B003774 - APPLIED MATHEMATICS

Italian

1) Fundamental concepts on complex numbers.
2) Complex functions
3) Laplace transform
4) Real Positive Functions
5) Zeta transform

0) Draft from the web (http://www.unifi.it/detmod)
1) M. Marini "Metodi Matematici per lo studio delle reti elettriche",
Ed. Cedam, 1999.
2) G.C. Barozzi "Matematica per l'Ingegneria dell'Informazione",
Ed. Zanichelli 2001.
3) L. Amerio "Analisi Matematica: Metodi Matematici e Applicazioni" ,
Vol.3- PartI e II, Ed. UTET, 1992.
4) M. Giaquinta, G. Modica "Note di Metodi Matematici per Ingegneria
Informatica", Edizioni Pitagora, 2005.
5) M. Codegone "Metodi Matematici per l'Ingegneria", Ed. Zanichelli,
1995.
6) M.Bramanti, C.D. Pagani, S. Salsa "Matematica", Zanichelli.

To present some mathematical aspects which are useful in Electronic
and Telecommunication Engineering

Basic notions from Linear Algebra and Advanced calculus

The course consists in some lectures (55-60 hours). Two intermediate
verification tests are planned

Some exercises are distribuited or assigned. The outlines of the lectures
are posted in real time on the web at http://www.modmat.unifi.it

There are two possibilities for passing the examination: either to get through two intermediate tests or to get through the final test. In both cases it is possible to complete the process with an oral test. The writtem test verifies the mathematical preparation on complex variable functions and on their applications to the theory of signal transmission and to the theory of electrical networks.

Review of fundamental concepts on complex numbers. Complex functions: properties ,the Cauchy-Riemann formulas, integrals, the Cauchy integral formulas, Taylor series, singularities, Laurent series, Residues and applications to the integral calculus, analitic properties (The Weierstrass theorem, the Casorati theorem, the Liouville theorem, the max-modulo theorem).
Zeta transform: review of fundamental concepts of power series, Ztransform of elementary sequences, properties, the discrete convolution, inversion formulas, applications to signal processing, applications to difference equations. Laplace transform: definition, properties, the convolution product, applications to the solvability of linear differential equations and systems, applications to the analysis of RLC passive networks.
Real positive functions: the rational case, the positiveness, The Talbot criterion, the Routh-Hurwitz criterion, the odd case, applications to the syntesis of RLC passive networks.

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