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

Roberto Camporesi (Autor)

Buch | Hardcover

VII, 120 Seiten

2016 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-49666-5 (ISBN)

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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.

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.

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

"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)

Erscheinungsdatum	05.01.2017
Reihe/Serie	PoliTO Springer Series
Zusatzinfo	VII, 120 p. 1 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Algebra • Calculus of Variations • Calculus of Variations and Optimal Control • Costant coefficients • Differential calculus and equations • Differential Operators • Factorization • Impulsive response • Linear and Multilinear Algebras, Matrix Theory • Mathematics • mathematics and statistics • matrix theory • Optimization • Ordinary differential equations • Variable coefficients
ISBN-10	3-319-49666-2 / 3319496662
ISBN-13	978-3-319-49666-5 / 9783319496665
Zustand	Neuware