MATHEMATICAL PHYSICS 2
Learning outcomes of the course unit
The aims of the course are the following:
a) to provide additional understanding of the theory of the functions of a complex variable, with applications in the calculation of generalised integrals;
b) to describe the Fourier and Laplace transforms and their applications in solving physical-mathematical problems;
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).
Course contents summary
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.
Fourier integral and transform.
Applications of symbolic calculus to problems of Mathematical Physics.
Differential operators in curvilinear coordinates.
Laplace’s and Poisson’s equations. Dirichlet and Neumann problems. Green’s Identities and Green’s function.
The heat equation.
The wave equation.
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. SAMARSKIJ, Equazioni della Fisica Matematica, MIR.
F.G. TRICOMI, Istituzioni di Analisi Superiore, CEDAM.