Difference between revisions of "Laplace Transform"
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| <math> \cosh{at} </math> || <math> \frac{s}{s^2-a^2} </math> | | <math> \cosh{at} </math> || <math> \frac{s}{s^2-a^2} </math> | ||
|- | |- | ||
− | | <math> e^{at}\sin{bt} </math> || <math> | + | | <math> e^{at}\sin{bt} </math> || <math> \frac{b}{(s-a)^2+b^2} </math> |
|- | |- | ||
− | | <math> e^{at}\cos{bt} </math> || <math> | + | | <math> e^{at}\cos{bt} </math> || <math> \frac{s-a}{(s-a)^2+b^2} </math> |
|- | |- | ||
− | | <math> e^{at}\sinh{bt} </math> || <math> | + | | <math> e^{at}\sinh{bt} </math> || <math> \frac{b}{(s-a)^2-b^2} </math> |
|- | |- | ||
− | | <math> e^{at}\cosh{bt} </math> || <math> | + | | <math> e^{at}\cosh{bt} </math> || <math> \frac{s-a}{(s-a)^2-b^2} </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 |