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

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

Login | Name | Tuitor | Teacher giving lectures |

BEL10 | Mgr. Jana Bělohlávková | ||

KOT31 | RNDr. Jan Kotůlek, Ph.D. | ||

ZID76 | Mgr. Arnošt Žídek, Ph.D. |

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

Form of study | Way of compl. | Extent |

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

Goals
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

Course description
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.

Passing the course, requirements
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.

Program of lectures
--------------------------------------------------
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.
Program of exercises and seminars:
--------------------------------------------------
1 Basic operations with matrices. Determinants. Calculation of determinant developing the elements of any series.
2 Rank of matrix, inverse matrix.
3 Solution of linear equations.
4 Solution of systems of linear equations.
5 1. test (calculate determinant, rank of matrix, solution of the system, the inverse matrix).
6 Functions of a simple, inverse, compound. Elementary functions. Trigonometric functions.
7 2.test (domain, inverse function). Limits of functions.
8 Differentiation of functions.
9 Derivations and differential, equations of tangents and normals point functions.
10 Calculation of the limit L'Hospital rule functions. Extremes of function.
11 Convex and concave function, inflection point.
12 3.test (derivative of the function, use). Asymptotes of the curve. A function.
13 Analytic geometry.
14 Reserve and credits.

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 | 30 |

Show history

Academic year | Programme | Field of study | Spec. | 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 | 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 |