Since the publication of an article by G. DoETSCH in 1927 it has been known that the Laplace transform procedure is a reliable sub stitute for HEAVISIDE's operational calculus*. However, the Laplace transform procedure is unsatisfactory from several viewpoints (some of these will be mentioned in this preface); the most obvious defect: the procedure cannot be applied to functions of rapid growth (such as the 2 function tr-+-exp(t)). In 1949 JAN MIKUSINSKI indicated how the un necessary restrictions required by the Laplace transform can be avoided by a direct approach, thereby gaining in notational as well as conceptual simplicity; this approach is carefully described in MIKUSINSKI's textbook "Operational Calculus" [M 1]. The aims of the present book are the same as MIKUSINSKI's [M 1]: a direct approach requiring no un-necessary restrictions. The present operational calculus is essentially equivalent to the "calcul symbolique" of distributions having left-bounded support (see 6.52 below and pp. 171 to 180 of the textbook "Theorie des distributions" by LAURENT SCHWARTZ).
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Taschenbuch. Zustand: Neu. Operational Calculus | Gregors Krabbe | Taschenbuch | xvi | Englisch | 2013 | Springer | EAN 9781461343943 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Artikel-Nr. 105322691
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - Since the publication of an article by G. DoETSCH in 1927 it has been known that the Laplace transform procedure is a reliable sub stitute for HEAVISIDE's operational calculus\*. However, the Laplace transform procedure is unsatisfactory from several viewpoints (some of these will be mentioned in this preface); the most obvious defect: the procedure cannot be applied to functions of rapid growth (such as the 2 function tr-+-exp(t)). In 1949 JAN MIKUSINSKI indicated how the un necessary restrictions required by the Laplace transform can be avoided by a direct approach, thereby gaining in notational as well as conceptual simplicity; this approach is carefully described in MIKUSINSKI's textbook 'Operational Calculus' [M 1]. The aims of the present book are the same as MIKUSINSKI's [M 1]: a direct approach requiring no un-necessary restrictions. The present operational calculus is essentially equivalent to the 'calcul symbolique' of distributions having left-bounded support (see 6.52 below and pp. 171 to 180 of the textbook 'Theorie des distributions' by LAURENT SCHWARTZ). Artikel-Nr. 9781461343943
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