CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2020/2021

# ITS Mathematical Tools

Code Completion Credits Range
11MAI Z,ZK 4 2P+2C
Lecturer:
Jan Přikryl (guarantor)
Tutor:
Jan Přikryl (guarantor)
Supervisor:
Department of Applied Mathematics
Synopsis:

Series, Fourier Series. Discrete Fourier Transform. Segmentation of signals, windows, localization. Short-term Fourier Transform. From Fourier Analysis to PDE. Fundamentals of Numerical Mathematics. Numerical solutions to ODEs and PDEs. Continuous traffic flow models described by PDE. Car-following models as ODEs.

Requirements:

Knowledge of operations with polynomials, complex functions, calculus of sums of infinite and functional series, discrete and continuous signals, signal sampling, system input / output, spectrum. The basics of MATLAB resp. python+NumPy.

Syllabus of lectures:
Syllabus of tutorials:
Study Objective:

Mastering Fourier series for signal analysis, use of STFT for non-stationary signals, knowledge of the use of spectrograms. Fundamentals of numerical solution of ordinary and partial differential equations occurring in traffic flow models.

Study materials:

Vetterli M., Kovacević J., Goyal V.K. Foundations of Signal Processing. Cambridge University Press, 2014, 738pp.

Howell K.B. Principles of Fourier Analysis. CRC Press, 2001, 792pp.

Heath M.T. Scientific Computing: An Introductory Survey. McGraw Hill, 2002, 563pp.

Li J., Chen Y.T. Computational Partial Differential Equations Using MATLAB. CRC

Note:
Time-table for winter semester 2020/2021:
Time-table is not available yet
Time-table for summer semester 2020/2021:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-10-23
For updated information see http://bilakniha.cvut.cz/en/predmet1925706.html