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Definition Assume that f(t) is a piecewise continuous function. The Laplace transform of f(t) is denoted L{ f (t )} and defined by, There is an optional notation for L

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Proof of: ∫ f(x) + g(x) dx = ∫ f(x) dx + ∫g(x) dx It is also a very easy proof. Assume that F(x) is an anti-derivative of f(x) and that G(x) is an anti-derivative of

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