Learning objectives
Mathematical methods for solutions of boundary and Cauchy problems relevant to ODEs and PDEs in Mathematical Physics.
Prerequisites
<br />First and second year mathematical tools
Course unit content
<br />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.
Bibliography
<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, EINAUDI,TORINO;<br />F.G.Tricomi, Istituzioni di Analisi Superiore,CEDAM,PADOVA.