math316: Mathematical Methods

Inner product space, sequences of functions and their modes of convergence,

Strum-Liouville problem (ordinary and singular), self-adjoint differential

operator, Fourier series, convergence in L

2

, pointwise convergence, Orthogonal

polynomials (Legendre, Hermite, Laguerre) and their properties, expansions of

functions, Bessel functions, properties, orthogonality , Fourier transform, Fourier
integral, applications