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

Subject guarantor | prof. RNDr. Radek Kučera, Ph.D. | Subject version guarantor | prof. RNDr. Radek Kučera, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | winter |

Study language | English | ||

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

Intended for the faculties | FS | Intended for study types | Follow-up Master |

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

Login | Name | Tuitor | Teacher giving lectures |

KRC76 | Mgr. Jiří Krček | ||

KUC14 | prof. RNDr. Radek Kučera, 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

Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions, Euler method for homogeneous systems of n equations for n functions. Integral calculus of functions of several independent variables: two-dimensional integrals, three-dimensional integrals, vector analysis, line integral of the first and the second kind, surface integral of the first and second kind. Infinite series: number series, series of functions, power series.

[1] Harshbarger, R., J., Reynolds, J., J.: Calculus with Applications. D. C. Heath and Company, Lexington1990. ISBN 0-669-21145-1
[2] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

[1] Harshbarger, R., J., Reynolds, J., J.: Calculus with Applications. D. C. Heath and Company, Lexington1990, ISBN 0-669-21145-1
[2] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

Seminar
Attending the seminar is required, only 20 % of missed lessons will be excused. It is also necessary to elaborate the home project in a form specified by the lecturer and a student is awarded 5 points for the project. Several tests will be carried out during the semester, a student can acquire up to 15 points.
Examination
The exam consists of two parts:
I) Practical part - tests the ability of solving practical problems. (60 points is a maximum, but at least 20 points are necessary)
II) Theoretical part - examines the understanding of the underlying theoretical concepts. (20 points is a maximum, but at least 5 points are necessary)

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

No more requirements are put on the student.

Subject has no prerequisities.

Subject has no co-requisities.

Syllabus of lecture
1 Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions
2 Euler method for homogeneous systems of n equations for n functions
3 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2
4 Transformation - polar coordinates, geometrical and physical applications
5 Three-dimensional integrals on coordinate cube, on bounded subset of R3
6 Transformation - cylindrical and spherical coordinates, geometrical and physical applications
7 Vector analysis, gradient
8 Divergence, rotation
9 Line integral of the first and of the second kind
10 Green´s theorem, potential
11 Geometrical and physical applications
12 Infinite number series
13 Infinite series of functions, power series
Syllabus of seminar
1 Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions
2 Euler method for homogeneous systems of n equations for n functions
3 Euler method for homogeneous systems of n equations for n functions, test
4 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2
5 Transformation - polar coordinates
6 Geometrical and physical applications
7 Three-dimensional integrals on coordinate cube, on bounded subset of R3
8 Transformation - cylindrical and spherical coordinates
9 Geometrical and physical applications, test
10 Vector analysis, gradient
11 Divergence, rotation
12 Line integral of the first kind
13 Line integral of the second kind, test
14 Geometrical and physical applications

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 (80) | 31 |

Practical part | Written examination | 60 | 25 |

Theoretical part | Oral examination | 20 | 5 |

Show history

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

2027/2028 | (N0715A270034) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2026/2027 | (N0715A270034) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2025/2026 | (N0715A270034) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2024/2025 | (N0715A270034) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2023/2024 | (N0715A270034) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2023/2024 | (N0715A270033) Applied Mechanics | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (N0715A270034) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2022/2023 | (N0715A270033) Applied Mechanics | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (N0713A070003) Energy Engineering | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (N0715A270009) Industrial Engineering | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (N0715A270034) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (N0715A270033) Applied Mechanics | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (N0715A270022) Mechanical Engineering Technology | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (N0714A270012) Control of Machines and Processes | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2021/2022 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (N2301) Mechanical Engineering | (2302T006) Energy Engineering | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (NFS010) Engineering Design | (S06) Construction of Mechanical Parts | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (NFS010) Engineering Design | (S01) Transport and process equipment | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (NFS010) Engineering Design | (S02) Production Machines and Design | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (NFS010) Engineering Design | (S05) Design of industrial products | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (NFS010) Engineering Design | (S04) Earthwork and Building Machines | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2021/2022 | (NFS010) Engineering Design | (S03) Engineering Diagnostics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (N0713A070003) Energy Engineering | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2020/2021 | (N0715A270009) Industrial Engineering | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2020/2021 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (N2301) Mechanical Engineering | (2302T006) Energy Engineering | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (N0715A270033) Applied Mechanics | P | Czech | Ostrava | 1 | Compulsory | study plan | |||||

2020/2021 | (N0715A270022) Mechanical Engineering Technology | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2019/2020 | (N2301) Mechanical Engineering | (3901T003) Applied Mechanics | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (N2301) Mechanical Engineering | (2302T006) Energy Engineering | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (N0715A270009) Industrial Engineering | P | English | Ostrava | 1 | Compulsory | study plan | |||||

2019/2020 | (N0713A070003) Energy Engineering | 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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