Question

derive Laplace of f(t)​

Answer 1

Answer:

Let f(t) be defined for t ≥ 0. The Laplace transform of f(t),

denoted by F(s) or L{f(t)}, is an integral transform given by the Laplace

integral:

L{f(t)} = ∫

∞ −

=

0

F(s) e f (t) dt st

.

Provided that this (improper) integral exists, i.e. that the integral is

convergent.

The Laplace transform is an operation that transforms a function of t (i.e., a

function of time domain), defined on [0, ∞), to a function of s (i.e., of

frequency domain)

*

. F(s) is the Laplace transform, or simply transform, of

f(t). Together the two functions f(t) and F(s) are called a Laplace transform

pair.

For functions of t continuous on [0, ∞), the above transformation to the

frequency domain is one-to-one. That is, different continuous functions will

have different transforms.