Gurantor department | Department of Applied Mathematics | Credits | 3 |

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

Study level | undergraduate or graduate | Requirement | Compulsory |

Year | 1 | Semester | summer |

Study language | Czech | ||

Year of introduction | 2010/2011 | Year of cancellation | 2013/2014 |

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

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

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

Extent of instruction for forms of study | ||
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Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+1 |

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.

There are not defined other requirements for student.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures:
Differential and integral calculus of functions of complex variables: the derivative,
conformal mappings. Complex integral, Cauchy integral theorem.
Taylor and Laurent series, convergence, residua classification of singular
points.
Direct and inverse Laplace transform, properties. Usage for the solution
of differential equations.
Orthogonal systems of functions. Fourier series, the foundations of harmonic analysis.
Direct and inverse Fourier transform, properties and uses.
exercise:
Solving problems on the topic: derivative, conformal mappings, complex integral.
Use of the integral Cauchy's formulas.
Solving problems on the topic: Taylor series, Laurent series, residua.
Solving problems on the topic: direct and inverse Laplace transformation. Usage for the solution
of differential equations.
Solving problems on the topic: orthogonal systems of functions and Fourier series.
projects:
Two individual jobs on the topic:
Fourier series.
Laplace transformation.

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 | 30 | 10 |

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 | |
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2012/2013 | (N2102) Mineral Raw Materials | (3911T001) Applied Physics of Materials | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2011/2012 | (N2102) Mineral Raw Materials | (3911T001) Applied Physics of Materials | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2010/2011 | (N2102) Mineral Raw Materials | (3911T001) Applied Physics of Materials | P | Czech | Ostrava | 1 | Compulsory | study plan |

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