Example 12.7.  Show that the Laplace transform of the step function given by  

            [Graphics:Images/LaplaceTransformMod_gr_89.gif]

            is  [Graphics:Images/LaplaceTransformMod_gr_90.gif].  

Explore Solution 12.7.

Enter the function  [Graphics:../Images/LaplaceTransformMod_gr_93.gif]  and compute the integral defining   [Graphics:../Images/LaplaceTransformMod_gr_94.gif].  

[Graphics:../Images/LaplaceTransformMod_gr_95.gif]




[Graphics:../Images/LaplaceTransformMod_gr_96.gif]

 

 

 

 

Aside. We can check this with Mathematica's  result using the LaplaceTransform package.

[Graphics:../Images/LaplaceTransformMod_gr_97.gif]




[Graphics:../Images/LaplaceTransformMod_gr_98.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell