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

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