Difference between revisions of "Laplace transform"
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(Created page with "Let $f \colon \mathbb{R} \rightarrow \mathbb{C}$ be a function, then the Laplace transform of $f$ is the function defined by $$\mathscr{L}\{f\}(z) = \displaystyle\int_0^{\inft...") |
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Let $f \colon \mathbb{R} \rightarrow \mathbb{C}$ be a function, then the Laplace transform of $f$ is the function defined by | Let $f \colon \mathbb{R} \rightarrow \mathbb{C}$ be a function, then the Laplace transform of $f$ is the function defined by | ||
$$\mathscr{L}\{f\}(z) = \displaystyle\int_0^{\infty} e^{-zt}f(t) dt.$$ | $$\mathscr{L}\{f\}(z) = \displaystyle\int_0^{\infty} e^{-zt}f(t) dt.$$ | ||
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| + | =Videos= | ||
| + | [https://www.youtube.com/watch?v=u3v6V7SXrl8 Laplace transform of power function with real exponent] <br /> | ||
| + | [https://www.youtube.com/watch?v=ca1LuQZRX6s Laplace transform of $\sin(\sqrt{t})$] | ||
Revision as of 05:00, 19 January 2015
Let $f \colon \mathbb{R} \rightarrow \mathbb{C}$ be a function, then the Laplace transform of $f$ is the function defined by $$\mathscr{L}\{f\}(z) = \displaystyle\int_0^{\infty} e^{-zt}f(t) dt.$$
Videos
Laplace transform of power function with real exponent
Laplace transform of $\sin(\sqrt{t})$
