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:
-
- IS nav.prez.11/12 (compulsory course in the program)
- IS nav.prez.12/13 (compulsory course in the program)
- IS nav.prez. 12/13- Karimova (compulsory course in the program)
- IS nav.prez.13/14 (compulsory course in the program)
- IS-EN nav.prez.14/15 (compulsory course)
- IS joint degree nav.prez.14/15 (compulsory course)
- IS joint degree nav.prez.13/14 (compulsory course in the program)
- IS joint degree nav.prez.12/13 (compulsory course in the program)
- IS nav.prez.15/16 čeština (compulsory course)
- IS-EN nav.prez.15/16 (compulsory course)
- IS joint degree nav.prez.15/16 (compulsory course)
- IS nav.prez.16/17 čeština (compulsory course)
- IS-EN nav.prez.16/17 (compulsory course)
- IS joint degree nav.prez.16/17 (compulsory course)
- IS nav.prez.17/18 čeština (compulsory course)
- IS-EN nav.prez.17/18 (compulsory course)
- IS joint degree nav.prez.17/18 (compulsory course)
- IS nav.prez.18/19 čeština (compulsory course)
- IS joint degree nav.prez.18/19 (compulsory course)
- IS-EN nav.prez.18/19 (compulsory course)
- IS nav.prez.19/20 čeština (obor IS) (compulsory course)
- IS-EN nav.prez.19/20 (compulsory course)
- IS joint degree nav.prez.19/20 (obor IS) (compulsory course)
- navaz. mag. PRE program IS v CZ 20/21 (nová akreditace) (compulsory course)
- navaz. mag. PRE program IS v EN 20/21 (nová akreditace) (compulsory course)