Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 10 |

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

Study level | postgraduate | Requirement | Optional |

Year | Semester | winter + summer | |

Study language | Czech | ||

Year of introduction | 2009/2010 | Year of cancellation | 2018/2019 |

Intended for the faculties | FMT, HGF, FEI, USP, FBI, FS | Intended for study types | Doctoral |

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

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

Extent of instruction for forms of study | ||
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Form of study | Way of compl. | Extent |

Full-time | Examination | 20+0 |

Part-time | Examination | 20+0 |

Students learn structural approach to mathematical formulation of engineering problems. They shlould know how
to analyze given problem,
to formulate mathematical task,
to choose and correctly use appropriate mathematical method.

Lectures

Individual consultations

Project work

The topic offers a complex view on mathematical modeling of physical states and
processes with emphasized orientation to the problems described by differential
equations. Applications are devoted to the solving of real problems comming out
from engineering praxis in regard to prevailing student specialization. The use of mathematical software is assumed, e.g. MATLAB and its toolboxes.

Vlček, J.: Mathematical modeling, http://homen.vsb.cz/~vlc20/
Mathematical Modelling (Ed. M.S. Klamkin). SIAM, 1989.
Mathematical Modeling with Multidisciplinary Applications. Edited by Xin-She Yang, John Wiley & Sons, Inc., UK, 2013

Friedman, A. - Littman, W.: Industrial Mathematics. SIAM, 1994.
Keener, J. P.: Principles of Applied Mathematics. Adison-Wesley Publ. Comp. 1994

www.mdg.vsb.cz

Elaboration of semestral project

Subject has no prerequisities.

Subject has no co-requisities.

1. Principles of mathematical modeling. Model quantities.
2. Basic relations, local and global balance.
3. One-dimensional stationary states.
4. Classification of boundary problems. Corectness of mathematical model.
5. Non-stationary processes - one-dimensional case. Initial problems.
6. First order PDE. Method of characteristics.
7. Application - free and thermal convection.
8. PDE of second order: classification, Fourier method.
9. Fourier method for parabolic and hyperbolic PDE.
10. Multi-dimensional stationary states.
11. Fourier method for elliptic PDE.
12. Boundary problems for multivariate problems.
13. Numerical methods - a brief introduction.
14. Facultative themes.

Conditions for completion are defined only for particular subject version and form of study

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

2010/2011 | (P2102) Mineral Raw Materials | (3902V010) Automation of Technological Processes | P | Czech | Ostrava | Optional | study plan | |||||

2010/2011 | (P1701) Physics | (1702V001) Applied Physics | P | Czech | Ostrava | Optional | study plan | |||||

2010/2011 | (P1701) Physics | K | Czech | Ostrava | Optional | study plan | ||||||

2010/2011 | (P1701) Physics | (1702V001) Applied Physics | K | Czech | Ostrava | Optional | study plan | |||||

2010/2011 | (P2102) Mineral Raw Materials | (3902V010) Automation of Technological Processes | K | Czech | Ostrava | Optional | study plan |

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