F'(t)为f(t)的导数df(t)f'(t) =dtdf(t)Lf'(t) = Ldt
F’(t) 为f(t)的导数 dt df t f t ( ) ( ) ' = d t d f t Lf t L ' ( ) ( ) =
导数的拉变式Lf'(t) = LQdt8df(t)st(e-stdf(t)dtedtJoO8S+s f(t)e-stdt= -f(O) + sLf(t)= f(t)e10L[] = SL[x]-x(O) = SX - X(O)
导数的拉变式 dt df t Lf t L ' ( ) ( ) = − = 0 ( ) e dt st dt df t − = 0 e df (t) st − − = + 0 0 f (t)e s f (t)e dt st st = − f (0) + sLf (t) L[ ] SL[x] x(0) SX X (0) d t d x = − = −
Table of Laplace transformsTime function,F(t)Laplace transorm,f(s)ASAtA52Ae-ktAS+kAA(1-e-k)S(S+k)k
Table of Laplace transforms Time function,F(t) Laplace transorm,f(s) A At S A 2 S A kt Ae− S k A + k A e kt (1 ) − − S (S k ) A +
单室模型静脉注射kXdx-kXdtsX - X(O)=-kXXoX=s+K
单室模型静脉注射 k X k kX dt dx = − sX − X(0) = −kX s K x X + = 0