Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |

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

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | winter |

Study language | English | ||

Year of introduction | 2019/2020 | Year of cancellation | 2022/2023 |

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

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

Login | Name | Tuitor | Teacher giving lectures |

KOT31 | RNDr. Jan Kotůlek, Ph.D. | ||

SKA141 | Mgr. Pavel Skalný, 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

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 study linear algebra. 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.

[1] BIRD, J.: Engineering Mathematics, 4th ed. Newnes 2003.
[2] DOLEŽALOVÁ, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3
[3] NEUSTUPA, J.: Mathematics I., ČVUT, Praha 2004

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington 1990, ISBN 0-669-21145-1
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456
James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6

- participation on tutorials is obligatory, 20% of absence can be excused,
- submission of problem sheets,
- passing 10 written tests, maximally 2 points each.
Point classification: 5-20 points.

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

Exam:
Practical part of an exam is classified by 0 - 60 points. Student passes the practical part if (s)he obtains at least 25 points.
Theoretical part of the exam is classified by 0 - 20 points. Student passes the theoretical part if (s)he obtains at least 5 points.
Point quantification in the interval 100 - 91 90 - 81 80 - 71 70 - 61 60 - 51 50 - 0
ECTS grade A B C D E F
Point quantification in the interval 100 - 86 85 - 66 65 - 51 51 - 0
National grading scheme excellent very good satisfactory failed

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

310-2110 | ZM | Basics of Mathematics | Compulsory |

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

310-2110 | ZM | Basics of Mathematics |

Syllabus of lectures
1 Functions of one real variable (definitions and basic properties). Inverse functions.
2 Elementary functions. Parametric and implicit functions.
3 Limit of the function, continuous functions.
4 Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives.
5 Applications of the derivatives, l'Hospital rule. Taylor polynomial.
6 Applications of the derivatives on the behaviour of the graph. Monotonic functions. Convex and concave functions.
7 Asymptotes. Constructing graph of a function.
8 Linear algebra. Vector spaces, bases, dimension.
9 Matrices, rank of a matrix.
10 Determinant. Matrix inversion.
11 Systems of linear equations, Gaussian elimination.
12 Analytic geometry in Euclidean space. Dot product and cross product.
13 Line and plane in 3D-Euclidean space.
14 Reserve.
Syllabus of tutorials
1 Functions of one real variable (definitions and basic properties). Inverse functions.
2 Elementary functions. Parametric and implicit functions.
3 Limit of the function, continuous functions.
4 Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives.
5 Applications of the derivatives, l'Hospital rule. Taylor polynomial.
6 Applications of the derivatives on the behaviour of the graph. Monotonic functions. Convex and concave functions.
7 Asymptotes. Constructing graph of a function.
8 Linear algebra. Vector spaces, bases, dimension.
9 Matrices, rank of a matrix.
10 Determinant. Matrix inversion.
11 Systems of linear equations, Gaussian elimination.
12 Analytic geometry in Euclidean space. Dot product and cross product.
13 Line and plane in 3D-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 | 5 | |

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

Praktická část | Written examination | 60 | 25 | |

Teoretická část | 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 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2020/2021 | (B0715A270012) Engineering | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2020/2021 | (B0713A070003) Energetics and Environments | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2019/2020 | (B2341) Engineering | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2019/2020 | (B0715A270012) Engineering | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2019/2020 | (B0713A070003) Energetics and Environments | P | English | 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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