Following the introduction of the linearized partial differen-tial equation for nonsteady three-dimensional compressible flow, general methods of solution are given for the two- and three-dimensional steady-state and two-dimensional unsteady-state equations. It is also pointed out that, in the absence of thickness effects, linear theory yields solutions consistent with the assumptions made when applied to lifting-surface problems for swept-back plan forms at sonic speeds. The solutions of the particular equations are determined in all cases by means of Green's theorem and thus depend on the use of Green's equivalent layer of sources, sinks, and doublets. Improper integrals in the supersonic theory are treated by means of Hadamard's "finite part" technique.
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