Extra Example 1.  Use Theorem 12.16 and find  [Graphics:Images/LaplaceShiftingMod_gr_56.gif].  

Explore Solution for Extra Example 1.

Use Theorem 12.16 and find  [Graphics:../Images/LaplaceShiftingMod_gr_57.gif].  
Enter the function  [Graphics:../Images/LaplaceShiftingMod_gr_58.gif], and apply Theorem 12.16 .

[Graphics:../Images/LaplaceShiftingMod_gr_59.gif]




[Graphics:../Images/LaplaceShiftingMod_gr_60.gif]

 

 

 

 

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

[Graphics:../Images/LaplaceShiftingMod_gr_61.gif]




[Graphics:../Images/LaplaceShiftingMod_gr_62.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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