Post-wall waveguide

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.

It is also known under the abbreviation IVT.

Let

$F(s)=\underset{0}{\overset{\mathrm{\infty }}{\int }}f(t)e^{-st}dt$

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

$\underset{t\to 0}{\lim }f(t)=\underset{s\to \mathrm{\infty }}{\lim }sF(s).$

See also

• Final value theorem
• Z-transform