Complements of complex variable function theory. Logarithmic indicator and Lagrange's formula. Mittag-Leffler and Sommerfeld-Watson expansions. Infinite products and expansions by Weierstrass. Asymptotic developments. Laplace method and saddle point methods. Ordinary differential equations. Green's functions. Sturm-Liouville problems. Series and transformed Fourier and Laplace. Special functions. Gamma, Beta and Zeta functions. Hypergeometric functions. Bessel functions. Notes on elliptic functions. Partial differential equations. Well-posed problems and fundamental solutions. Solution of boundary problems. Distributions and their applications to Differential Equations. Linear operators on Hilbert spaces. Riesz's theorem. Spectral theory. Punctual, residual, continuous spectra. Examples of operators in elle2, differential operators, and integral operators. Null modes and the alternative theorem.
