Categorical Forms of Green's Function; The One-Dimensional Time Response Function: Forced Harmonic Oscillator

Abstract

An introductory technique to solve one-dimensional time-dependent boundary value problems using Green's function, aiming at postgraduate students, and science researchers who have no prior experience with the method. The aim here is to have a rather simple look at Green's functions as a solution to boundary value problems in their explicit functional forms, rather than their explicit expressions, and finally to be acquainted with them.  Using the method of variations of parameters, one can provide a satisfactory format of Green's functions, which would make it easier to introduce Green's functions and accept their abstract format in more complex problems including higher dimensions.