Abstract
The main applications of the Laplace transform are directed toward problems in which the time t is the independent variable. We shall therefore use this variable in this chapter. Let f(t) be a complex-valued function of the real variable t such that f(t)e -ct is abolutely integrable over 0 < t < ∞, where c is a real number. Then the Laplace transform of f(t), t ≥ 0, is defined as
where s = σ + iω. The Laplace transform defined by (1) has the following basic properties.
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© 2004 Springer Science+Business Media New York
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Kanwal, R.P. (2004). The Laplace Transform. In: Generalized Functions. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8174-6_8
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DOI: https://doi.org/10.1007/978-0-8176-8174-6_8
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4343-0
Online ISBN: 978-0-8176-8174-6
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