https://en.formulasearchengine.com/index.php?action=history&feed=atom&title=Post-wall_waveguide 2026-04-10T20:12:07Z Revision history for this page on the wiki MediaWiki 1.43.0-wmf.28 https://en.formulasearchengine.com/index.php?title=Post-wall_waveguide&diff=23642&oldid=prev 2013-05-14T15:01:10Z

<p>link to <a href="/index.php?title=Via_fence&amp;action=edit&amp;redlink=1" class="new" title="Via fence (page does not exist)">via fence</a></p> <p><b>New page</b></p><div>In [[mathematical analysis]], the &#039;&#039;&#039;initial value theorem&#039;&#039;&#039; is a theorem used to relate [[frequency domain]] expressions to the [[time domain]] behavior as time approaches [[zero]].&lt;ref&gt;http://fourier.eng.hmc.edu/e102/lectures/Laplace_Transform/node17.html&lt;/ref&gt;<br /> <br /> It is also known under the abbreviation IVT.<br /> <br /> Let<br /> <br /> : &lt;math&gt; F(s) = \int_0^\infty f(t) e^{-st}\,dt &lt;/math&gt;<br /> <br /> be the (one-sided) [[Laplace transform]] of &#039;&#039;&amp;fnof;&#039;&#039;(&#039;&#039;t&#039;&#039;). The initial value theorem then says&lt;ref&gt;Robert H. Cannon, &#039;&#039;Dynamics of Physical Systems&#039;&#039;, [[Courier Dover Publications]], 2003, page 567.&lt;/ref&gt;<br /> <br /> : &lt;math&gt;\lim_{t\to 0}f(t)=\lim_{s\to\infty}{sF(s)}. \, &lt;/math&gt;<br /> <br /> ==See also==<br /> * [[Final value theorem]]<br /> * [[Z-transform]]<br /> <br /> ==Notes==<br /> &lt;references/&gt;<br /> <br /> [[Category:Theorems in analysis]]<br /> {{mathanalysis-stub}}</div>

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