A fresh look at linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Camporesi, Roberto
• Is Part Of: International journal of mathematical education in science and technology. Volume 47:Issue 1(2016)
• Page Start: 82
• Page End: 99
• Publication Date: 2016-01-02
• Subjects: ordinary differential equations -- Green functions -- instructional exposition; Mathematics -- Study and teaching -- Periodicals; Mathematics -- Periodicals; 510.07
• DOI: 10.1080/0020739X.2015.1057246
• Languages: English
• ISSNs: 0020-739X

Abstract

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.