Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 3 |

Subject guarantor | doc. RNDr. Jaroslav Vlček, CSc. | Subject version guarantor | doc. RNDr. Jaroslav Vlček, CSc. |

Study level | undergraduate or graduate | Requirement | Choice-compulsory |

Year | 1 | Semester | winter |

Study language | Czech | ||

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

Intended for the faculties | USP, HGF, FMT | Intended for study types | Follow-up Master |

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

Login | Name | Tuitor | Teacher giving lectures |

KUC14 | prof. RNDr. Radek Kučera, Ph.D. | ||

VLC20 | doc. RNDr. Jaroslav Vlček, CSc. |

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

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+1 |

Students learn to use tensor calculus. They shlould know how
to analyze a problem,
to choose and correctly use appropriate algorithm,
to apply their knowledge to solve technical problems.

Lectures

Individual consultations

Tutorials

Project work

The main goal consist in the elements of tensor algebra and tensor analysis in
cartesian coordinate systems. The properties of
tensor fields are studied using local and global characteristics. Applications
are illustrated above all in the frame of static and dynamic elasticity as well
as on several problems of the electromagnetic fields in anisotropic media.

Akivis, M. A. - Goldberg, V.V.: An Introduction to Linear Algebra and Tensors. Dover Publ., N.Y. 1993
MEJLBRO, L. Calculus 2b – Real Functions in Several Variables. http://bookboon.com/cs/calculus-2b-3-ebook. ISBN 87-7681-206-5
Hess, S.: Tensors for Physics, Springer, 2015

Maxum, B.: Field Mathematics for Electromagnetics, Photonics and Materials Science. SPIE Press, Bellingham (USA), 2005
SPIEGEL, R. M., LIPSCHUTZ, S., SPELLMAN, D. Vector Analysis, 2nd edition, McGraw-Hill, 2009, ISBN 978-7161-545-7

Course-credit:
-participation on tutorials is obligatory, 20% of absence can be apologized,
-pass the written test (30 points),
Point classification: 0-30 points.
Exam
Semestral thesis classified by 25 – 50 points.
Theoretical part of the exam is classified by 0 - 20 points.

www.mdg.vsb.cz

Participation on tutorials is obligatory, 20% of absence can be apologized
Elaboration of semestral project

Subject has no prerequisities.

Subject has no co-requisities.

1. Orthogonal transformation, Cartesian tensors
2. Tensor algebra
3. Vector and tensor field, derivatives and differential operators
4. Local and global characteristics of vector fields
5. Fundamentals of tensor apparatus in static theory of elasticity
6. Stress and strain tensor, Hooke's law
7. Equations of dynamic theory of elasticity
8. Facultative themes: material anisotropy in optics, thermoelasticity, etc.

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 | 30 | 10 |

Examination | Examination | 70 | 21 |

Show history

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

2020/2021 | (N0719A270002) Nanotechnology | P | Czech | Ostrava | 1 | Choice-compulsory type B | study plan | |||||

2019/2020 | (N3942) Nanotechnology | (3942T001) Nanotechnology | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2019/2020 | (N0719A270002) Nanotechnology | P | Czech | Ostrava | 1 | Choice-compulsory type B | study plan |

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