Difference between revisions of "Laplace Transform"

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| <math> 1 </math> || <math> \frac{1}{s} </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <math> s > 0 </math>
 
| <math> 1 </math> || <math> \frac{1}{s} </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <math> s > 0 </math>
|-
 
| <math> e^{at} </math> || <math> \frac{1}{s-a} </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <math> s > a </math>
 
 
|-
 
|-
 
| <math> t </math> || <math> \frac{1}{s^2} </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <math> s > 0 </math>
 
| <math> t </math> || <math> \frac{1}{s^2} </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <math> s > 0 </math>
Line 13: Line 11:
 
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| <math> t^{n}e^{at} </math> || <math> \frac{n!}{s^{n+1}} </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <math> s > a </math>
 
| <math> t^{n}e^{at} </math> || <math> \frac{n!}{s^{n+1}} </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <math> s > a </math>
 +
|-
 +
| <math> e^{at} </math> || <math> \frac{1}{s-a} </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <math> s > a </math>
 
|-
 
|-
 
| <math> \sin{at} </math> || <math> \frac{a}{s^2+a^2} </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <math> s > 0 </math>
 
| <math> \sin{at} </math> || <math> \frac{a}{s^2+a^2} </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <math> s > 0 </math>

Revision as of 16:37, 20 September 2021

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