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- Parte I 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.
Learning Objectives
To present some mathematical aspects which are useful in Electronics
and Telecommunication Engineering
Prerequisites
Basic notions from Linear Algebra and Advanced calculus
Teaching Methods
The course consists in some lectures (55 hours). Two intermediate
verification tests are planned
Further information
Some exercises are distribuited or assigned. The outline of the lectures
are posted in real time on the web at http://www.unifi.it/detmod
Type of Assessment
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.
Course program
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).
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.
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.