MATHEMATICAL PHYSICS I
Learning outcomes of the course unit
Mathematical methods for solutions of boundary and Cauchy problems relevant to ODEs and PDEs in Mathematical Physics.
First and second year mathematical tools
Course contents summary
Complete sets and Fourier series. Outlines on the theory of distributions. Sturm-Liouville problems, eigenvalues and eigenfunctions. Nonhomogeneous boundary problems and Green function. Classification of second-order linear partial differential equations.The Cauchy problem. First-order quasi-linear partial differential equations, solutions by method of characteristics. Second-order quasi- linear partial differential equations. An outline of weak solutions.
G.Spiga, Problemi matematici della Fisica e dell'Ingegneria, PITAGORA, BOLOGNA;
A.N.Tichonov, A.A.Samarskij, Equazioni della Fisica Matematica, MIR, MOSCA;
F.G.Tricomi, Equazioni differenziali, EINAUDI,TORINO;
F.G.Tricomi, Istituzioni di Analisi Superiore,CEDAM,PADOVA.