• 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).
  • Stacey Warren - Expert
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
  • katieb
I got my questions answered at in under 10 minutes. Go to now for free help!
  • 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. :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.