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

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

Study level | postgraduate | Requirement | Choice-compulsory |

Year | Semester | winter + summer | |

Study language | Czech | ||

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

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

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

Login | Name | Tuitor | Teacher giving lectures |

DOL30 | doc. RNDr. Jarmila Doležalová, CSc. | ||

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

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

Form of study | Way of compl. | Extent |

Full-time | Examination | 20+0 |

Combined | Examination | 20+0 |

Main study goals:
(i) to be acquainted with actual progress in this mathematical discipline,
(ii) to extend needed theoretical knowledge with emphasized orientation to its applicability,
(iii) to increase communication ability of specialists in different branches.
With regard to professional orientation of students learning themes modification is offered to fulfill presented aims.

Lectures

Individual consultations

Tutorials

Project work

Fourier series: orthogonal functions, Fourier coefficients, even and odd
functions, convergence of the Fourier series, complex form, solution of second
order linear differential equations.
Partial differential equations: general discussion, first-order and second-
order
partial differential equations (initial and boundary conditions, methods of
solution), second-order linear partial differential equations (method of the
characteristics, method of separation of variables), the wave equation, the
heat-conduction equation, the Laplace equation, Maxwell's equations.

James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6

Strauss, W.A.: Partial differential equations: an introduction. New York: Wiley, 1992. ISBN 0-471-54868-5

Each student has to create a project on a given topic.
Exam
Writen part consits of solving three examples (Fourier series, first-order PDE, second-order PDE)
The theoretical part consists of defending the program.

hhttp://www1.maths.leeds.ac.uk/~kersale/Teach/M3414/Notes/m3414_1.pdftp://mathworld.wolfram.com/PartialDifferentialEquation.html
https://arxiv.org/pdf/1901.03022.pdf

Each student must discharge:
a) examples,
b) project.

Subject has no prerequisities.

Subject has no co-requisities.

Syllabus of lecture
1. Fourier series: periodic functions, Fourier coefficients, functions of the period 2 PI, function of the period T, even and odd functions
2. Even and odd functions, half - range cosine and sine series, convergence of Fourier series
3. Solution of 2nd order linear differential equations with constant coefficients by Fourier series
4. Partial differential equations: general discussion
5. Methods of solutions of partial differential equations of the first order
6. Methods of solutions of partial differential equations of the second order
7. Fourier´s method of separation
8. 2nd order partial linear differential equations
9. Canonical form of 2nd order partial linear differential equations
10. Laplace equation: separated solutions, boundary conditions
11. Solution of the one-dimensional wave equation: d’Alembert solution, method of the
separation of variables,
12. Solution of a boundary problem
13. Solution of the heat-conduction: one dimensional heat conduction equation, separation method.
14. Reserve

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

Examination | Examination |

Show history

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

2019/2020 | (P3924) Materials Science and Engineering | P | Czech | Ostrava | Choice-compulsory | study plan | |||||

2019/2020 | (P3924) Materials Science and Engineering | K | Czech | Ostrava | Choice-compulsory | study plan | |||||

2019/2020 | (P2346) Mechanical Engineering | (2301V001) Transport and Material Handling | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P2346) Mechanical Engineering | (2301V013) Robotics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P2346) Mechanical Engineering | (2302V006) Energy Engineering | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P2346) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P2346) Mechanical Engineering | (2303V002) Mechanical Engineering Technology | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P2346) Mechanical Engineering | (3901V003) Applied Mechanics | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P2346) Mechanical Engineering | (3902V056) Control of Machines and Processes | P | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P2346) Mechanical Engineering | (2301V001) Transport and Material Handling | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P2346) Mechanical Engineering | (2301V013) Robotics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P2346) Mechanical Engineering | (2302V006) Energy Engineering | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P2346) Mechanical Engineering | (2302V019) Contruction of Production Machines and Equipment | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P2346) Mechanical Engineering | (2303V002) Mechanical Engineering Technology | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P2346) Mechanical Engineering | (3901V003) Applied Mechanics | K | Czech | Ostrava | Choice-compulsory | study plan | ||||

2019/2020 | (P2346) Mechanical Engineering | (3902V056) Control of Machines and Processes | K | Czech | Ostrava | Choice-compulsory | study plan |

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