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. | ||

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

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

URB0186 | RNDr. Zbyněk Urban, 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 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.

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

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

2021/2022 | (B2110) Geological Engineering | (2101R003) Geological Engineering | P | Czech | Ostrava | 2 | 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 | 2 | Compulsory | study plan | |||||

2021/2022 | (B0724A290004) Petroleum Engineering | P | Czech | Ostrava | 2 | Compulsory | study plan | |||||

2021/2022 | (B0724A290001) Mining of Mineral Resources | P | Czech | Ostrava | 2 | Compulsory | study plan | |||||

2021/2022 | (B0532A330034) Geoinformatics | P | Czech | Ostrava | 2 | Compulsory | study plan | |||||

2021/2022 | (B0724A290006) Process Engineering in Raw Materials | P | Czech | Ostrava | 2 | Compulsory | study plan | |||||

2021/2022 | (B0724A290007) Mining Surveying | P | Czech | Ostrava | 2 | Compulsory | study plan | |||||

2021/2022 | (B0532A330033) Engineering Geodesy | P | Czech | Ostrava | 2 | Compulsory | study plan | |||||

2021/2022 | (B0719A290001) Water – Strategic Resource | P | Czech | Ostrava | 2 | Compulsory | study plan | |||||

2021/2022 | (B0712A290001) Waste Management and Mineral Processing | P | Czech | Ostrava | 2 | Compulsory | study plan | |||||

2021/2022 | (B2102) Mineral Raw Materials | (3904R005) Environmental Engineering | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2021/2022 | (B3646) Geodesy and Cartography | (3646R001) Mining Surveying | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2021/2022 | (B3646) Geodesy and Cartography | (3646R007) Engineering Geodesy | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2021/2022 | (B2102) Mineral Raw Materials | (2102R001) Economics and Management in the Field of Raw Materials | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

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

2021/2022 | (B2102) Mineral Raw Materials | (2102R006) Water Technologies and Water Management | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

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

2020/2021 | (B0724A290003) Mineral Economics | P | Czech | Ostrava | 2 | Compulsory | study plan | |||||

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

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

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

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

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

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

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

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

2020/2021 | (B0724A290006) Process Engineering in Raw Materials | P | Czech | Ostrava | 2 | Compulsory | study plan | |||||

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

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

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

2019/2020 | (B0712A290001) Waste Management and Mineral Processing | P | Czech | Ostrava | 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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