Theorem 12.13  (Differentiation of f(t) ). Let [Graphics:Images/LaplaceDiffIntegrateMod_gr_1.gif] be continuous for [Graphics:Images/LaplaceDiffIntegrateMod_gr_2.gif], and of exponential order. Then

            [Graphics:Images/LaplaceDiffIntegrateMod_gr_3.gif],  

where [Graphics:Images/LaplaceDiffIntegrateMod_gr_4.gif].   

Proof.

Proof of Theorem 12.13.

Proof of Theorem 12.13 is in the book.

Complex Analysis for Mathematics and Engineering

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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