Subject description - AE3M01MKI

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AE3M01MKI Mathematics for Cybernetics Extent of teaching:4P+2S
Guarantors:  Roles:P,V Language of
teaching:
EN
Teachers:  Completion:Z,ZK
Responsible Department:13101 Credits:8 Semester:Z

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

Webpage:

http://math.feld.cvut.cz/hamhalte/A3M01MKI.htm

Subject is included into these academic programs:

Program Branch Role Recommended semester
MEKME1 Wireless Communication V 1
MEKME5 Systems of Communication V 1
MEKME4 Networks of Electronic Communication V 1
MEKME3 Electronics V 1
MEKME2 Multimedia Technology V 1
MEKYR1 Robotics P 1
MEKYR4 Aerospace Systems P 1
MEKYR3 Systems and Control P 1
MEKYR2 Sensors and Instrumentation P 1
MEOI1 Artificial Intelligence V 1
MEOI5NEW Software Engineering V 1
MEOI5 Software Engineering V 1
MEOI4 Computer Graphics and Interaction V 1
MEOI3 Computer Vision and Image Processing V 1
MEOI2 Computer Engineering V 1
MEEEM1 Technological Systems V 1
MEEEM5 Economy and Management of Electrical Engineering V 1
MEEEM4 Economy and Management of Power Engineering V 1
MEEEM3 Electrical Power Engineering V 1
MEEEM2 Electrical Machines, Apparatus and Drives V 1


Page updated 6.12.2019 17:52:32, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)