Gurantor department | Department of Applied Mathematics | Credits | 6 |

Subject guarantor | doc. RNDr. Marek Lampart, Ph.D. | Subject version guarantor | doc. RNDr. Marek Lampart, Ph.D. |

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | winter |

Study language | English | ||

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

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

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

Login | Name | Tuitor | Teacher giving lectures |

LAM05 | doc. RNDr. Marek Lampart, Ph.D. | ||

MRO0010 | Ing. Martin Mrovec |

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

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 3+3 |

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

To give students knowledge of basic concepts of complex functions of complex variable and integral transformations.

Lectures

Tutorials

Project work

Functions of complex variable and integral transformations are one of the basic tools of effective solution of technical problems. The students will get knowledge of basic concepts
of functions of complex variable and integral transformations.

G. James and D. Burley, P. Dyke, J. Searl, N. Steele, J. Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994.
William L. Briggs, Van Emden Henson: An Owner's Manual for the Discrete Fourier Transform, SIAM, 1995, ISBN 0-89871-342-0.
Michael W. Frazier: An introduction to wavelets through Linear Algebra, Springer,1999, ISBN 0-387-98639-1.

Howie J.M., Complex Analysis, Springer-Verlag London, 2003, ISBN 978-1-85233-733-9.
Needham T., Visual complex analysis, Oxford University Press, 1997, ISBN 0-19-853446-9.

Verification of study:
Test of complex variable - max. 10 points.
Test of Laplace transform - max. 10 points.
Individual project of Laplace transform - max. 10 points.
Individual project of Fourier series - max. 10 points.
Conditions for credit:
Two tests - max. 20 points.
Two individual projects - max. 20 points.
Maximal number of points from exercises - 40 points.
Minimal number of points from exercises - 20 points.

No additional requirements are imposed on the student.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures:
Complex functions and mappings. Complex differentiation, contour integration and deforming the contour.
Complex series: power series, Taylor and Laurent series. Residue theorem. Applications.
Introduction to Fourier series. Orthogonal systems of functions. Generalized Fourier series. Applications.
Introduction to integral transforms. Convolution.
Laplace transform, fundamental properties. Inverse Laplace transform. Applications.
Fourier transform, fundamental properties. Inverse Fourier transform. Applications.
Z-transform, fundamental properties. Inverse Z-transform. Applications.
Exercises:
Practising of complex functions, linear and quadratic mappings.
Practising of complex differentiation, conformal mappings, contour integration and deforming the contour.
Examples of Taylor and Laurent series and applications.
Examples of orthogonal systems of functions, Fourier series and applications.
Practising of Laplace transform. Solution of differential equation.
Practising of Fourier transform and examples.
Practising of Z-transform. Solution of difference equation.
Projects:
Two individual works and their presentation on the theme:
Fourier series.
Laplace transform.

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 | 40 (40) | 20 |

Test 1. | Written test | 10 | 0 |

Test 2. | Written test | 10 | 0 |

Projekt 1. | Project | 10 | 0 |

Projekt 2. | Project | 10 | 0 |

Examination | Examination | 60 | 11 |

Show history

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

2020/2021 | (N0714A270004) Mechatronics | CMS | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (N3943) Mechatronics | (3906T006) Mechatronic Systems | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (N0714A270004) Mechatronics | CMS | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2018/2019 | (N3943) Mechatronics | (3906T006) Mechatronic Systems | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (N3943) Mechatronics | (3906T006) Mechatronic Systems | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2016/2017 | (N3943) Mechatronics | (3906T006) Mechatronic Systems | P | English | Ostrava | 1 | Compulsory | study plan | ||||

2015/2016 | (N3943) Mechatronics | (3906T006) Mechatronic Systems | P | English | Ostrava | 1 | Compulsory | study plan |

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