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

Subject guarantor | doc. Ing. Petr Seďa, Ph.D. | Subject version guarantor | doc. Ing. Petr Seďa, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | summer |

Study language | Czech | ||

Year of introduction | 2019/2020 | Year of cancellation | |

Intended for the faculties | EKF | Intended for study types | Follow-up Master |

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

Login | Name | Tuitor | Teacher giving lectures |

KOZ214 | Ing. Mgr. Petr Kozel, Ph.D. | ||

SED02 | doc. Ing. Petr Seďa, Ph.D. |

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

Form of study | Way of compl. | Extent |

Part-time | Graded credit | 6+6 |

The main aim of the course is to teach students how to use mathematics effectively and to increase knowledge and understanding of microeconomic and macroeconomic problems.
Students will get the following knowledge, skills and abilities:
• will be able to use mathematics as a tool for deeper understanding of microeconomics and macroeconomics,
• will be able to study economics effectively,
• will learn how to apply methods and procedures of mathematical analysis to solve practical economic problems at the microeconomic and macroeconomic level,
• will be able to describe solutions of selected economic problems using mathematical tools, check individual steps of given solution, generalize conclusions and evaluate the correctness of results with respect to given conditions.

Lectures

This course connects the existing knowledge of mathematics and economics obtained at bachelor level of study so that students apply the knowledge of mathematics in the area of microeconomics and macroeconomics. The aim of this course is to enable students to understand the benefits of using mathematics as a very useful tool for understanding objective economic reality using mathematical abstraction. Students should discover connections and relationships by comparing economic phenomena having different content but same formal description. This approach allows students to achieve a deeper knowledge of economics.

DOWLING, Edward T. Schaum's Outline of Introduction to Mathematical Economics. New York: McGraw-Hill, 2011. 552 s. ISBN 978-0071762519.
KLEIN, Michael. Mathematical Methods for Economics. London: Pearson College, 2019. 580 s. ISBN 978-0201726268.
MAVRON, Vassilis a Timothy PHILLIPS. Elements of Mathematics for Finance. London: Springer, 2007. 322 s. ISBN 978-3-540-05117-6.

CHIANG, Alpha a Kevin WAINWRIGHT. Fundamental Methods of Mathematical Economics. New York: McGraw-Hill/Irwin, 2004. 704 s. ISBN 0-07-066219-3.
SYDSAETER, Knut a Peter HAMMOND. Essential Mathematics for Economic Analysis. London: Pearson College, 2008. 721 s. ISBN 978-0273713241.
YU Kam. Mathematical Economics: Prelude to the Neoclassical Model. Heidelberg: Springer, 2019. 227 s. ISBN 978-3030272913.

Knowledge is controlled through 2 written tests and tasks according to specification of teachers.

The course is supported by on-line LMS (Learning Management System).

Not required by teachers.

Subject has no prerequisities.

Subject has no co-requisities.

Topics for selfstudy:
1. Introduction.
Mathematical modelling in economics. Classification of economic and mathematical models. Functional dependency.
2. Approximation of real functions.
Interpolation by algebraic polynomials. Lagrange interpolation method. Approximation by the least squares method.
3. Differential calculus of functions of one variable in economic applications.
Economic functions and their properties, the slope of a function. Total, average and marginal variables in economics, elasticity of a function.
4. Differential calculus of multivariable functions in economic applications I.
The methods of optimizing the multivariable functions in economics - the substitution method, the method of Lagrange multipliers, the method of comparison of marginal rates of substitutions.
5. Differential calculus of multivariable functions in economic applications II.
Constrained extrema of multivariable functions in economics. Model with multiply inputs. Evaluation of efficiency.
6. Differential calculus of multivariable functions in economic applications III.
The methods of optimization in imperfect models markets.
7. Integral calculus in economics.
Application of definite and indefinite integrals in economics. Flow quantities in economics and their accumulation over time.
8. Functional dependence as a tool for modelling static economic phenomena.
Models of static equilibrium. Models of comparative statics in economics.
9. Mathematical basis of discrete linear dynamic models in economics I.
Difference equation – a mathematical tool for modelling the discrete macroeconomic dynamic processes in economics.
10. Mathematical basis of continuous linear dynamic models in economics I.
Analogy of discrete and continuous models. Differential equations - a mathematical tool for modelling the continuous macroeconomic dynamic processes in economics.
11. Mathematical basis of discrete linear dynamic models in economics II.
Difference equations - mathematical tool for modelling the discrete microeconomic dynamic processes in economics.
12. Mathematical basis of continuous linear dynamic models in economics II.
Differential equations – a mathematical tool for modelling the continuous microeconomic dynamic processes in economics.
Tutorials:
1. Mathematical modelling in economics. Differential calculus in economic applications. Economic functions and their properties. Total, average and marginal variables in economics, elasticity of function.
2. Mathematical analysis of selected multivariable functions in economic applications. Models with multiple inputs. Integral calculus in economics.
3. Mathematical basis of discrete and continuous dynamic models in economics. Differential equations. Continuous dynamic processes in economics. Difference equations. Discrete dynamic processes in economics.

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

Graded credit | Graded credit | 100 (100) | 51 | 3 |

Test 1 | Written test | 45 | 23 | 2 |

Test 2 | Written test | 45 | 23 | 2 |

Correspondence task | Other task type | 10 | 6 | 2 |

Show history

Conditions for subject completion and attendance at the exercises within ISP: Attendance at tutorials is recommended. It is necessary to pass 2 written tests and individual task, just like in the case of students without ISP.

Show history

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

2024/2025 | (N0311A050012) Applied economics | (S01) International Economic Relations | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2024/2025 | (N0312A050001) Public Economics and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2024/2025 | (N0413A050014) Economics and Management | (S02) Management | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2024/2025 | (N0413A050014) Economics and Management | (S01) Business Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2023/2024 | (N0311A050012) Applied economics | (S01) International Economic Relations | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2023/2024 | (N0312A050001) Public Economics and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2023/2024 | (N0413A050014) Economics and Management | (S01) Business Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2023/2024 | (N0413A050014) Economics and Management | (S02) Management | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2022/2023 | (N0311A050012) Applied economics | (S01) International Economic Relations | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2022/2023 | (N0312A050001) Public Economics and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (N0413A050014) Economics and Management | (S01) Business Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2022/2023 | (N0413A050014) Economics and Management | (S02) Management | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (N0312A050001) Public Economics and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (N0413A050014) Economics and Management | (S01) Business Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (N0413A050014) Economics and Management | (S02) Management | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (N0311A050012) Applied economics | (S01) International Economic Relations | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (N0312A050001) Public Economics and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2020/2021 | (N0413A050014) Economics and Management | (S01) Business Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (N0413A050014) Economics and Management | (S02) Management | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (N0311A050012) Applied economics | (S01) International Economic Relations | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (N0312A050001) Public Economics and Administration | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2019/2020 | (N0311A050012) Applied economics | (S01) International Economic Relations | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (N0413A050014) Economics and Management | (S02) Management | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (N0413A050014) Economics and Management | (S01) Business Administration | K | Czech | Ostrava | 1 | Compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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2022/2023 Summer |

2021/2022 Summer |

2020/2021 Summer |

2019/2020 Summer |