Learning objectives
The aims of the course are the following: <br />
a) to provide additional understanding of the theory of the functions of a complex variable, with applications in the calculation of generalised integrals; <br />
b) to describe the Fourier and Laplace transforms and their applications in solving physical-mathematical problems; <br />
c) to study problems connected with the classic partial differential equations commonly referred to as “equations of Mathematical Physics” (equation of potential, heat equation, wave equation). <br />
Course unit content
Elements of the theory of complex functions of a complex variable and their applications: Taylor and Laurent series; residuals; Jordan’s lemma; applications in the calculation of generalised integrals. <br />
Fourier integral and transform. <br />
Laplace transform. <br />
Applications of symbolic calculus to problems of Mathematical Physics. <br />
Differential operators in curvilinear coordinates. <br />
Laplace’s and Poisson’s equations. Dirichlet and Neumann problems. Green’s Identities and Green’s function. <br />
The heat equation. <br />
The wave equation. <br />
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Bibliography
L. AMERIO, Funzioni analitiche e trasformata di Laplace, Politecnica C.Tamburini. <br />
G. SPIGA, Problemi matematici della Fisica e dell'Ingegneria, Pitagora. <br />
A.N. TICHONOV, A.A. SAMARSKIJ, Equazioni della Fisica Matematica, MIR. <br />
F.G. TRICOMI, Istituzioni di Analisi Superiore, CEDAM. <br />