An Introduction to Linear Ordinary Differential Equations Using the Impulsive Response Method and Factorization

1. Auflage 2016
ISBN: 978-3-319-49666-5
Verlag: Springer

Buch, Englisch, 120 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 364 g

Reihe: PoliTO Springer Series

This book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is addressed using Mammana’s result for the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients.

Zielgruppe

Graduate

Autoren/Hrsg.

Camporesi, Roberto

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

1 Introduction.- 2 The case of constant coefficients.- 3 The case of variable coefficients. - 4 Conclusions

Über Autor(innen)

Roberto Camporesi is currently Associate Professor of Mathematical Analysis at the Politecnico di Torino. He received his Ph.D. in Physics at the University of Maryland, College Park in 1991. He was a post-doctoral fellow at the University of Alberta, Edmonton, Canada. His research interests include geometry and harmonic analysis on Damek-Ricci spaces, harmonic analysis for homogeneous vector bundles (in particular, spinor fields) on symmetric spaces and representation theory of semisimple Lie groups.