Gurantor department | Department of Mathematics | Credits | 5 |

Subject guarantor | doc. Ing. Martin Čermák, Ph.D. | Subject version guarantor | doc. Ing. Martin Čermák, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | winter |

Study language | Czech | ||

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

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

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. |

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

Form of study | Way of compl. | Extent |

Combined | 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

Other activities

Basics of vector calculus. Functions of several variables: partial differentiation,
extremal values. Integral calculus of functions of two variables and its application.
Line integral and its applications. Basics of vector fields.

http://mdg.vsb.cz/portal/
Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X.
Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1.
Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1.

Škrášek, J. - Tichý, Z.: Základy aplikované matematiky I, II, III, SNTL, Praha 1990.
Burda, P., Doležalová, J.: Cvičení z matematiky IV. Skriptum VŠB-TUO, Ostrava 2002, ISBN 80-248-0028-4.
James, G.: Modern Engineering Mathematics, Addison-Wesley, 1992, 0-201-1805456.
Doležalová, Jarmila: Mathematics I, VŠB - TUO, Ostrava 2005, 80-248-0796-3.

Tests and credits
=================
Exercises: completion of programs, max. 20 CP.
Exam:
- written exam 0-60 CP, successful completion at least 25 CP
- oral exam 0-20 CP, successful completion at least 5 CP
The exam questions are analogous to the program of the lectures.

They are no other requests for students.

Subject has no prerequisities.

Subject has no co-requisities.

Program of lectures
-------------------
1st Block: Vector calculus, scalar, cross and triple product, vector functions.
2nd Block: Differential calculus of functions of two or more real variables: domain, graph, limit and continuity. Partial derivatives, total differential, tangent plane and normal to a surface. Implicit function and its derivatives.
Extremes of functions, calculation via derivatives. Constrained extremes, Lagrange's method. Global extremes. Taylor's theorem.
3rd Block: Two-dimensional integrals on a rectangle and on a general domain. Calculations of two-dimensional integrals, applications in geometry and physics. Three-dimensional integrals, calculation and application. Line integral of the first and second kind, calculation methods. Applications of curved integrals, Green's theorem, independence of the integration path. Surface integrals and their calculation.
4th Block:- Introduction to the field theory: gradient, potential, divergence rotation, Gauss-Ostrogradsky's and Stoke's theorem.

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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2019/2020 | (N2110) Geological Engineering | (2101T003) Geological Engineering | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

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2019/2020 | (N2102) Mineral Raw Materials | (3904T022) Waste Treatment and Disposal | K | Czech | Most | 1 | Compulsory | study plan | |||

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2019/2020 | (N2102) Mineral Raw Materials | (2102T001) Economics and Management in the Field of Raw Materials | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

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2019/2020 | (N2102) Mineral Raw Materials | (3904T005) Environmental Engineering | K | Czech | Most | 1 | Compulsory | study plan | |||

2019/2020 | (N2102) Mineral Raw Materials | (3904T005) Environmental Engineering | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2019/2020 | (N2102) Mineral Raw Materials | (2102T006) Water Technologies and Water Management | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2019/2020 | (N2102) Mineral Raw Materials | (2102T006) Water Technologies and Water Management | K | Czech | Most | 1 | Compulsory | study plan | |||

2019/2020 | (N3654) Geodesy, Cartography and Geoinformatics | (3608T002) Geoinformatics | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2019/2020 | (N0724A290001) Mining of Mineral Resources | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (N0724A290001) Mining of Mineral Resources | K | Czech | Most | 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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