Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |

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

Study level | undergraduate or graduate | ||

Study language | English | ||

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

Intended for the faculties | FEI, HGF, FS, FAST, FMT, FBI | Intended for study types | Bachelor |

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

Login | Name | Tuitor | Teacher giving lectures |

BEL10 | Mgr. Jana Bělohlávková | ||

KOT31 | RNDr. Jan Kotůlek, Ph.D. |

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

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

After completing this course, students should have the following skills:
* Use rules of differentiation to differentiate functions.
* Sketch the graph of a function using asymptotes, critical points.
* Apply differentiation to solve problems.
* Solve a system of linear algebraic equations.
* Work with basic objects in three dimensional Euclidean space.

Lectures

Individual consultations

Tutorials

I. Calculus.
Function of one variable (basic notions, inverse function, elementary functions);
Limits and Continuity of a function;
Differentiation of a function (differentiation rules, application, L'Hospital's rule).
II. Linear algebra.
Vector spaces;
Matrices and determinants;
Systems of linear algebraic equations (Gaussian elimination, Frobeniu theorem).
III. Introduction to analytic geometry (lines and planes in E3, intersection, distance, angle).

Neustupa J.: Mathematics I. ČVUT, Praha 2004.
Demlova M., Hamhalter J.: Calculus I. ČVUT, Praha 1998, ISBN 80-01-01110-0.
Doležalová, J., Mathematics I. VŠB-TU Ostrava 2005, ISBN 80-248-0796-3.

Neustupa J.: Mathematics I. ČVUT, Praha 2004.
Demlova M., Hamhalter J.: Calculus I. ČVUT, Praha 1998, ISBN 80-01-01110-0
Doležalová, J., Mathematics I. VŠB-TU Ostrava 2005, ISBN 80-248-0796-3.

Course-credit
-participation on tutorials is obligatory, 20% of absence can be apologized,
-elaborate programs,
-pass the written tests,
Point classification: 5-20 points.
Exam
Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points.
Theoretical part of the exam is classified by 0 - 20 points. Theoretical part is successful if student 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

http://www.studopory.vsb.cz (in Czech)

There is no further requirements.

Subject has no prerequisities.

Subject has no co-requisities.

1 Linear algebra. Operations with matrices. Determinants. Properties of determinants.
2 Rank of a matrix. Inverse matrix.
3 Solution of linear equations. Frobenius theorem. Cramer's rule.
4 Gaussian elimination algorithm.
5 Real functions of one real variable. Definitions, graph. Function bounded, monotonous,
even, odd, periodic. One-to-one function, inverse and composite functions.
6 Elementary functions.
7 Limit of a function. Continuous and discontinuous functions.
8 Differential calculus of one variable. Derivative of a function, its geometrical and
physical applications. Rules of differentiation.
9 Derivatives of elementary functions.
10 Differential functions. Derivative of a function defined parametrically. Derivatives of
higher orders. L'Hospital's rule.
11 Use of derivatives to detect monotonicity, convexity and concavity features.
12 Extrema of functions. Asymptotes. Graph of a function.
13 Analytic geometry in E3. Scalar, cross and triple product of vectors and their properties.
14 Equation of a line. Equation of a plane. Relative positions problems.
Metric or distance problems.

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 | 30 | 3 |

Show history

Conditions for subject completion and attendance at the exercises within ISP:

Show history

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

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

ECTS - MechEng - Bachelor Studies | 2022/2023 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block | |||

ECTS Bc.-Mgr. | 2022/2023 | Full-time | English | Choice-compulsory | 200 - Faculty of Civil Engineering - Dean's Office | stu. block | |||

FMT+9360 | 2021/2022 | Full-time | English | Optional | 600 - Faculty of Materials Science and Technology - Dean's Office | stu. block | |||

ECTS - MechEng - Bachelor Studies | 2021/2022 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block | |||

ECTS Bc.-Mgr. | 2021/2022 | Full-time | English | Choice-compulsory | 200 - Faculty of Civil Engineering - Dean's Office | stu. block | |||

FMT+9360 | 2020/2021 | Full-time | English | Optional | 600 - Faculty of Materials Science and Technology - Dean's Office | stu. block | |||

ECTS FCE Bc-Mgr | 2020/2021 | Full-time | English | Choice-compulsory | 200 - Faculty of Civil Engineering - Dean's Office | stu. block | |||

ECTS - MechEng - Bachelor Studies | 2020/2021 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block | |||

ECTS FCE Bc-Mgr | 2019/2020 | Full-time | English | Choice-compulsory | 200 - Faculty of Civil Engineering - Dean's Office | stu. block | |||

Additional Subjects | 2019/2020 | Full-time | English | Choice-compulsory | 301 - Study and International Office | stu. block | |||

FMST | 2019/2020 | Full-time | English | Compulsory | 601 - Study Office | stu. block |

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