Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 6 |

Subject guarantor | RNDr. Jan Kotůlek, Ph.D. | Subject version guarantor | RNDr. Alžběta Lampartová |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | winter |

Study language | Czech | ||

Year of introduction | 2021/2022 | Year of cancellation | |

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

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

Login | Name | Tuitor | Teacher giving lectures |

JAH0037 | Mgr. Monika Jahodová, Ph.D. | ||

KOT31 | RNDr. Jan Kotůlek, Ph.D. | ||

LAM0028 | RNDr. Alžběta Lampartová | ||

MUL0086 | RNDr. PhDr. Ivo Müller, Ph.D. | ||

RIE0053 | Mgr. Tomáš Riemel, Ph.D. | ||

SVO19 | Mgr. Ivona Tomečková, Ph.D. |

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

Form of study | Way of compl. | Extent |

Part-time | Credit and Examination | 16+10 |

Mathematics is an essential part of the engineering programmes. Nevertheless, it is not a a goal on its own, but rather a necessary tool for understanding the technical subjects.
Therefore, we aim to both introducing the basic mathematical concepts and deepen the logical and analytical thinking of our students.

Lectures

Individual consultations

Tutorials

Other activities

The subject is divided into four chapters.
In the first chapter we study real functions of one real variable and their properties, in the second chapter we introduce the notion of derivative and study its properties and applications.
In the third chapter we introduce Gauss elimination method for solution of systems of linear algebraic equations. In the last chapter we apply it to the geometric problems in three-dimensional Euclidean space.

BIRD, J. O. Higher engineering mathematics. Eighth edition. London: Routledge, Taylor & Francis Group, 2017. ISBN 978-1-138-67357-1.
NEUSTUPA, Jiří. Mathematics. 2. Vyd. Praha: Vydavatelství ČVUT, 2004. ISBN 80-01-02946-8.
BĚLOHLÁVKOVÁ, Jana, Jan KOTŮLEK, Worksheets for Mathematics I. 1. vyd. Ostrava: VŠB-TUO, 2020.

ANDREESCU, Titu. Essential linear algebra with applications: a problem-solving approach. New York: Birkhäuser, [2014]. ISBN 978-0-8176-4360-7.
HARSHBARGER, Ronald J. a REYNOLDS, James J. Calculus with applications. 2nd ed. Lexington: D.C. Heath, 1993. xiv, 592 s. ISBN 0-669-33162-7.
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

Written and oral exam.

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

The exam consists of the following three parts: Computation of the derivatives of elementary functions (5 tasks, 15 minutes), the practical part (6 problems, 60 minutes, maximum 60 points) and the theoretical test with 10 questions (correct answer 2 points, no answer 0 points, wrong answer -1 point).
A student has to compute correctly 3 derivatives, obtain at least 25 points at the practical part and at least 5 points at the theoretical test.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures
=================
I. Functions of one real variable (4 h)
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Definition, graph and basic properties. Elementary functions. Operations with functions. Parametric and implicit functions. Limit of the function, continuous functions.
II. The calculus (6 h)
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Definition of the derivative, basic rules for differentiation. Parametric differentiation, higher-order derivatives. Applications of the derivatives: tangent line, Taylor polynomial, extremes of a function,
behaviour of the graph (monotony, convexity, critical and inflection points), inverse functions,
computation of limits by l'Hospital rule, asymptotes.
III. Linear algebra and Analytic geometry (6 h)
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Systems of linear equations, Gaussian elimination. Matrices, rank of a matrix. Matrix inversion, Determinant, its computation and properties. Cramer rule.
Analytic geometry in Euclidean space. Dot product and cross product. Line and plane in 3D-Euclidean space.
Tutorials:
=================
1. Pre-calculus. simplifying of algebraic expressions, rules for computation of powers, exponentials, logarithms, solution of (in)equalities.
2. Domains of functions of one real variable.
3. Graphs and properties of elementary functions .
4. Differentiation: rules of computation (for any variable), simplifying, chain rule.
5. Analytic geometry in Euclidean space.

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 (20) | 5 | |

Computing of the derivatives | Written test | 10 | 5 | |

Semestral project | Semestral project | 10 | 0 | |

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

Practical part | Written examination | 60 | 25 | |

Theoretical part | Written test | 20 | 5 |

Show history

Conditions for subject completion and attendance at the exercises within ISP: Written test on derivatives of elementary functions and submission of homework, attndance is not required.

Show history

Academic year | Programme | Branch/spec. | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2024/2025 | (B0715A040001) Transport Systems and Equipment | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2024/2025 | (B0713A070002) Energetics and Environments | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2024/2025 | (B0715A270011) Engineering | K | Czech | Uherský Brod | 1 | Compulsory | study plan | |||||

2024/2025 | (B0715A270011) Engineering | K | Czech | Šumperk | 1 | Compulsory | study plan | |||||

2024/2025 | (B0715A270011) Engineering | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2023/2024 | (B0713A070002) Energetics and Environments | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2023/2024 | (B0715A040001) Transport Systems and Equipment | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2023/2024 | (B0715A270011) Engineering | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2023/2024 | (B0715A270011) Engineering | K | Czech | Šumperk | 1 | Compulsory | study plan | |||||

2023/2024 | (B0715A270011) Engineering | K | Czech | Uherský Brod | 1 | Compulsory | study plan | |||||

2022/2023 | (B0715A040001) Transport Systems and Equipment | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B0713A070002) Energetics and Environments | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B0715A270011) Engineering | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (B0715A270011) Engineering | K | Czech | Šumperk | 1 | Compulsory | study plan | |||||

2022/2023 | (B0715A270011) Engineering | K | Czech | Uherský Brod | 1 | Compulsory | study plan | |||||

2021/2022 | (B0715A270011) Engineering | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (B0715A270011) Engineering | K | Czech | Uherský Brod | 1 | Compulsory | study plan | |||||

2021/2022 | (B0715A270011) Engineering | K | Czech | Šumperk | 1 | Compulsory | study plan | |||||

2021/2022 | (B0713A070002) Energetics and Environments | K | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (B0715A040001) Transport Systems and Equipment | K | Czech | 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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2023/2024 Winter |

2022/2023 Winter |

2021/2022 Winter |