Complex Number Functions and Integral and Discrete Transforms in Applications

Course guarantor:

Jan Halama

Lecturer:

Jan Halama

Tutor:

Jan Halama

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:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue	roomKN:D-104 Halama J. 10:45–12:15 (lecture parallel1) Karlovo nám. roomKN:D-104 Halama J. 12:30–13:15 (lecture parallel1 parallel nr.101) Karlovo nám.
Wed
Thu
Fri

The course is a part of the following study plans: