An Introduction to Linear Ordinary Differential Equations Using the Impulsive Response Method and Factorization (PoliTO Springer Series) - Hardcover

Camporesi, Roberto

Hardcover

ISBN 10: 3319496662 ISBN 13: 9783319496665

Verlag: Springer, 2016

Inhaltsangabe

<P>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.</P>

Über diesen Titel

Críticas

“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)

Reseña del editor

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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2016
• ISBN 10: 3319496662
• ISBN 13: 9783319496665
• Einband: Tapa dura
• Sprache: Englisch
• Anzahl der Seiten: 130