Applied Mathematics/Laplace Transforms

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The Laplace transform is an integral transform which is widely used in physics and engineering. Laplace transform is denoted as .

The Laplace transform is named after mathematician and astronomer Pierre-Simon Laplace.

Definition[edit]

For a function f(t), using Napier's constant"e" and complex number "s", the Laplace transform F(s) is defined as follow:

The parameter s is a complex number:

with real numbers σ and ω.

This is the Laplace transform of f(t).

Examples of Laplace transform[edit]

Examples of Laplace transform
function result of Laplace transform
(constant)
(n is natural number)
(n>0)
(Delta function)
(Heaviside function)

Examples of calculation[edit]

(1)Suppose (C = constant)


(2)Suppose