Formal polynomial and the linear operator of functions.

Description
Formal polynomial in D and the linear operator of functions are defined. The phenomenon of resonance is explained. The differential equation of resonance is solved.The general strategy in finding solutions is based on superposition which splits the problem of finding the general solution into two parts (1) particular solution, and then (2) find the general solution. Exponential Response Formula is stated and proved.
Prof. Arthur Mattuck, Maths, 18.03.Differential Equations, Spring 2010: 14: Interpretation of the Exceptional Case: Resonance: Massachusetts Institute of Technology: MIT Open Course Ware),http://ocw.mit.edu (Accessed November 8, 2011). License: Creative Commons BY-NC-SA: http://ocw.mit.edu/terms/#cc