An operational calculus approach and its representative applications are considered. Operational methods are described, as well as their program implementation using the computer algebra system Mathematica.

            The Heaviside algorithm for solving Cauchy problems for linearordinary differential equations with constant coefficients is considered in the context of the Heaviside-Mikusinski operational calculus.

            An extension of the Heaviside algorithm, developed by I. Dimovski and S. Grozdev for periodic solutions of linear ordinary differential equations with constant coefficients both in the non-resonance and in the resonance cases is described.

            An operational calculus approach for solving boundary value problems for some linear partial differential equations is applied. A combination of two classical methods is considered - the Fourier method and the Duhamel principle - in the frames of a two-dimensional operational calculus, suggested by I. Dimovski. It allows to be obtained Duhamel--type representations of the solutions of local and nonlocal boundary value problems for some equations of the mathematical physics (the heat, the wave and the beam equations). These representations can de used for numerical computation of the solutions.

            Program packages for the considered methods are developed using the computer algebra system Mathematica. Their features are considered and illustrative examples are supplied.

            A comparison with other methods for solving the same types of problems is included and the advantages of the direct operational approach are outlined.