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

Subject guarantor | doc. Ing. David Horák, Ph.D. | Subject version guarantor | doc. Ing. David Horák, Ph.D. |

Study level | undergraduate or graduate | Requirement | Choice-compulsory |

Year | 1 | Semester | summer |

Study language | Czech | ||

Year of introduction | 1992/1993 | Year of cancellation | 2009/2010 |

Intended for the faculties | FEI | Intended for study types | Master |

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

Login | Name | Tuitor | Teacher giving lectures |

HOR33 | doc. Ing. David Horák, Ph.D. | ||

KOZ75 | prof. Ing. Tomáš Kozubek, Ph.D. |

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

Form of study | Way of compl. | Extent |

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

Combined | Credit and Examination | 10+10 |

Student should understand to basic tools and rules of integral transforms and get familiar with correct approaches for the solution of concrete problems and discuss the chosen way of their solution.

Lectures

Tutorials

Project work

Subject Integral transforms belongs to basic mathematical subjects at technical universities. The students will get knowledge about the theory and usage of Laplace transform and Z transform, Fourier series, Fourier, Window Fourier and Wavelet transforms including their applications for signal processing as time-frequency analysis, compression and denoising.

Častová, N.,Kozubek,T:Integral transforms, www.am.vsb.cz
Galajda P., Schrötter Š.: Function of complex variable and operator calculus, Alfa-Bratislava, 1991.
G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994.

Škrášek J., Tichý Z.: The basics of applied mathematics II, SNTL, Praha, 1986.

Verification of study:
Test of Fourier series - 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.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures:
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.
Distribution. Dirac impuls.
Exercises:
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 |
---|---|---|---|

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

Exercises evaluation | Credit | 40 (40) | 0 |

Project | Project | 20 | 0 |

Written exam | Written test | 20 | 0 |

Examination | Examination | 60 (60) | 0 |

Written examination | Written examination | 60 | 0 |

Show history

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

2009/2010 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | |||

2009/2010 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Choice-compulsory | study plan | |||

2008/2009 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | |||

2008/2009 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Choice-compulsory | study plan | |||

2007/2008 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | |||

2007/2008 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Choice-compulsory | study plan | |||

2006/2007 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | |||

2006/2007 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Choice-compulsory | study plan |

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