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. N

    I Why use the Legendre transform over back substitution

    In thermodynamics we use a variation of the Legandere Legendre transform to move from one description of the system to another ( depending on what is the control variable...), but I don't understand why choose to use the Legandere Legendre transform over writing x in terms of s=dy/dx and back...
  2. Joppy

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  3. W

    MHB I am trying to figure out the right fast fourier transform size.

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  4. P

    MHB Collin's question via email about a Laplace Transform

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  5. entropy1

    B Time-evolving Fourier transform

    I am a little familiar with Fourier Analysis, but I don't know where to get tools to get the answer to this question: Consider a discrete signal A[0..N-1], consisting of N samples. Suppose we Fourier transform it and get a series of harmonics. Now, consider the discrete signal A[1..N], that is...
  6. P

    MHB Henry's question via email about an Inverse Laplace Transform

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  7. I

    I Fourier transform of Coulomb potential

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  8. C

    Question on Laplace Transform of a constant voltage source

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  9. H

    MATLAB Trying to compute Hilbert transform numerically

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  10. C

    I Fourier Transform for Solving Parameter Perturbation Problem

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  11. Houeto

    Difference Equation Bank Account Problem

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  12. Houeto

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  13. M

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  14. DoobleD

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  15. Vajhe

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  16. L

    I Why is the Fourier transform of a sinusoid assumed as this?

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  17. B

    I Laplace transform using differential equations

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  18. F

    Laplace transform of (e^-s) / [ (s)(s-3) ]

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  19. M

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  20. V

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  21. H

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  22. sa1988

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  23. R

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  24. R

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  25. J

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  26. S

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  27. T

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  28. R

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  29. R

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  30. 1

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  31. S

    I Fourier transform of Dirac delta

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  32. R

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  33. MAGNIBORO

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  34. B

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  35. F

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  36. S

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  37. henry wang

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  38. Zarmina Zaman Babar

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  39. P

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  40. Ben Wilson

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  41. R

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  42. I

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  43. T

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  44. E

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  45. Ben Wilson

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  46. Ben Wilson

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  47. evinda

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  48. R

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  49. P

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  50. D

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