< Applied Mathematics
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
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
function | result of Laplace transform |
---|---|
(constant) | |
(n is natural number) | |
(n>0) | |
(Delta function) | |
(Heaviside function) |
Examples of calculation
(1)Suppose (C = constant)
(2)Suppose
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