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

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Page updated 2.7.2020 07:53:05, semester: Z,L/2020-1, L/2019-20, Send comments about the content to the Administrators of the Academic Programs

Proposal and Realization: I. Halaška (K336), J. Novák (K336)