ITS Mathematical Tools

Garant předmětu:

Lecturer:

Tutor:

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:

Entry requirements: see https://zolotarev.fd.cvut.cz/mni/ -

among other things, knowledge of basic operations with polynomials, functions of complex variable, calculations of sums of infinite and functional series, concepts of discrete and continuous signal, signal sampling, system input / output, spectrum. Basic knowledge of statistical learning methods in the scope of the subject 11MAMY. Working knowledge of the MATLAB system resp. python + NumPy + SciPy + pandas + statmodels.

Requirements for passing the course: see https://zolotarev.fd.cvut.cz/mni/ - submission of independently prepared homework assignments (etronically, dates published on the fly during lectures and on the web), submission of semester work no later than by the end of August.

Syllabus of lectures:

See https://zolotarev.fd.cvut.cz/mni/

Syllabus of tutorials:

See https://zolotarev.fd.cvut.cz/mni/

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:

Kovacevic, J., Goyal, V. K., & Vetterli, M. (2013). Fourier and wavelet signal processing. Fourier Wavelets.org, 294pp. With permission of authors the preprint is available from our webpage as PDF here.

Broughton, S. A., & Bryan, K. (2018). Discrete Fourier analysis and wavelets: applications to signal and image processing. 2nd edition. John Wiley & Sons.

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning. New York: Springer. Electronic version, errata, and supplementary material available from https://www.statlearning.com/.

Friedman, J., Hastie, T., & Tibshirani, R. (2009). The elements of statistical learning. Springer Series in Statistics. 2nd edition. New York: Springer. Electronic version, errata, and supplementary material available from https://web.stanford.edu/~hastie/ElemStatLearn/.

Heath, M. T. (2018). Scientific Computing: An Introductory Survey, Revised Second Edition. 2nd externed edition. Society for Industrial and Applied Mathematics.

Li, J., & Chen, Y. T. (2019). Computational partial differential equations using MATLAB®. 2nd edition. CRC press. ​

Note:

Further information:

https://zolotarev.fd.cvut.cz/mni/

No time-table has been prepared for this course

The course is a part of the following study plans:

• navaz. mag. PRE program IS v EN 21/22 (nová akreditace) (compulsory course)
• navaz. mag. PRE program IS joint degree 21/22 (nová akreditace) (compulsory course)
• navaz. mag. PRE program SC 21/22 (pro studenty, kteří absolvují některé předměty 1.roč. na UTEP) (compulsory course in the program)
• navaz. mag. PRE program IS v EN 22/23 (nová akreditace) (compulsory course)
• navaz. mag. PRE program IS joint degree 22/23 (nová akreditace) (compulsory course)
• navaz. mag. PRE program SC 22/23 (pro studenty, kteří absolvují některé předměty 1.roč. na UTEP) (compulsory course in the program)
• navaz. mag. PRE program IS v EN 23/24 (compulsory course)
• navaz. mag. PRE program IS joint degree 23/24 (compulsory course)
• navaz. mag. PRE program SC 23/24 (pro studenty, kteří absolvují některé předměty 1.roč. na UTEP) (compulsory course in the program)