Difference between revisions of "Laplace Transform"
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| Line 7: | Line 7: | ||
|- | |- | ||
| <math> e^{at} </math> || <math> \frac{1}{s-a} </math> | | <math> e^{at} </math> || <math> \frac{1}{s-a} </math> | ||
| + | |- | ||
| + | | <math> t </math> || <math> \frac{1}{s^2} </math> | ||
|- | |- | ||
| <math> t^{n} </math> || <math> \frac{n!}{s^{n+1}} </math> | | <math> t^{n} </math> || <math> \frac{n!}{s^{n+1}} </math> | ||
|- | |- | ||
| − | | <math> t^{n}e^{at} </math> || <math> | + | | <math> t^{n}e^{at} </math> || <math> \frac{n!}{s^{n+1}} </math> |
|- | |- | ||
| − | | <math> \sin{at} </math> || <math> | + | | <math> \sin{at} </math> || <math> \frac{a}{s^2+a^2} </math> |
|- | |- | ||
| − | | <math> \cos{at} </math> || <math> | + | | <math> \cos{at} </math> || <math> \frac{s}{s^2+a^2} </math> |
|- | |- | ||
| − | | <math> \sinh{at} </math> || <math> | + | | <math> \sinh{at} </math> || <math> \frac{a}{s^2-a^2} </math> |
|- | |- | ||
| − | | <math> \cosh{at} </math> || <math> | + | | <math> \cosh{at} </math> || <math> \frac{s}{s^2-a^2} </math> |
|- | |- | ||
| <math> e^{at}\sin{bt} </math> || <math> </math> | | <math> e^{at}\sin{bt} </math> || <math> </math> | ||
