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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]].<ref>http://fourier.eng.hmc.edu/e102/lectures/Laplace_Transform/node17.html</ref>

It is also known under the abbreviation IVT.

Let

: <math> F(s) = \int_0^\infty f(t) e^{-st}\,dt </math>

be the (one-sided) [[Laplace transform]] of ''&fnof;''(''t'').  The initial value theorem then says<ref>Robert H. Cannon, ''Dynamics of Physical Systems'', [[Courier Dover Publications]], 2003, page 567.</ref>

: <math>\lim_{t\to 0}f(t)=\lim_{s\to\infty}{sF(s)}. \, </math>

==See also==
* [[Final value theorem]]
* [[Z-transform]]

==Notes==
<references/>

[[Category:Theorems in analysis]]
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