Subject description - A3M01MKI
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| A3M01MKI |
Mathematics for Cybernetics |
| Roles: | |
Extent of teaching: | 4P+2S |
| Department: | 13101 |
Language of teaching: | CS |
| Guarantors: | |
Completion: | Z,ZK |
| Lecturers: | |
Credits: | 8 |
| Tutors: | |
Semester: | Z |
Web page:
http://math.feld.cvut.cz/veronika/vyuka/b3b01kat.htm
Anotation:
The goal is to explain basic principles of complex analysis and its applications. Fourier transform, Laplace transform and Z-transform are treated in complex field. Finally random processes (stacinary, markovian, spectral density) are treated.
Course outlines:
| 1. | | Complex plane. Functions of compex variables. Elementary functions. |
| 2. | | Cauchy-Riemann conditions. Holomorphy. |
| 3. | | Curve integral. Cauchy theorem and Cauchy integral formula. |
| 4. | | Expanding a function into power series. Laurent series. |
| 5. | | Expanding a function into Laurent series. |
| 6. | | Resudie. Residue therorem. |
| 7. | | Fourier transform. |
| 8. | | Laplace transform. Computing the inverse trasform by residue method. |
| 9. | | Z-transform and its applications. |
| 10. | | Continuous random processes and time series - autocovariance, stacionarity. |
| 11. | | Basic examples - Poisson processes, gaussian processes, Wiener proces, white noice. |
| 12. | | Spectral density of the stacionary process and its expression by means of Fourier transform. Spectral decomposition of moving averages. |
| 13. | | Markov chains with continuous time and general state space. |
Exercises outline:
| 1. | | Complex plane. Functions of compex variables. Elementary functions. |
| 2. | | Cauchy-Riemann conditions. Holomorphy. |
| 3. | | Curve integral. Cauchy theorem and Cauchy integral formula. |
| 4. | | Expanding a function into power series. Laurent series. |
| 5. | | Expanding a function into Laurent series. |
| 6. | | Resudie. Residue theroem |
| 7. | | Fourier transform |
| 8. | | Laplace transform. Computing the inverse trasform by residue method. |
| 9. | | Z-transform and its applications. |
| 10. | | Continuous random processes and time series - autocovariance, stacionarity. |
| 11. | | Basic examples - Poisson processes, gaussian processes, Wiener proces, white noice. |
| 12. | | Spectral density of the stacionary process and its expression by means of Fourier transform. Spectral decomposition of moving averages. |
| 13. | | Markov chains with continuous time and general state space. |
Literature:
| [1] | | S.Lang. Complex Analysis, Springer, 1993. |
| [2] | | L.Debnath: Integral Transforms and Their Applications, 1995, CRC Press, Inc. |
| [3] | | Joel L. Shiff: The Laplace Transform, Theory and Applications, 1999, Springer Verlag. |
Requirements:
Informace viz
http://math.feld.cvut.cz/0educ/pozad/b3b01kat.htm
Subject is included into these academic programs:
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| Page updated 20.4.2025 09:54:05, semester: L/2026-7, L/2024-5, Z/2026-7, Z/2024-5, Z,L/2025-6, Send comments about the content to the Administrators of the Academic Programs |
Proposal and Realization: I. Halaška (K336), J. Novák (K336) |