Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 7 |

Subject guarantor | Mgr. Jiří Vrbický, Ph.D. | Subject version guarantor | Mgr. Jiří Vrbický, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | winter |

Study language | Czech | ||

Year of introduction | 1999/2000 | Year of cancellation | 2013/2014 |

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

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

Login | Name | Tuitor | Teacher giving lectures |

OND10 | Mgr. Ivana Onderková, Ph.D. |

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

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+3 |

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

Linear Algebra: An algebraic vector, basic terms. A matrix, the rank of a
matrix, elementary treatments of a matrix. Systems of linear equations. A
determinant, determinant properties. Foundations of the matrix calculus.
The Real-Valued Function of a Real Variable: Definition, the domain of
definition, the range of values, the graph of a function. Properties of
functions. Inverse, composite functions. Basic elementary functions. The
sequence of real numbers and the limit of the sequence. The limit of a function
at a point. The continuity of a function.
The Derivation of a Function: Derivation definition and the geometric
significance of the derivation. The derivation of basic elementary functions.
Derivation Applications: A tangent and a normal. Monotony. Local and absolute
extreme values of a function. Convexity, concavity, inflection points.
Asymptotes. The behaviour of a function.
The Differential Calculus of Functions of Several Variables: The definition of
functions of two and several variables, the domain of definition. The partial
derivations of the first and higher orders.
The Indefinite Integral: An indefinite integral and a primitive function.
Basic formulas. Integration by parts. The method of substitution.

Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3
Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications.
D.C.Heath and Company, Lexington1990, 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

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
http://mdg.vsb.cz/M/

No special requirements.

Subject has no prerequisities.

Subject has no co-requisities.

1 Linear algebra: Vectors, matrice (basic properties).
2 Determinants (basic properties, calculation, evaluation).
3 Matrix inversion.
4 Systems of linear equations, Cramer’s rule, Gaussian elimination.
5 Functions of one real variable (definitions and basic properties).
6 Elementary functions.
7 Limit of the function, continuity of the functions , basic rules.
8 Differential calculus functions of one real variable. The derivative of function (basic rules for differentiation).
9 Derivatives of selected functions.
10 Differential of the function, parametric differentiation, highes-order derivative.
11 Applications of the derivatives.
12 Monotonic functions and extremes of function, convexity and concavity of a function.
13 Integral calculus: antiderivative and indefinite integral for functions of one variable.
14 Integration methods - substitution, integration by parts.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |

Examination | Examination | 70 | 30 |

Exercises evaluation | Credit | 30 | 7 |

Show history

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

2013/2014 | (B2109) Metallurgical Engineering | (2109R031) Art Foundry Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2012/2013 | (B2109) Metallurgical Engineering | (2109R031) Art Foundry Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2011/2012 | (B2109) Metallurgical Engineering | (2109R031) Art Foundry Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2010/2011 | (B2109) Metallurgical Engineering | (2109R031) Art Foundry Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2009/2010 | (B2109) Metallurgical Engineering | (2109R031) Art Foundry Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2008/2009 | (B2109) Metallurgical Engineering | (2109R031) Art Foundry Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2007/2008 | (B2109) Metallurgical Engineering | (2109R031) Art Foundry Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2006/2007 | (B2109) Metallurgical Engineering | (2109R031) Art Foundry Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2005/2006 | (B2109) Metallurgical Engineering | (2109R031) Art Foundry Engineering | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2004/2005 | (B2113) Materiálové technologie | (2109R031) Artistic Foundry | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2003/2004 | (B2113) Materiálové technologie | (2109R031) Artistic Foundry | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2002/2003 | (B2113) Materiálové technologie | (2109R031) Artistic Foundry | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2001/2002 | (B2113) Materiálové technologie | (2109R031) Artistic Foundry | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2000/2001 | (B2113) Materiálové technologie | (2109R031) Artistic Foundry | P | 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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