Applied Mathematics/Laplace Transforms
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.
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|
|(n is natural number)|
Examples of calculation
(1)Suppose (C = constant)