Difference between revisions of "Laplace Transform"
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! <math> f(t) </math> !! <math> F(s) = \mathcal{L}|f(t)| </math> | ! <math> f(t) </math> !! <math> F(s) = \mathcal{L}|f(t)| </math> | ||
|- | |- | ||
| − | | <math> 1 </math> || <math> | + | | <math> 1 </math> || <math> \frac{1}{s} </math> |
|- | |- | ||
| − | | <math> e^{at} </math> || <math> | + | | <math> e^{at} </math> || <math> \frac{1}{s-a} </math> |
|- | |- | ||
| − | | <math> t^{n} </math> || <math> </math> | + | | <math> t^{n} </math> || <math> \frac{n!}{s^{n+1}} </math> |
| + | |- | ||
| + | | <math> t^{n}e^{at} </math> || <math> </math> | ||
|- | |- | ||
| <math> \sin{at} </math> || <math> </math> | | <math> \sin{at} </math> || <math> </math> | ||
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|- | |- | ||
| <math> e^{at}\cosh{bt} </math> || <math> </math> | | <math> e^{at}\cosh{bt} </math> || <math> </math> | ||
| − | |||
| − | |||
|} | |} | ||
==Resources== | ==Resources== | ||
* [https://tutorial.math.lamar.edu/classes/de/LaplaceIntro.aspx Laplace Transforms], Paul's Online Notes | * [https://tutorial.math.lamar.edu/classes/de/LaplaceIntro.aspx Laplace Transforms], Paul's Online Notes | ||
