Theorem 12.10  (Laplace Transform).  If    is of exponential order, then its Laplace Transform   exists and is given by

            ,   

where  .  The defining integral for    exists at points    in the right half plane  .

Proof.

Proof of Theorem 12.10.

Proof of Theorem 12.10 is left for the reader in the book.

Complex Analysis for Mathematics and Engineering

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