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Laplace transform

The integral transform ∫₀^∞ d𝑠 𝑓(𝑡)⁢exp(−𝑠𝑡)

Entityintegral transform mathematical conceptQ199691

Also known as Laplace domain · one-sided Laplace transform

Instance of: integral transform
, mathematical concept
Subclass of: integral transform

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, the Laplace transform, named after Pierre-Simon Laplace, is an integral transform that converts a function of a real variable to a function of a complex variable . The functions are often denoted using a lowercase symbol for the time-domain function and the corresponding uppercase symbol for the frequency-domain function, e.g. and ⁠⁠.

Overview

All data

58 statements · 16% with external sources · numbers in brackets are citations

Named after: Pierre-Simon Laplace
Defining formula: \left(\mathcal{L} f\right)(s) = \int\limits_0^{\infty} \mathrm{e}^{-s t} f(t) \mathrm{d}t
1
Sources
1.Stated in ISO 80000-2:2019 Quantities and units — Part 2: Mathematics
View statement on Wikidata ↗
Mathematical inverse: inverse Laplace transform relative to: function composition
In defining formula: \mathcal{L} f symbol represents: Laplace transform
f symbol represents: function
s symbol represents: complex frequency
Different from: Laplace transformation
Short name: 拉氏变换
拉氏轉換
Uses: complex frequency

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Source last edited September 28, 2026. AIDb refreshes this page daily.

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AIDb. (2026). Laplace transform (Q199691). Retrieved from https://aidb.si/e/laplace-transform-Q199691