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

1. Front Matter

   Pages i-vii

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2. Introduction

   • Roberto Camporesi

   Pages 1-7

3. The Case of Constant Coefficients

   • Roberto Camporesi

   Pages 9-54

4. The Case of Variable Coefficients

   • Roberto Camporesi

   Pages 55-117

5. Back Matter

   Pages 119-120

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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.

• Ordinary differential equations
• Impulsive response
• Factorization
• Differential operators
• Costant coefficients
• Variable coefficients
• matrix theory

“In this monograph the author presents the impulse response method for solving linear ordinary differential equations … . The book is well organized and well written. I recommend it to anyone interested in differential equations, not only the teachers and students in a first course on this subject.” (Anton Zettl, Mathematical Reviews, August, 2017)

• Dipartimento di Scienze Matematiche “G. L. Lagrange”, Politecnico di Torino, Turin, Italy

  Roberto Camporesi

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.

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