A generalized operational two-variable calculus is proposed which uses algebraic properties of differential polynomials only and deals with partial differential equations with space- and time-dependent coefficients. The main result is an extension of the decomposition formula of Heaviside which provides a new approach to non-stationary distributed parameter systems. Two applications are given: a general method for solving linear partial differential equations with space-dependent coefficients; and an approach to the synthesis of non-stationary distributed parameter systems which may be considered as an extension of the Guillemin and Truxal's method for lumped parameter systems. The block-diagram of the compensating network so obtained is given and its feasibility is pointed out