Learning objectives
The aim of the course is, on the one hand, to provide some supplements to the <br />
Analytical Mechanics course and, on the other, to tackle some problems connected with <br />
the classical equations commonly indicated <br />
as 'Differential equations of Mathematical Physics' (potential <br />
equation, heat equation, wave equation, etc.).
Prerequisites
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Course unit content
<br />Elements of calculus of variations. <br />
Variational principles of classical Mechanics. <br />
Canonical transformations. <br />
Hamilton-Jacobi theory. <br />
Fourier series. <br />
<br />
Sturm-Liouville problems, eigenvalues and eigenfunctions. <br />
Non-homogeneous boundary value problems and Green's function. <br />
Laplace and Poisson equations. Dirichlet and Neumann problems. <br />
The heat equation. <br />
The wave equation. <br />
Cauchy problems. Boundary value problems.
Full programme
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Bibliography
E.PERSICO, Introduzione alla Fisica Matematica, Zanichelli, Bologna. <br />
G.SPIGA, Problemi matematici della Fisica e dell'Ingegneria, Pitagora, Bologna. <br />
A.N.TICHONOV - A.A.SAMARSKIJ, Equazioni della Fisica Matematica, MIR, Mosca. <br />
F.G.TRICOMI, Equazioni differenziali, Boringhieri, Torino
Teaching methods
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Assessment methods and criteria
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Other information
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