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Book synopsis

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).

Book details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Operational Calculus
• Author: Gregors Krabbe
• Language: English
• Binding: Paperback
• Number of pages: 349
• EAN: 9781461343943
• ISBN: 1461343941
• ID: 05257690
• Publisher: Springer-Verlag New York Inc.
• Weight: 538 g
• Dimensions: 229 × 152 × 20 mm
• Date of publishing: 06. December 2013

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