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

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

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 2 | Semester | winter |

Study language | Czech | ||

Year of introduction | 2015/2016 | Year of cancellation | 2018/2019 |

Intended for the faculties | FS, USP | Intended for study types | Bachelor |

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+2 |

This subject offers integrated view on mathematical methods and tools needed to a solution practical problems described by differential equations. The applications are oriented to the problem solving of engineering practice with regard to prevailing speciality of students. Established goals tend namely to following knowledges:
- an orientation in typology of ordianary and partial differential equations;
- acquirement of basic analytical methods for solving of ordinary DE;
- an use of selected numerical methods;
- an ability to perform adequate mathematical model of real problem.

Lectures

Tutorials

This objective presents the part of basic mathematical course in the bachelor degree.

VLČEK, J., Mathematical modeling - http://homen.vsb.cz/~vlc20
AHMAD, S., AMBROSETTI, A.: A Textbook of Ordinary Differential Equations. Springer, 2014. ISBN 978-3-319-02129-4

LOGAN, J. D. A First Course in Differential Equations, Springer, 2011, 386 pp., ISBN 978-1-4419-7592-8

pass two written test (2 x 10 points)
elaboration of semestral project (10 points)

participation on tutorials is obligatory, 20% of absence can be apologized

Subject has no prerequisities.

Subject has no co-requisities.

1. Introduction: basic notions, solution of DE, Cauchy problem, exitence and uniqueness of solution.
2. Solving methods of ordinary first-order DE: separation of variables, linear and Bernoulli DE, direction field and othogonal trajectories; special types of 1st order ODE.
3.Simple numerical methods: Picard approximation, Euler method.
4. Applications: kinematic equations, evolution an logistic models.
5. Linear ODE of higher order I - homogeneous equations: structure and properties of solution, equations with constant coefficients.
6. Linear ODE of higher order II: complete equation with constant coefficients, equation with special right side; selected applications: mechanical vibrations, electrical circuits.
7. Systems of DE: linear systems, homogeneous systems with constant coefficients.
8. Non-homogeneous linear systems: structure of solution, analytical methods for solving.
9. Phase-mapping of solution of homogeneous 2nd order system, introduction to the stability theory.
10. The backgrounds of partial DE: basic notions, method of characteristics for the 1st order PDE.
11. Second order PDE: typology, important equations in mathematical physics.

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 | 15 |

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 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2018/2019 | (B3968) Applied Sciences and Technologies | (3901R076) Applied Sciences and Technologies | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2017/2018 | (B3968) Applied Sciences and Technologies | (3901R076) Applied Sciences and Technologies | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2016/2017 | (B3968) Applied Sciences and Technologies | (3901R076) Applied Sciences and Technologies | P | Czech | Ostrava | 2 | Compulsory | study plan | ||||

2015/2016 | (B3968) Applied Sciences and Technologies | (3901R076) Applied Sciences and Technologies | P | Czech | Ostrava | 2 | Compulsory | study plan |

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