What is Transform: Definition and 1000 Discussions

In mathematics, the Laplace transform, named after its inventor Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable



t


{\displaystyle t}
(often time) to a function of a complex variable



s


{\displaystyle s}
(complex frequency). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms linear differential equations into algebraic equations and convolution into multiplication.For suitable functions f, the Laplace transform is the integral






L


{
f
}
(
s
)
=

∫

0


∞


f
(
t
)

e

−
s
t



d
t
.


{\displaystyle {\mathcal {L}}\{f\}(s)=\int _{0}^{\infty }f(t)e^{-st}\,dt.}

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  1. U

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  4. N

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  5. S

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  9. rannasquaer

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  11. S

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  12. Frankenstein19

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  13. B

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  14. M

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  15. thaiqi

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  16. B

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  18. agnimusayoti

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  19. S

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  20. A

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  22. M

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  35. L

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  37. P

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  43. P

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  47. G

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