anonymous
  • anonymous
Is there a deeper explanations for why Laplace transforms work (like Fourier transforms, which have the theory that any periodic function is an infinite sum of sines and cosines), or is it just a (mundane) trick that happens to work? Note that I know almost nothing of Laplace transforms, what they are used for (specifically, I know they're useful in differential equations).
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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zepdrix
  • zepdrix
I don't have a great understanding of the Laplace Transform. But I think it's mostly just a trick that happens to work `most of the time`. Using the familiar notation, it's often used to transform a function from the time domain \(\large f(t)\) to something else, often frequency \(\large F(s)\). The reason I say it only works `most of the time` is because it can't be applied to all functions. Take for example: \[\large f(t)=e^{t^2}\] \(\large \int_0^{\infty} e^{t^2}e^{-st}\;dt\) Our function f(t) is increasing a lot faster than the e^{-st} is decreasing, so this integral will not converge. I dunno. Like I said, I don't have a lot of great info on the topic, just adding my two cents. :)

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