An introduction to linear ordinary differential equations using the impulsive response method and factorization / Roberto Camporesi.
Camporesi, Roberto, author.
2016
QA372
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Title
An introduction to linear ordinary differential equations using the impulsive response method and factorization / Roberto Camporesi.
Author
Camporesi, Roberto, author.
ISBN
9783319496672 (electronic book)
3319496670 (electronic book)
9783319496665
DOI
https://doi.org/10.1007/978-3-319-49667-2
Published
Cham, Switzerland : Springer, 2016.
Language
English
Description
1 online resource.
Item Number
10.1007/978-3-319-49667-2 doi
Call Number
QA372
Dewey Decimal Classification
515/.354
510
Summary
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.
Bibliography, etc. Note
Includes bibliographical references.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed January 16, 2017).
Series
PoliTO Springer series.
Available in Other Form
Print version: 9783319496665
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Abstract; 1 Introduction; 2 The Case of Constant Coefficients; 2.1 n=1; 2.2 n=2; 2.3 The General Case; 2.4 Explicit Formulas for the Impulsive Response; 2.5 The Method of Undetermined Coefficients; 3 The Case of Variable Coefficients; 3.1 n=1; 3.2 n=2; 3.3 The General Case; 3.3.1 The Factorization Problem; 3.3.2 The Non-homogeneous Equation; 3.3.3 The Homogeneous Equation; 3.4 The Connection with Variation of Parameters; 3.5 The Approach by Linear Systems and the Peano-Baker Series; References.

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