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- Laplace_transform abstract "The Laplace transform is a widely used integral transform in mathematics with many applications in physics and engineering. It is a linear operator of a function f(t) with a real argument t (t ≥ 0) that transforms f(t) to a function F(s) with complex argument s, given by the integralThis transformation is bijective for the majority of practical uses; the most-common pairs of f(t) and F(s) are often given in tables for easy reference. The Laplace transform has the useful property that many relationships and operations over the original f(t) correspond to simpler relationships and operations over its image F(s).It is named after Pierre-Simon Laplace (/ləˈplɑːs/), who introduced the transform in his work on probability theory.The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes of vibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations. In physics and engineering it is used for analysis of linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems. In such analyses, the Laplace transform is often interpreted as a transformation from the time-domain, in which inputs and outputs are functions of time, to the frequency-domain, where the same inputs and outputs are functions of complex angular frequency, in radians per unit time. Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.".
- Laplace_transform wikiPageExternalLink aux-inttrans.htm.
- Laplace_transform wikiPageExternalLink Laplace_Transform.
- Laplace_transform wikiPageExternalLink LaplaceTransformMod.html.
- Laplace_transform wikiPageExternalLink wims.cgi?lang=en&+module=tool%2Fanalysis%2Ffourierlaplace.en.
- Laplace_transform wikiPageExternalLink kmath508.htm.
- Laplace_transform wikiPageExternalLink ?i=laplace+transform+example.
- Laplace_transform wikiPageID "18610".
- Laplace_transform wikiPageRevisionID "606785529".
- Laplace_transform hasPhotoCollection Laplace_transform.
- Laplace_transform id "p/l057540".
- Laplace_transform title "Laplace Transform".
- Laplace_transform title "Laplace transform".
- Laplace_transform urlname "LaplaceTransform".
- Laplace_transform subject Category:Differential_equations.
- Laplace_transform subject Category:Fourier_analysis.
- Laplace_transform subject Category:Integral_transforms.
- Laplace_transform subject Category:Transforms.
- Laplace_transform type Abstraction100002137.
- Laplace_transform type Communication100033020.
- Laplace_transform type DifferentialEquation106670521.
- Laplace_transform type DifferentialEquations.
- Laplace_transform type Equation106669864.
- Laplace_transform type MathematicalStatement106732169.
- Laplace_transform type Message106598915.
- Laplace_transform type Statement106722453.
- Laplace_transform comment "The Laplace transform is a widely used integral transform in mathematics with many applications in physics and engineering. It is a linear operator of a function f(t) with a real argument t (t ≥ 0) that transforms f(t) to a function F(s) with complex argument s, given by the integralThis transformation is bijective for the majority of practical uses; the most-common pairs of f(t) and F(s) are often given in tables for easy reference.".
- Laplace_transform label "Laplace transform".
- Laplace_transform label "Laplace-Transformation".
- Laplace_transform label "Laplacetransformatie".
- Laplace_transform label "Transformada de Laplace".
- Laplace_transform label "Transformada de Laplace".
- Laplace_transform label "Transformata Laplace’a".
- Laplace_transform label "Transformation de Laplace".
- Laplace_transform label "Trasformata di Laplace".
- Laplace_transform label "Преобразование Лапласа".
- Laplace_transform label "تحويل لابلاس".
- Laplace_transform label "ラプラス変換".
- Laplace_transform label "拉普拉斯变换".
- Laplace_transform sameAs Laplaceova_transformace.
- Laplace_transform sameAs Laplace-Transformation.
- Laplace_transform sameAs Μετασχηματισμός_Λαπλάς.
- Laplace_transform sameAs Transformada_de_Laplace.
- Laplace_transform sameAs Transformation_de_Laplace.
- Laplace_transform sameAs Transformasi_Laplace.
- Laplace_transform sameAs Trasformata_di_Laplace.
- Laplace_transform sameAs ラプラス変換.
- Laplace_transform sameAs 라플라스_변환.
- Laplace_transform sameAs Laplacetransformatie.
- Laplace_transform sameAs Transformata_Laplace’a.
- Laplace_transform sameAs Transformada_de_Laplace.
- Laplace_transform sameAs m.04qbb.
- Laplace_transform sameAs Q199691.
- Laplace_transform sameAs Q199691.
- Laplace_transform sameAs Laplace_transform.
- Laplace_transform wasDerivedFrom Laplace_transform?oldid=606785529.
- Laplace_transform isPrimaryTopicOf Laplace_transform.