy and Administration | (6202R010) Finance | P | English | Ostrava | 1 | Compulsory | study plan |

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