| Abstract: | The particular solution yp (t) of a linear non-homogeneous differential equation with constant coefficients can be expressed in term of a convolution integral, namely, yp(t)=g(t)?T(t), where t(t) is the nonhomogeneous (forcing) term and g(t) is the Green's function for the associated differential operator. g(t) is also the Laplace inverse of the transfer function T(s) = l/P(s), P(s) being the characteristic polynomial of the differential operator. Owing to its versatile application, mathematical sophistication and elegance, and its simplicity, it is suggested, that the Green's function method be introduced while teaching Laplace transform, in a manner described in this article. Some simple results on convolution integrals involving discontinuous functions have been shown to be useful for computing the particular solution when the forcing function r(t) is discontinuous. An attempt has been made to justify the proposed method through a number of simple examples. |
