The Laplace TransformCheng GangCollege of PharmacyShenyang Pharmaceutical University
The Laplace Transform Cheng Gang College of Pharmacy Shenyang Pharmaceutical University
模型bodyfecesurinedoseparentKkfmuXXukmmetabolitekmukmFmuXmmt
模型 k Xu kmu x kf Xf dose Xmf km Xm Xmu kmu km feces body urine parent metabolite
拉氏是一种积分变换，用来解释微分方程定义：f(t)的拉变式8F(s)=Lf(t)=( f(t)e-stdt0称F(s)或Lf(t)是f(t)的拉变变换f(t)象原函数
拉氏是一种积分变换，用来解释微分方程。 − 0 f (t)e dt F(s)=Lf(t)= st 称F(s)或Lf(t)是f(t)的拉变变换 f(t)象原函数 称F(s)或Lf(t)是f(t)的拉变变换 f(t)象原函数 定义：f(t)的拉变式
例1 f(t)=k8stdtke则 Lf(t)=0k8-ste0= k/s=S
例1 f(t)=k 则 Lf(t)= − 0 ke dt st − − 0 st e s k = = k/s
kt例2 f(t)=e则 Lf(t)=Kto-stdt018k+s)tdts+k0
例2 f(t)= 则 Lf(t)= = kt e − − − 0 e e dt kt st − + 0 ( ) e dt k s t = s + k 1
-kt例3 f(t)=Ae8ktstdtAeC?则 Lf(t)=0+k
例3 f(t)=A 则 Lf(t)= kt e − = − − 0 Ae e dt kt st s k A +
A例4 f(t)=KTkA一则 Lf(t)=e-sttdt(1kCATe-stdt-(s+k)td1eRk0C
例4 f(t)= 则 Lf(t)= - = (1 ) kt e k A − − − − − 0 (1 e )e dt k A kt st − 0 e dt k A st − + 0 ( ) e dt k A s k t
A例4 f(t)=Kk(一则 Lf(t)=s+ks(s+k
例4 f(t)= 则 Lf(t)= = (1 ) kt e k A − − ( ) 1 1 k s s k A − + s(s k ) A +
拉式变换性质则L(f(t)+g(t)-Lf(t)+Lg(t)L[Af (t) J=A Lf(t)Lf (t) = SLf(t) - f(O)
拉式变换性质 则 L(f(t)+g(t))=Lf(t)+Lg(t) L[Af（t）]=A Lf(t) ( ) ( ) (0) ' Lf t = SLf t − f
f(0) 为t=0时f(t)的值Lf'(t) = SLf(t) - f(O)df(t)Lf'(t)= Ldt
f(0) 为t=0时f(t)的值 ( ) ( ) (0) ' Lf t = SLf t − f d t d f t Lf t L ' ( ) ( ) =