# Initial value theorem

In mathematical analysis, the initial value theorem is a theorem used to relate frequency domain expressions to the time domain behavior as time approaches zero.[1]

It is also known under the abbreviation IVT.

Let

$F(s) = \int_0^\infty f(t) e^{-st}\,dt$

be the (one-sided) Laplace transform of ƒ(t). The initial value theorem then says[2]

$\lim_{t\to 0}f(t)=\lim_{s\to\infty}{sF(s)}. \,$