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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Complex Number Functions and Integral and Discrete Transforms in Applications

The course is not on the list Without time-table
Code Completion Credits Range Language
2011078 ZK 3 2P+1C Czech
Lecturer:
Tutor:
Supervisor:
Department of Technical Mathematics
Synopsis:

Course requires the knowledge of mathematics of the bachelor level „alpha“. Brief summary: introduction to complex functions, Laplace transform, Z transform, Fourier series, Fourier transform, discrete Fourier transform, aplications for ODE‘s and PDE‘s, signal spectra, filters, introduction to time-frequency analysis.

Requirements:
Syllabus of lectures:

•Complex function, derivative, integral, Taylor and Laurent series, residue in singularity.

•Laplace transform, existence of transform, properties, inverse transform.

•Applications for ODE‘s and PDE‘s, transfer function, convolution, Duhamel integral.

•Z-transform, aplication for discrete equations, stability of numerical method for ODE.

•Fourier series, Fourier method for PDE‘s, Fourier integral.

•Fourier transform, existence of transform, properties, similarity to Laplace transform.

•Discrete Fourier transform, discrete convolution, amplitude spectra, filters.

•Windowed Fourier transform, wavelet transform. Hilbert-Huang transform.

Syllabus of tutorials:
Study Objective:
Study materials:

•P. Dyke: An Introduction to Laplace Transforms and Fourier Series, Springer, 2014

• E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 1993

http://www.wavelet.org/

Note:
Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2019-09-17
For updated information see http://bilakniha.cvut.cz/en/predmet5900806.html