Theorem 12.16   (Shifting the Variable  t).  If is the Laplace transform of , and , then  

                         ,

where   and    are illustrated in Figure 12.23.

            Figure 12.23.  Comparison of the functions    and  .  

Proof.

Proof of Theorem 12.16.

Proof of Theorem 12.16 is in the book.

Complex Analysis for Mathematics and Engineering

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