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More Properties of Laplace Transform
Linearity
For functions x(t) and y(t) and constants a and b, $ L(a*x(t) + b*y(t)) = a*L(x(t)) + b*L(y(t)) $
Shifting in s-domain
$ L(e^{s_0 t} x(t)) = X(s-s_0) $. If X(s) converges in the region R, $ X(s-s_0) $ converges in $ \{s-s_0 | s \in R\} $
Time reversal
This is a special case of time scaling, with $ a = -1 $: $ L(x(-t)) = X(-s) $. If X(s) converges in the region R, X(-s) converges in $ \{-s | s \in R\} $
