8 15-5 Several basis theorems for the Laplace transform 1.The linearity theorem Lf(t)+f(0=F(s)+F2(s) Example: Iv(s) Find(t)=L-V(s)) (s+a)(s+B) a-B a-B 十 (s+a)(s+B) S+a u(t=L v(s)=La-B a-B S+a s十 B cptu(t e eu()+ e B-a B-a B-a ko(t)<kv(s)§15-5 Several basis theorems for the Laplace transform 1.The linearity theorem  ( ) ( ) ( ) ( ) 1 2 1 2 L f t + f t = F s + F s Example: ( )  ( ) ( )( ) 1 ( ) 1 Find t L V s s s If V s − = + + =            + − + + − − = + + = s s s s V s 1 1 ( )( ) 1 ( ) ( ) 1 ( ) 1 e u t e u t  t  t     − − − − + − = u(t) e e t t     − − = − −                 + − + + − − = = − −        s s t L V s L 1 1 ( ) ( ) 1 1 k(t)  kV(s)