The types of problems we have considered for the heat, wave, and Laplace equations have solutions th a t are determined uniquely by the prescribed d ata (boundary conditions, initial conditions, and any nonhomogeneous term in the equation). It is natural, therefore, to seek a formula th a t gives the solution directly in terms of the data. Such closed-form solutions are constructed by means of the so-called Green’s function of the given problem, and are of great importance in practical applications.