Linear differential operators -- One-dimensional wave equation -- The Sturm-Liouville problem -- Distributions -- Convolution and Fourier transform -- Harmonic functions -- The heat equation -- Sobolev spaces. A generalized solution of Dirichlet's problem -- The eigenvalues and eigenfunctions of the Laplace operator -- The wave equation -- Properties of the potentials and their calculations -- Wave fronts and short-wave asymptotics for hyperbolic equations.
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