Initial value theorem
It is also known under the abbreviation IVT.
Based on the definition of Laplace transform of derivative we have:
But is indeterminate between t=0− to t=0+; to avoid this, the integration can be performed in two intervals:
In the first expression where 0−<t<0+, e−st=1. In the second expression, the order of integration and limit-taking can be changed. Also where 0+<t<∞ is zero. Therefore:
By substitution of this result in the main equation we get:
- Robert H. Cannon, Dynamics of Physical Systems, Courier Dover Publications, 2003, page 567.
- Robert H., Jr. Cannon (4 May 2012). Dynamics of Physical Systems. Courier Dover Publications. p. 569. ISBN 978-0-486-13969-2.
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