


Politecnico di Torino  
Anno Accademico 2009/10  
01LSIJA Mathematical methods 

Corso di Laurea in Electronic And Computer Engineering  Vercelli 





Obiettivi dell'insegnamento
To provide the fundamental concepts about Fourier and Laplace transforms, distribution theory, integration of complexvalued functions, with some applications to partial differential equations.

Competenze attese
At the end of the course the student is expected to be able to compute Fourier and Laplace transforms of a given function, possibly by using methods coming from complex integration theory, and to deal with similar problems in the more general setting of distribution theory. He should be acquainted with some basic examples of partial differential equations and know how to deal with them using Fourier series and Fourier/Laplace transforms.

Prerequisiti
Analysis in one and in several variables, as given in the courses of Calculus IIIIII, has to be known in order to deal with the topics of the present course. Basic linear algebra is necessary as well.

Programma
Integration theory in the complex plane. Analytic and holomorphic functions. The CauchyRiemann conditions. The residue Theorem and its applications to the calculation of real integrals. Fourier and Laplace transform and their main properties. The use of complex integration in computing Fourier and Laplace transforms. Basics of distribution theory, including Fourier series of distributions and FourierLaplace transforms of distributions. Laplace and wave equations, basics on Fourier methods for their solution.

Laboratori e/o esercitazioni
There will be class exercises on each part of the course.

Bibliografia
Notes.

Controlli dell'apprendimento / Modalità d'esame
The exam will consist of a written examination on the topics indicated above. An oral examination can be required as well in addition.

Orario delle lezioni 
Statistiche superamento esami 
