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 ODEs and PDEs, 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 ODEs and PDEs, transfer function, convolution, Duhamel integral.

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

Fourier series, Fourier method for PDEs, 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 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

	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
Wed	roomKN:D-105 Halama J. 08:00–09:45 (lecture parallel1) Karlovo nám. roomKN:D-105 Halama J. 09:45–10:30 (lecture parallel1 parallel nr.101) Karlovo nám.
Thu
Fri

The course is a part of the following study plans: