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000772388 019__ $$a971059567
000772388 020__ $$a9783319496672$$q(electronic book)
000772388 020__ $$a3319496670$$q(electronic book)
000772388 020__ $$z9783319496665
000772388 0247_ $$a10.1007/978-3-319-49667-2$$2doi
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000772388 1001_ $$aCamporesi, Roberto,$$eauthor.
000772388 24513 $$aAn introduction to linear ordinary differential equations using the impulsive response method and factorization /$$cRoberto Camporesi.
000772388 264_1 $$aCham, Switzerland :$$bSpringer,$$c2016.
000772388 300__ $$a1 online resource.
000772388 336__ $$atext$$btxt$$2rdacontent
000772388 337__ $$acomputer$$bc$$2rdamedia
000772388 338__ $$aonline resource$$bcr$$2rdacarrier
000772388 347__ $$atext file$$bPDF$$2rda
000772388 4901_ $$aPoliTO Springer series
000772388 504__ $$aIncludes bibliographical references.
000772388 5050_ $$aAbstract; 1 Introduction; 2 The Case of Constant Coefficients; 2.1 n=1; 2.2 n=2; 2.3 The General Case; 2.4 Explicit Formulas for the Impulsive Response; 2.5 The Method of Undetermined Coefficients; 3 The Case of Variable Coefficients; 3.1 n=1; 3.2 n=2; 3.3 The General Case; 3.3.1 The Factorization Problem; 3.3.2 The Non-homogeneous Equation; 3.3.3 The Homogeneous Equation; 3.4 The Connection with Variation of Parameters; 3.5 The Approach by Linear Systems and the Peano-Baker Series; References.
000772388 506__ $$aAccess limited to authorized users.
000772388 520__ $$aThis book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is addressed using Mammana's result for the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients.
000772388 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed January 16, 2017).
000772388 650_0 $$aDifferential equations, Linear.
000772388 650_0 $$aMathematics.
000772388 650_0 $$aMatrix theory.
000772388 650_0 $$aAlgebra.
000772388 650_0 $$aDifferential equations.
000772388 650_0 $$aCalculus of variations.
000772388 77608 $$iPrint version:$$z9783319496665
000772388 830_0 $$aPoliTO Springer series.
000772388 852__ $$bebk
000772388 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-49667-2$$zOnline Access$$91397441.1
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000772388 980__ $$aEBOOK
000772388 980__ $$aBIB
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000772388 983__ $$aOnline
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