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The initial- and final-value theorems in Laplace transform theory

✍ Scribed by Bernard Rasof

Publisher: Elsevier Science
Year: 1962
Tongue: English
Weight: 549 KB
Volume: 274
Category: Article
ISSN: 0016-0032
DOI: 10.1016/0016-0032(62)90939-0

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✦ Synopsis

The initial-and final-value theorems, generally neglected in Laplace transform theory, for some purposes are among the most powerful results in that subject. Here are advanced some useful applications of these theorems: ~,,e show how they may be employed as necefsar~ checks on the accuracy of response transtbrms, to evaluate (directly, in a uniform manner, and with remarkable ease) certain definite integrals, to derive an important general result, and to evaluate (again uniformly and easily) certain limits and indeterminate forms (this is believed to be a new application). Then the theorems are generalized, and the first of these is applied to generate, directly from a Laplace transform itself, the Maclaurin expansion of the inverse Laplace transform.

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