
15.3 LAPLACE TRANSFORMS OF SOME COMMON RIGHT-SIDED
FUNCTIONS
Integral of sum of two functions is the sum of integral of each function. Thus, Laplace
transformation is a linear operation. If v
1
(t) and v
2
(t) are two right-sided functions and a
1
and
a
2
are two real numbers, then, a
1
v
1
(t) + a
2
v
2
(t) ⇔ a
1
V
1
(s) + a
2
V
2
(s) is a Laplace transform
pair. This is called Property of Linearity of Laplace transforms. Now, we work out the
Laplace transforms for many commonly used right-sided functions using the defining
integral and property of linearity.
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Thus, similarly located bands in the two half-sections of the vertical line on which
the inversion integral is ...