Theorem 12.19 (Nonrepeated Linear Factors).  Let [Graphics:Images/LaplaceInverseMod_gr_5.gif] be a polynomial of degree at most [Graphics:Images/LaplaceInverseMod_gr_6.gif].  If [Graphics:Images/LaplaceInverseMod_gr_7.gif] has degree n, and has distinct complex roots  [Graphics:Images/LaplaceInverseMod_gr_8.gif],  then equation (12.36) becomes   

(12.37)            [Graphics:Images/LaplaceInverseMod_gr_9.gif].  

Proof.

Proof of Theorem 12.19 is left for the reader in the book.

Complex Analysis for Mathematics and Engineering

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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