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italian version
Aims :
To
impart the basic elements of Complex Analysis,
the knowledge and use of Fourier and Laplace Transforms.
Topics
:
Functional
sequence:Uniform convergence; Integrals dependent
on a parameter; Improper integrals dependent on
a parameter ; Euler integrals : Gamma and Beta
functions.
Fourier series and Fourier Integral;The Fourier
Transform; Distributions; The Fourier Transform
of Distributions; Applications: The impulse response;
The frequency response; Boundary and Initial value
Problems for Partial Differential Equations.
Single-valued functions of a complex variable:
Differentiation and Itegration; Cauchy ' s Integral
theorem; Taylor Series, Laurent Series; Singular
Points and Zeros; Cauchy 's Residues Theorem;
Behaviour of a Function at Infinity; Logarithmic
Residues; Z-Transform; The Inverse Z-transform
of Rational Functions; Convolution.
Textbooks :
Spiegel: Laplace Transforms
McGraw Hill
Course Notes
Exam :
The exam consits in an oral part.
Tutorial Session :
2 hours per week scheduled in accordance with
students.
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