微分性质若[(O)=F(s) 则有()=sF(s)-f(0)(23) 证根据分部积分公式和拉氏变换公式 uav=uv vdu CIf(t]=Lf'(tedt=l esd f(t) + e sf(oo-Jf()de -f(0)+s f(e"dt=s/f(J-f(O) EPI(t]=sF(s)-f(o)(Re(s)>c)4 微分性质 若L [f(t)]=F(s), 则有 L [f '(t)=sF(s)-f(0) (2.3) 证 根据分部积分公式和拉氏变换公式 [ ( )] ( ) (0) (Re( ) ) (0) ( ) e d [ ( )] (0) e ( ) ( )de [ ( )] ( ) e d e d ( ) d | d 0 0 0 0 0 f t sF s f s c f s f t t s f t f f t f t f t f t t f t u v uv v u s t s t s t s t s t b a b a b a  = -  = - + = - = -  =  = = -       + - + - + - + - + - L L L 即