An Introduction To Linear Ordinary Differential Equations Using The Impulsive Response Method And Factorization (polito Springer Series)
by Roberto Camporesi /
2016 / English / PDF
1.6 MB Download
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.
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.