Gurantor department | Department of Mathematics | Credits | 5 |

Subject guarantor | Mgr. Dagmar Dlouhá, Ph.D. | Subject version guarantor | RNDr. Zbyněk Urban, 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 | HGF | Intended for study types | Bachelor |

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

Login | Name | Tuitor | Teacher giving lectures |

CER365 | doc. Ing. Martin Čermák, Ph.D. | ||

DLO44 | Mgr. Dagmar Dlouhá, Ph.D. | ||

DUB02 | RNDr. Viktor Dubovský, Ph.D. | ||

JAR71 | Mgr. Marcela Jarošová | ||

POS220 | Ing. Lukáš Pospíšil, Ph.D. | ||

STA50 | RNDr. Jana Staňková, Ph.D. | ||

URB0186 | RNDr. Zbyněk Urban, Ph.D. | ||

VIT0060 | Mgr. Aleš Vítek, Ph.D. | ||

VOL18 | RNDr. Jana Volná, Ph.D. | ||

VOL06 | RNDr. Petr Volný, Ph.D. |

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

Form of study | Way of compl. | Extent |

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

Mathematics is essential part of education on technical universities.
It should be considered rather the method in the study of technical
courses than a goal. Thus the goal of mathematics is train logical
reasoning than mere list of mathematical notions, algorithms and
methods.Students should learn how toanalyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics.

Lectures

Individual consultations

Tutorials

The contents of the course is the introduction of common mathematical concepts and interpretation of their relations in connection to the methods of solving selected problems of three basic parts of mathematics, according to which the learning material is structured. In Differential Calculus, the main motive is the preparation to general use of derivatives of real functions of one variable. Under Linear algebra is an emphasis on interpretation of the basic methods for solving systems of linear equations. In Analytic geometry, there are, based on vector calculus, described basic linear formations of three-dimensional Euclidean space and some tools to evaluate their mutual position from qualitative and also quantitative point of view.

Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3.
http://mdg.vsb.cz/portal/en/Mathematics1.pdf
Bartsch, Hans Jochen: Handbook of Mathematical Formulas.
Burdette, A.C.:An Introduction to Analytic Geometry and Calculus,Academic Press,1973.

Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1.
Leon, S., J.: Linear Algebra with Aplications, Macmillan Publishing Company, New York, 1986, ISBN 0-02-369810-1.
Jain, P.K.:A Textbook of Analytical Geometry of Three Dimensions,New Age International Publisher,1996.
Moore,C: Math quations and inequalities, Science & Nature, 2014.

Conditions for obtaining the course-unit credit: participation in exercises, 30% of absences can be excused, submission of programs assigned by the supervisor in the prescribed course, passing of written tests. The student will get 5 b for fulfilling the conditions. The student can get 0 - 15 b for the tests. (The student who gets the credit will be evaluated 5 - 20 b).
The condition for participation in the exam is a written credit from the relevant course. The exam consists of a written and an oral part. Students must pass both parts of the exam and achieve the necessary number of points.

http://www.studopory.vsb.cz
http://mdg.vsb.cz/portal

other requirements are not

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

230-0400 | ZM | Basics of Mathematics | Compulsory |

Subject has no co-requisities.

1. Real function of one real variable. Operations with functions. (Basic) elementary functions.
2. Properties of functions - intersections with axes, sign of function, boundary, monotonicity, extremes, convexity, concavity, parity, simplicity, invertibility, periodicity.
3. Limit of a function, limit theorems, asmyptotes to a function graph.
4. Continuity and discontinuity of function.
5. Derivative of function - geometric and physical meaning. Derivative of basic elementary functions. Differentiation rules. Derivatives of higher orders.
6. Use of derivatives - L'Hospital rule, basic theorems of differential calculus, analysis of the course of a function.
7. Function differential, Taylor polynomial.
8. Arithmetic vector space. Linear independence vectors.
9. Matrices - types, special matrices, operations.
10. Determinant. Inverse matrix. Rank.
11. Systems of linear equations. Frobenius theorem. Gaussian elimination method. Cramer rule.
12. Line and plane in Euclidean space. Scalar, vector and mixed product of vectors.
13. Line and plane equations in E3 and their relative positions.
14. Distances and deviations of basic objects in E3.

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

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

Credit | Credit | 20 | 5 | |

Examination | Examination | 80 (80) | 30 | 3 |

Písemná zkouška | Written test | 60 | 25 | |

Ústní zkouška | Oral examination | 20 | 5 |

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Conditions for subject completion and attendance at the exercises within ISP:

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

2023/2024 | (B0532A330033) Engineering Geodesy | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B0712A290001) Waste Management and Mineral Processing | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B0532A330033) Engineering Geodesy | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B0532A330034) Geoinformatics | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B0719A290001) Water – Strategic Resource | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B0724A290001) Mining of Mineral Resources | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B0724A290003) Mineral Economics | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B0724A290004) Petroleum Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B0724A290006) Process Engineering in Raw Materials | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B0724A290007) Mining Surveying | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B1088A330001) Geoscience and Industrial Tourism | P | Czech | Ostrava | 2 | Optional | study plan | |||||

2022/2023 | (B0724A290008) Environmental Protection within Industry | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B0532A330040) Applied Geology | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B2102) Mineral Raw Materials | (3904R005) Environmental Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (B2110) Geological Engineering | (2101R003) Geological Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (B1088A330001) Geoscience and Industrial Tourism | P | Czech | Ostrava | 2 | Optional | study plan | |||||

2021/2022 | (B0724A290003) Mineral Economics | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (B0724A290004) Petroleum Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (B0724A290001) Mining of Mineral Resources | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (B0532A330034) Geoinformatics | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (B0724A290006) Process Engineering in Raw Materials | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (B0724A290007) Mining Surveying | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (B0532A330033) Engineering Geodesy | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (B0719A290001) Water – Strategic Resource | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (B0712A290001) Waste Management and Mineral Processing | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (B2102) Mineral Raw Materials | (3904R005) Environmental Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (B3646) Geodesy and Cartography | (3646R001) Mining Surveying | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (B3646) Geodesy and Cartography | (3646R007) Engineering Geodesy | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (B1316) Geodesy, Cartography and Geoinformatics | (3646R006) Geoinformatics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (B2110) Geological Engineering | (2101R003) Geological Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (B0724A290003) Mineral Economics | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2020/2021 | (B0724A290001) Mining of Mineral Resources | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2020/2021 | (B2102) Mineral Raw Materials | (2102R006) Water Technologies and Water Management | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (B3646) Geodesy and Cartography | (3646R007) Engineering Geodesy | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (B2102) Mineral Raw Materials | (2102R001) Economics and Management in the Field of Raw Materials | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (B2102) Mineral Raw Materials | (3904R005) Environmental Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (B1088A330001) Geoscience and Industrial Tourism | P | Czech | Ostrava | 2 | Optional | study plan | |||||

2020/2021 | (B1316) Geodesy, Cartography and Geoinformatics | (3646R006) Geoinformatics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (B3646) Geodesy and Cartography | (3646R001) Mining Surveying | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (B2110) Geological Engineering | (2101R004) Geoscience and Industrial Tourism | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2020/2021 | (B2110) Geological Engineering | (2101R004) Geoscience and Industrial Tourism | P | Czech | Most | 2 | Optional | study plan | ||||

2020/2021 | (B0712A290001) Waste Management and Mineral Processing | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2020/2021 | (B0724A290006) Process Engineering in Raw Materials | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2020/2021 | (B0719A290001) Water – Strategic Resource | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2020/2021 | (B0724A290004) Petroleum Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2019/2020 | (B0724A290001) Mining of Mineral Resources | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2019/2020 | (B0712A290001) Waste Management and Mineral Processing | P | Czech | Ostrava | 1 | Compulsory | study plan |

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

2021/2022 Summer |

2020/2021 Summer |

2019/2020 Summer |