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

Subject guarantor | RNDr. Pavel Rucki, Ph.D. | Subject version guarantor | RNDr. Pavel Rucki, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | winter |

Study language | English | ||

Year of introduction | 2018/2019 | Year of cancellation | |

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

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

RUC05 | RNDr. Pavel Rucki, Ph.D. |

Extent of instruction for forms of study | ||
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Form of study | Way of compl. | Extent |

Full-time | Graded credit | 2+2 |

Knowledge
• Define the function of one variable.
• Find the domain and range and basic properties.
• Draw graphs of elementary functions.
• Compute limits and derivates of functions.
• Find the properties of no elementary functions a draw theirs graphs.
• Obtain easier imagine about economic functions.
• Order knowledge about vectors in the plain.
• Identify the types of matrices.
• Solve the system of linear equations.
Comprehension
• Express economic dependences using a mathematical function.
• Explain the slope of a function.
• Restate the terms “concavity” and “convexity” into the “degressive” and “progressive”.
• Generalise the functions on the dependences in the real live.
• Express knowledge of vectors to the space.
Applications
• Relate economic and mathematical functions.
• Discover the tools suitable for describing of dependences in economics and other sciences.
• Develop the technique of graphs drawing.
• Apply knowledge of linear algebra in economics, e.g. traffic problems, structural analysis.
• Solve basic problems of linear programming.

Lectures

Individual consultations

Tutorials

Other activities

The subject continues fulfilling general methodical and professional goals of
Mathematics, i.e. to train the rational thinking and the ability to conceive
and work with quantitative information concerning the real world. This is being
done especially by mathematization of the practical as well as theoretical
economic problems. This subject supplies the students’ education with realms of
higher Mathematics which is applicable namely to the creation and investigation
of economic models.

[1] THOMAS, George B., HASS, Joel R., HEIL, Christopher, WEIR, Maurice D. Thomas' Calculus. Pearson, 14th edition, 2018, ISBN 978-0-13-443898-6.
[2] STEWART, James. Calculus: Early Transcendentals 8th Edition (metric version). Cengage Learning, 8th edition, 2016, ISBN 978-1-285-74155-0.

[1] CARVAJAL, Andrés M., HAMMOND, Peter J., STRØM, Arne, SYDSAETER, Knut. Essential mathematics for economic analysis. Pearson, 5th edition, 2016, ISBN 978-1-292-07461-0.
[2] STOCKER, Christopher J., ZIEGLER, Michael R., BYLEEN, Karl E., BARNETT, Raymond A. College mathematics for business, economics, life sciences, and social sciences. Pearson, 14th edition, 2019, ISBN 978-0-13-467414-8.

Credit requirements:
1. Passing the credit test (succes rate - at least 50%)
2. Fulfiling of all task assigned by a teacher
3. Active participation at seminars - at most three absence without leave
4. Familiarity with lecture topics and ability to solve assigned problems
Credit requirements in case of individual study:
It is possible to replace active participation at seminars (req. 3) with written tasks assigned by a teacher. Other requirements remain valid.

https://lms.vsb.cz/course/view.php?id=88522

Credit requirements:
1. Passing the credit test (succes rate - at least 50%)
2. Fulfiling of all tasks assigned by a teacher
3. Active participation at seminars - at most three absence without leave
4. Familiarity with lecture topics and ability to solve assigned problems
Credit requirements in case of individual study:
It is possible to replace active participation at seminars (req. 3) with written tasks assigned by a teacher. Other requirements remain valid.

Subject has no prerequisities.

Subject has no co-requisities.

1. Real sequences – basic concepts, properties, graph.
2. Real sequences – arithmetic and geometric sequence and their application, summation.
3. Real sequences – limit of a sequence, improper limit of a sequence, definition of Euler's number e.
4. Function of a single real variable – definition, domain and range, classification, graphs, even and odd functions, monotonic functions (strictly increasing, strictly decreasing).
5. Function of a single real variable – inverse functions, elementary functions, graph of a function and its transformation, points of intersection.
6. Function of a single real variable – continuous function, limit of a function at a point, properties of limits, one-sided limits.
7. Function of a single real variable – improper limit of a function, limit of a funciton at infinity, properties of continuous functions.
8. Function of a single real variable – derivative of a function, slope of a tangent line at a point, equation of a tangent line and normal line to a curve at a point, differentiation techniques, higher order derivatives.
9. Function of a single real variable - differential of a function, Rolle's and Lagrange'S Theorem, l'Hospital's Theorem, Taylor and Maclaurin polynomial.
10. Function of a single real variable - monotonoic function, local and global extrema of a function.
11. Function of a single real variable – convex and concave function, inflexion points, asymptotes - horizontal, vertical, oblique.
12. Linear algebra – matrix, matrix operation.
13. Linear algebra – rank of a matrix, determinant of a matrix, properties of determinant, Sarrus' scheme, Laplace's formula.
14. Linear algebra – inverse matrix, matrix equations.

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

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

Zápočtová písemka | Written test | 100 | 51 |

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 | |||||

2020/2021 | (B6208) Economics and Management | (6208R174) European Business Studies | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (B6208) Economics and Management | (6208R174) European Business Studies | 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 | (B6208) Economics and Management | (6208R174) European Business Studies | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2018/2019 | (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 |
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