Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |

Subject guarantor | Mgr. Ivona Tomečková, Ph.D. | Subject version guarantor | Mgr. Ivona Tomečková, Ph.D. |

Study level | undergraduate or graduate | Requirement | Optional |

Year | 1 | Semester | summer |

Study language | Czech | ||

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

Intended for the faculties | FEI | Intended for study types | Master, Follow-up Master |

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

Login | Name | Tuitor | Teacher giving lectures |

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

SVO19 | Mgr. Ivona Tomečková, Ph.D. |

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

Form of study | Way of compl. | Extent |

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

Part-time | Credit and Examination | 10+0 |

Distance | Credit and Examination | 10+0 |

Students will learn a structural approach to move from meaningful physical assumptions and observed conclusions to mathematical problems known from previous studies and engineering practice.
The acquired knowledge will then be used to analyse of specific tasks via
- a suitable mathematical formulation through differential equations,
- recognizing the appropriate calculation method and the correct calculation of the mathematical issue and
- a final meaningful physical interpretation of the results.

Lectures

Individual consultations

Tutorials

Project work

The course offers a unified view of mathematical modeling of physical states and
processes with a focus on tasks described by differential equations. Applications are
devoted to the solving real problems of engineering practice with regard to the prevailing professional focus of students. Students' knowledge of some mathematical software is assumed, for example MatLab, to get the result or its visualization.

[1]
William E.: Partial Differential Equation Analysis in Biomedical Engineering - Case Studies with MATLAB, 2013
[2]
Kulakowski, Bohdan T.; Gardner, John F.; Shearer, J. Lowen: Dynamic Modeling and Control of Engineering Systems, 3rd Edition, 2007
[3]
Mathematical Modelling: Classroom Notes in Applied Mathematics (Ed. M.S. Klamkin). SIAM Philadelphia, 3rd printing, 1995.

Friedman, A. - Littman, W.: Industrial Mathematics. SIAM, 1994

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 50 points.
Theoretical 20 points

Individual application project.

Subject has no prerequisities.

Subject has no co-requisities.

Principles of mathematical modeling. Model quantities.
Basic relations, local and global balance.
One-dimensional stationary states.
Classification of boundary problems. Corectness of mathematical model.
Non-stationary processes - one-dimensional case. Initial problems.
Method of characteristics for the PDEs of the first order.
Application - free thermal convection.
PDEs of the second order: classification, Fourier method.
Fourier method for parabolic and hyperbolic PDEs.
Multi-dimensional stationary states.
Fourier method for elliptic PDEs. Boundary problems for multivariate problems.
Facultative themes.

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

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

Credit | Credit | 30 | 10 | |

Examination | Examination | 70 | 21 | 3 |

Show history

Conditions for subject completion and attendance at the exercises within ISP: Credit: - successful completion of one unseen written paper with practical tasks. Exam: - a written part: elaboration of a term paper of sufficient quality, - an oral part: the term paper defense and demonstration of the theoretical knowledge regarding to the course topics.

Show history

Academic year | Programme | Branch/spec. | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | 1 | Optional | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | 1 | Optional | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | 1 | Optional | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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2023/2024 Summer |