ABSTRACT
We have previously (in Section 2.1.2) drawn the reader’s attention to the important superposition principle, which is one of the principal tools listed in dealing with linear systems. It states, in essence, that the general solution of a linear differential equation can be composed of the sum of all independent particular solutions. Its application in that section was restricted to ordinary differential equations (ODEs), and in Section 2.3.2, we used it successfully to compose solutions of linear ODEs with constant coefficients from the sum of exponential functions of the so-called eigenvalues (D-operator method). Later, in Section 2.3.4, we extended the method to linear systems with variable coefficients and saw the emergence of infinite sums of particular solutions, a feature we shall encounter again at the PDE level.
