rules for Laplace transform

If  {f(t)}=F(s),  then

  • {eatf(t)}=F(s-a)  for  s>a,

  • {f(ta)}=aF(as)   for  a>0.

For deriving these rules, we start from the definition of Laplace transformDlmfMathworldPlanetmath.  In the first case, we shall use the notation  s-a=r:


In the second case, we make the change of variable  ta=u  and later use the notation  sa=r:

Title rules for Laplace transform
Canonical name RulesForLaplaceTransform
Date of creation 2013-03-22 18:31:08
Last modified on 2013-03-22 18:31:08
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 7
Author pahio (2872)
Entry type Derivation
Classification msc 44A10
Related topic TableOfLaplaceTransforms