An Introduction to Laplace Transforms and Fourier Series by Phil Dyke

Author:Phil Dyke [Dyke, Phil]
Language: eng
Format: epub
Tags: Applied, Calculus, Complex Analysis, Mathematical & Computational, Science, Mathematical Analysis, Functional Analysis, Mathematics, Physics
ISBN: 9781447163954
Google: Wuq7BAAAQBAJ
Publisher: Springer Science & Business Media
Published: 1999-01-02T00:00:00+00:00

where, as usual,

Fig. 5.2The domain

It remains difficult in general to determine the inverse Laplace transform, so various properties of the Laplace transform are invoked as an alternative to complete inversion. One device is particularly useful and amounts to using a special case of Watson’s lemma, a well known result in asymptotic analysis. If for small values of has a power series expansion of the form

and is bounded for some and , then the result of Chap. 2 following the Final Value Theorem (Theorem 2.7) can be invoked and we can deduce that as the Laplace transform of has an equivalent asymptotic expansion

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