Vector space (finite dimension). Gram-Schmidt method. Linear operators, matrix eigenvalue and eigenvectors. Matrix functions . Coordinate transformations: unitary matrixes. First and second order linear differential equations. Systems of differential equations. L2 function space, linear operators in L2. Hermite and Legendre polynomials. Generating functions of Hermite and Legendre polynomials, recurrence relations. Rodrigues’s formula. Complete set of functions, Bessel inequality. Parseval’s equality. Fourier’s series expansion. Functions of complex variables. Analytical functions, Cauchy- Riemann conditions. Laurent’s series expansion. Contour integrals. Cauchy’s integral and the residue theorem. Fourier and Laplace transform. Free particle Green’s function. Special operators in curvilinear coordinates: the gradient, the curl and the Laplacian.
Co-teaching: Dott. Perfetto Enrico