A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization |
| |
Authors: | Roberto Camporesi |
| |
Institution: | 1. Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italycamporesi@polito.it |
| |
Abstract: | We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The approach presented here can be used in a first course on differential equations for science and engineering majors. |
| |
Keywords: | ordinary differential equations Green functions instructional exposition |
|
|