# Subject description - A3M01MKI

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 A3M01MKI Mathematics for Cybernetics Extent of teaching: 4+2 Guarantors: Hamhalter J. Roles: P,V Language ofteaching: CS Teachers: Hamhalter J. 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:

Podmínkou získámí zápočtu je aktivní účast na cvičení, základní znalosti z přednášky, absolvování zápočtového testu nebo odevzdání předepsaných domácích úloh. Nutnou podmínkou pro úspěšné absolvování testu je mít správně alespoň polovinu zkouškové písemky. Další informace: http://math.feld.cvut.cz/hamhalte/A3M01MKI.htm

Webpage:

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

Subject is included into these academic programs:

 Program Branch Role Recommended semester MPIB Common courses V – MPKME1 Wireless Communication V 1 MPKME5 Systems of Communication V 1 MPKME4 Networks of Electronic Communication V 1 MPKME3 Electronics V 1 MPKME2 Multimedia Technology V 1 MPEEM1 Technological Systems V 1 MPEEM5 Economy and Management of Electrical Engineering V 1 MPEEM4 Economy and Management of Power Engineering V 1 MPEEM3 Electrical Power Engineering V 1 MPEEM2 Electrical Machines, Apparatus and Drives V 1 MPKYR1 Robotics P 1 MPKYR4 Aerospace Systems P 1 MPKYR3 Systems and Control P 1 MPKYR2 Sensors and Instrumentation P 1

 Page updated 14.6.2019 17:52:56, 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)