Learning objectives
The aims of the course are: a) application of the theory of functions of one complex variable to the calculation of generalized integrals and numerical series; b)studies on some integral transforms and their application; c) a study on some problems connected with
the classical PDEs commonly indicated as "Differential equations of Mathematical Physics" (potential equation, heat equation, wave equation, etc.)
Prerequisites
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Course unit content
Applications of the function of one complex variable to the calculation of generalized integrals and numerical series.
Fourier's integral and transform.
Laplace's transform.
Second order linear PDE "of Mathematical Physics"
Full programme
Theory of complex functions of one complex variable: Taylor and Laurent series; residua; Jordan lemmas; application to the calculation of generalized integrals and numerical series.
Fourier integral and transform.
Laplace transform.
Application of integral transforms to the solution of differential and integral equations.
Differential operator in general coordinates.
Laplace and Poisson equations: Dirichlet and Neumann problems. Green identity and Green function.
The heat equation.
The wave equation.
Bibliography
L.Amerio, Funzioni analitiche e trasformata di Laplace, Politecnica C.Tamburini.
G.Spiga, Problemi matematici della Fisica e dell'Ingegneria, Pitagora.
A.N.Tichonov - A.A.Samarskii, Equazioni della Fisica Matematica, MIR.
F.G.Tricomi, Istituzioni di Analisi Superiore, CEDAM
Teaching methods
Hall lectures.
Assessment methods and criteria
Oral examination.
Other information
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