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Laplace transform

In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function of a real variable (usually ⁠ t {\displaystyle t} ⁠, in the time domain) to a function of a complex variable s {\displaystyle s} (in the complex-valued frequency domain, also known as s-domain or s-plane). The functions…

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Overview

History

Formal definition

Region of convergence

Properties and theorems

Relationship to other transforms

Table of selected Laplace transforms

S-domain equivalent circuits and impedances

Examples and applications

Modern

Historical

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Laplace transform

Nodes218
Edges217
Triples279
Avg. degree1.99
Density0.009174
Components1

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Laplace transform

Top relations

related to Further reading · 75
Laplace transform → Application, Archive, Arendt, Batty, Bengt, Benjamin, BF00418754, BF01395660, Birkhäuser Basel, Boca Raton, Brian, Cambridge, Cauchy Problems, Chapter VI, Charles, Circuits, Comm, CRC Press, David Vernon, Dover Books
related to Modern · 35
Laplace transform → An, Applications, Boston, Bracewell, David Vernon, Engineers, Fourier, George Allen, Hungarian, II, ISBN, Its Applications, IV, John Wiley, Korn, Laplace Transforms, Magyar Hiradastechnika, Mathematical Handbook, McGraw-Hill, McGraw-Hill Companies
related to External links · 19
Laplace transform → Archived, Code, EMS Press, Encyclopedia, EqWorld, Eric, Integral Transforms, Laplace, Laplace Calculator, Laplace Transforms, Mathematical Equations, Mathematics, MathPagesComputational Knowledge Engine, MathWorldGood, Online Computation, The World, Transform, Wayback MachineLaplace Transforms, Weisstein
related to Tauberian theory · 13
Laplace transform → Formally, Hardy, Ikehara Tauberian, It, Laplace, Littlewood Tauberian, Tauberian, The Laplace, The Wiener, They, To, Two Tauberian, Wiener's Tauberian
related to Fourier transform · 12
Laplace transform → As, Fourier, Indeed, Laplace, Lebesgue, Let, Techniques, The, The Laplace, Then, This, Unlike
has application · 9
Laplace transform → English, For, Given, Heaviside, Laplace, Oliver Heaviside, Performing, The, The Laplace
related to Birth and death processes · 7
Laplace transform → Consider, However, Laplace, Poisson, Suppose, Then, This
related to Inverse Laplace transform · 7
Laplace transform → In, Laplace, Lebesgue, The Laplace, This, Two, Typical
related to Probability theory · 7
Laplace transform → By, Here, If, In, Laplace, Markov, The Laplace
related to Bilateral Laplace transform · 6
Laplace transform → Heaviside, If, Laplace, The, The Laplace, When

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laplace transform displaystyle function int infty mathcal integral functions transforms frac inverse fourier left dt right complex convergence time probability

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SubjectPredicateObjectConfidenceSrc
Laplace transformis aone-to-one mapping from one function space into another in many other function spaces as well0.90text
Laplace transformis acontinuous analog of a power series0.90text
Laplace transformis afollowing0.90text
Laplace transformis alinear operator0.90text
that given below.The Laplace transform is definedinstance ofThis is often aided by referencing tables0.80text
a new method for inversioninstance ofwho developed other aspects of the theory0.80text
Markov chainsinstance ofincluding first passage times of stochastic processes0.80text
and renewal theory.Of particular use is the ability to recover the cumulative distribution function of a continuous random variable X by means of the Laplace transform as followsinstance ofincluding first passage times of stochastic processes0.80text
Laplace transformhas applicationThe Laplace0.60section
Laplace transformhas applicationPerforming0.60section
Laplace transformhas applicationLaplace0.60section
Laplace transformhas applicationFor0.60section

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