italian version

Aims :

It is planned to give basic knowledge concerning holomorphic function of one
variable and Fourier and Laplace transform, together with their usage in
concrete problems.

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 :

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