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

  • Roberto Camporesi

Part of the PoliTO Springer Series book series (PTSS)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Roberto Camporesi
    Pages 1-7
  3. Roberto Camporesi
    Pages 9-54
  4. Roberto Camporesi
    Pages 55-117
  5. Back Matter
    Pages 119-120

About this book

Introduction

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.

Keywords

Ordinary differential equations Impulsive response Factorization Differential operators Costant coefficients Variable coefficients

Authors and affiliations

  • Roberto Camporesi
    • 1
  1. 1.Dipartimento di Scienze Matematiche “G. L. Lagrange”Politecnico di TorinoTurinItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-49667-2
  • Copyright Information Springer International Publishing AG 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-49666-5
  • Online ISBN 978-3-319-49667-2
  • Series Print ISSN 2509-6796
  • Series Online ISSN 2509-7024
  • About this book