italian version

Aims :

To impart the basic elements and techniques of complex analysis, the knowledge and use of Laplace and Fourier transform.

Topics :

Sequences, series, limits in the complex field. Continuous and differentiable functions in C. C.R. equations. Olomorphic and analytic functions. Properties of analytic functions. Integration in C. Jordan theorem. Cauchy theorem. Fresnel integrals. Integral Cauchy formula. Sequences and series of functions. Types of convergence. Liouville theorem. Fundamental theorem of algebra and of maximum modulus. Laurent series. Residues and integration. Hermite theorem. Lebesgue's spaces. Fubini's and Tonelli's theorems. Dominated convergence theorem. Fourier transform and its properties. Inversion formula. Schwartz spaces. Plancherel identity. Laplace transform and its properties. Relation with Fourier Transform. Initial and final value theorems. Solving differential equations by means of Laplace and Fourier transform. Laplace transform of periodic functions. Convolution and Fourier and Laplace transform. Inversion formula for the Laplace transform. Bromwhich formula. and use of residues. special functions and their Laplace transform.

Textbooks :

G.C. Barozzi: Matematica per l’Ingegneria dell’informazione – Zanichelli editore.
Spiegel, Trasformate di Laplace, McGraw Hill
Spiegel, Variabile Complessa, McGraw Hill

Exam :

The exam consists in an oral part and a written one

Tutorial Session :

two hours per week scheduled in accordance with students