Gurantor department | Department of Mathematics | Credits | 5 |

Subject guarantor | Mgr. Dagmar Dlouhá, Ph.D. | Subject version guarantor | Mgr. Dagmar Dlouhá, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 2 | Semester | winter |

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 |

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

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

URB0186 | RNDr. Zbyněk Urban, Ph.D. |

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

Form of study | Way of compl. | Extent |

Part-time | Credit and Examination | 18+0 |

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 to
analyze 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 advanced parts of mathematics, according to which the learning material is structured. In Integral Calculus, the main motive is the preparation to general use of definite and indefinite integrals 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 Differential Equations is an emphasis on interpretation of the basic procedures for the solution of selected types of differential equations.

Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X
http://mdg.vsb.cz/portal/en/Mathematics2.pdf
Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1.
James, G.: Modern Engineering Mathematics, Addison-Wesley, 1992, 0-201-1805456.

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.
Moore,C: Math quations and inequalities, Science & Nature, 2014.
James, G.: Modern Engineering Mathematics. Addison – Wesley Publishing
Company, Wokingham, 1994, ISBN 0-201-18504-5.

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.

no more requirements

Subject has no prerequisities.

Subject has no co-requisities.

1. Integral calculus: antiderivative and indefinite integral for functions of one variable.
2. Integration methods - substitution, integration by parts.
3. Integration of rational functions, irrational functions, trigonometric functions.
4. Definite integrals: basic concepts, properties, Newton-Leibniz rule.
5. Substitution method and integration by parts for the definite integral.
6. Applications of integrals in geometry.
7. Differential calculus for functions of two variables: definition, domain, limits and continuity.
8. Partial derivatives of first order and higher orders. Total differential.
9. The equation of the tangent plane and of the normal.
10. Extrema of functions of two variables.
11. Implicit function and its derivatives.
12. Ordinary differential equation of the 1st order: types of solutions, separable, homogeneous and linear.
13. Linear differential equations of the 2nd order with constant coefficients: variation of constants, determination of coefficients.
14. Linear differential equations of higher orders.

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 | 20 | 5 |

Examination | Examination | 80 (80) | 30 |

Písemná zkouška | Written examination | 60 | 25 |

Ústní zkouška | Oral examination | 20 | 5 |

Show history

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2021/2022 | (B1316) Geodesy, Cartography and Geoinformatics | (3646R006) Geoinformatics | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

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2020/2021 | (B2110) Geological Engineering | (2101R003) Geological Engineering | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2020/2021 | (B0724A290003) Mineral Economics | K | Czech | Most | 2 | Compulsory | study plan | |||||

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2020/2021 | (B0724A290001) Mining of Mineral Resources | K | Czech | Most | 2 | Compulsory | study plan | |||||

2020/2021 | (B2102) Mineral Raw Materials | (2102R006) Water Technologies and Water Management | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2020/2021 | (B2102) Mineral Raw Materials | (2102R006) Water Technologies and Water Management | K | Czech | Most | 2 | Compulsory | study plan | ||||

2020/2021 | (B3646) Geodesy and Cartography | (3646R007) Engineering Geodesy | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2020/2021 | (B3646) Geodesy and Cartography | (3646R007) Engineering Geodesy | K | Czech | Most | 2 | Compulsory | study plan | ||||

2020/2021 | (B2102) Mineral Raw Materials | (2102R001) Economics and Management in the Field of Raw Materials | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2020/2021 | (B2102) Mineral Raw Materials | (2102R001) Economics and Management in the Field of Raw Materials | K | Czech | Most | 2 | Compulsory | study plan | ||||

2020/2021 | (B2102) Mineral Raw Materials | (3902R064) System Engineering in Industry | K | Czech | Most | 2 | Compulsory | study plan | ||||

2020/2021 | (B2102) Mineral Raw Materials | (3904R005) Environmental Engineering | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2020/2021 | (B3646) Geodesy and Cartography | (3646R001) Mining Surveying | K | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2020/2021 | (B0712A290001) Waste Management and Mineral Processing | K | Czech | Most | 2 | Compulsory | study plan | |||||

2020/2021 | (B0712A290001) Waste Management and Mineral Processing | K | Czech | Ostrava | 2 | Compulsory | study plan | |||||

2020/2021 | (B0719A290001) Water – Strategic Resource | K | Czech | Ostrava | 2 | Compulsory | study plan | |||||

2020/2021 | (B0724A290004) Petroleum Engineering | K | Czech | Ostrava | 2 | Compulsory | study plan | |||||

2019/2020 | (B0724A290001) Mining of Mineral Resources | K | Czech | Ostrava | 2 | Compulsory | study plan | |||||

2019/2020 | (B0724A290001) Mining of Mineral Resources | K | Czech | Most | 2 | Compulsory | study plan | |||||

2019/2020 | (B0712A290001) Waste Management and Mineral Processing | K | Czech | Ostrava | 2 | Compulsory | study plan | |||||

2019/2020 | (B0712A290001) Waste Management and Mineral Processing | K | Czech | Most | 2 | Compulsory | study plan |

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