I have been working on a few problems around Laplace Transform on Yahoo Answer (in fact, the one in Hong Kong/Taiwan). It would be a waste for those content to only post there, so I am posting them here. Feel free to checkout my profile there if you are interested
This post is about Laplace Transform, the Laplace Transform of a function can be simply written as $ Y(s) = \mathcal{L}(y) = \int\limits_{0}^{\infty}{y(t)e^{-st}dt} $.
There are a few things to note:
This post is about Laplace Transform, the Laplace Transform of a function can be simply written as $ Y(s) = \mathcal{L}(y) = \int\limits_{0}^{\infty}{y(t)e^{-st}dt} $.
There are a few things to note:
- $ s $ is in general a complex number, $ t $ is usually real.
- The integral is improper, in particular, by writing $\int\limits_{0}^{\infty}{y(t)e^{-st}dt} $, we really mean $ \lim_{T \to \infty}{\int\limits_{0}^{\infty}{y(t)e^{-st}dt}} $.
- When necessary, we pick ranges of $ s $ such that the limit converges and define $ Y(s) $ there only.
That's it for this post. Next we will talk about some common Laplace Transform pair and properties.
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