Fourier series solutions are obtained for mixed boundary value problems for the Laplace equation in the plane and in the sphere. The nature of the boundary conditions presents difficulties in ...

Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution ...

The validity of standard singular integral solutions to classic dual trigonometric series equations is rigorously established in the case that the right-hand sides of the equations are functions of ...