Operational Methods in the Solution of LaPlace's Equation, ∇2φ = 0, in Rectangular Coordinates

The rules of LaPlace transforms are invoked in the solution of the above equation. In solving LaPlace's equation, the assumption that the variables separarate has always been made. Now separation of variables need not be assumed. By directly applying transforms techniques, we obtain the correct result. Hence this method is of significant value. The standard boundary conditions for LaPlace's equation were used. Also the method is extended to determine the Green's function. For this problem, the boundary conditions were zero and the impulse value was δ(x−a)δ(y−b)δ(z−c), where a, b, c were in the boundary.