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Lecturer(s)
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Karamazov Simeon, prof. Ing. Dr.
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Rak Josef, RNDr. Ph.D.
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Vozáb Jaroslav, Mgr.
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Marek Jaroslav, Mgr. Ph.D.
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Course content
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1. Functions of complex variable. Singular points. 2. Derivative of complex functions. 3. Laurent series, Residue theorem. 4. Integral of complex functions. 5. Conformal mappings. 6. Eigen values of matrices, spectral decomposition, Jordan canonical form and its applications. 7. Matrix norms, Quadratic forms. 8. Decompositions LU, QR and SVD, and its applications. 9. Cayley-Hamilton theorem, polynomial matrices. 10. Metric, Normed and Hilbert spaces. 11. Orthogonal systems. 12. Fourier series. 13. Fourier transformation.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing)
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Learning outcomes
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The aim of the course is to provide the students with basic acquirements to use the selected knowledge from complex and functional analysis, and some topics in linear algebra.
A student acquires a basic view of some topics of complex and functional analysis, and some topics in linear algebra. The obtained knowledge enable students to use the mathematical appliance in special courses of their specialization.
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Prerequisites
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The course demands knowledge of the basic course in calculus and linear algebra.
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Assessment methods and criteria
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Oral examination
Credit requirements: active participation in seminars with at most three hours absent, and at least 50% success in written test. The course is completed by an oral exam; student should demonstrate an active knowledge of predefined topics.
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Recommended literature
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ANGOT, A. Užitá matematika pro elektrotechnické inženýry. SNTL Praha, 1971.
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ARAMANOVIČ, J.G., LUNC,G.L., ELSGOLC,L.C. Funkcie komplexnej promennej. Operátorový počet. Teória stability.. Alfa Bratislava, SNTL Praha, 1973.
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FUKS,B.A., ŠABAT,B.V. Funkce komplexní proměnné. ČSAV Praha, 1961.
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GANTMACHER, F.R. Teorija Matric. Nauka Moskva, 1988.
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JEVGRAFOV,M.A. Funkce komplexní proměnné. SNTL Praha, 1981.
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KOLMOGOROV, A.N., FOMIN, S.V. Základy teorie funkcí a funkcionální analýzy, Vyd. 1.. Nakladatelství technické literatury Praha, 1975.
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MARCUS, M. Matrices and Matlab. A tutorial.. Prentice Hall, 1993.
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Meyer, C. D. Matrix Analysis and Applied Linear Algebra. 2001.
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SCHMIDTMAYER, J. Maticový počet a jeho použití v technice. SNTL Praha, 1974.
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SVATOKRÍŽNY, P. Lineárna algebra v úlohach. Alfa Bratislava, 1984.
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