Inverse Laplace transformation

ZakjexZK ZakjexZK Best Answer 1 year ago

-step explanation:In MATHEMATICS, the inverse Laplace transform of a FUNCTION F(s) is the piecewise-continuous and exponentially-restricted real function f(t) which has the property:{\displaystyle {\mathcal {L}}\{f\}(s)={\mathcal {L}}\{f(t)\}(s)=F(s),}{\mathcal {L}}\{f\}(s)={\mathcal {L}}\{f(t)\}(s)=F(s),where {\displaystyle {\mathcal {L}}}{\mathcal {L}} denotes the Laplace transform.It can be PROVEN that, if a function F(s) has the inverse Laplace transform f(t), then f(t) is uniquely determined (considering functions which differ from each other only on a point set having Lebesgue measure zero as the same). This result was first proven by Mathias Lerch in 1903 and is KNOWN as Lerch's theorem.[1][2]The Laplace transform and the inverse Laplace transform together have a NUMBER of properties that make them useful for analysing linear dynamical systems.

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