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2.2 THEOREM 2 : THE FIRST SHIFTING THEOREM
The first shifting formula states that f(s) is the Laplace Transform of f(t), where ‘a’ is a
constant. We obtained F(s+a) by replacing every ‘s’ in F(s) by ‘s+a’. The variable ;s; has been
shifted by amount ' a'
Example 1
By using the First Shifting Theorem determine the Laplace Transforms of
the followings.
{ }
at
e
L
at
Let e = e at 1 . so f ( ) 1=t
L { tf ( )} = L ) 1 ( = 1
s
e
t
at
Hence L { e at f ( )} = L { . } 1
1
=
s − a
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