# 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]

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