Definition Laplace变换是一种积分变換,它把f(t)变换为 F(p) F(p)=/e-pt f(t)dt 这里的是实数,p是复数,p=s+ia F()称为∫(切)的 Laplace换式,简称拉氏换式 e是 Laplace变换的核
Laplace Transform Inverse Laplace Transform Definition of Laplace Transform Properties of Laplace Transform Definition LaplaceC´«È©C§§rf(t)C F(p) F(p) = Z ∞ 0 e −ptf(t) dt ùpt´¢ê§p´Eê§p = s + iσ F(p)¡f(t)Laplaceª§{¡.¼ª e −pt´LaplaceCØ C. S. Wu 1où LaplaceC
Definition Laplace变换是一种积分变换,它把f(t)变换为 F(p) F(p) e-ptff(t)dt 名称:f(1)一 Laplace变换的原函数 F(p) Laplace变换的像函数
Laplace Transform Inverse Laplace Transform Definition of Laplace Transform Properties of Laplace Transform Definition LaplaceC´«È©C§§rf(t)C F(p) F(p) = Z ∞ 0 e −ptf(t) dt ¶¡µf(t) LaplaceC¼ê F(p) LaplaceC¼ê {PÒ F(p) = ▲ {f(t)} ½ F(p) : f(t) f(t) = ▲ −1 {F(p)} ½ f(t) ; F(p) C. S. Wu 1où LaplaceC
Definition Laplace变换是一种积分变换,它把f(t)变换为 F(p) F(p) e-ptff(t)dt 名称:∫(t)— Laplace变换的原函数 F(p)— Laplace变换的像函数 简写记号 )={f() 或F()=f() F)或f()=F(0)
Laplace Transform Inverse Laplace Transform Definition of Laplace Transform Properties of Laplace Transform Definition LaplaceC´«È©C§§rf(t)C F(p) F(p) = Z ∞ 0 e −ptf(t) dt ¶¡µf(t) LaplaceC¼ê F(p) LaplaceC¼ê {PÒ F(p) = ▲ {f(t)} ½ F(p) : f(t) f(t) = ▲ −1 {F(p)} ½ f(t) ; F(p) C. S. Wu 1où LaplaceC
Definition Laplace变换是一种积分变换,它把f(t)变换为 F(p) F(p) e-ptff(t)dt 名称:∫(t)— Laplace变换的原函数 F(p)— Laplace变换的像函数 简写记号 F(p)=ef(t) F(p)=f(t) r()=x(F()}或(0)=F()
Laplace Transform Inverse Laplace Transform Definition of Laplace Transform Properties of Laplace Transform Definition LaplaceC´«È©C§§rf(t)C F(p) F(p) = Z ∞ 0 e −ptf(t) dt ¶¡µf(t) LaplaceC¼ê F(p) LaplaceC¼ê {PÒ F(p) = ▲ {f(t)} ½ F(p) : f(t) f(t) = ▲ −1 {F(p)} ½ f(t) ; F(p) C. S. Wu 1où LaplaceC
Inverse 例14.1 函数f(t)=1的 Laplace换式为 1 e p dt= Rep>o 这里的限制条件Re>0是为了保证积分收敛, 或者说,是 Laplace变换存在的条件 尜
Laplace Transform Inverse Laplace Transform Definition of Laplace Transform Properties of Laplace Transform ~14.1 ¼êf(t) = 1Laplaceª 1 ; Z ∞ 0 e −ptdt = − 1 p e −pt ∞ 0 = 1 p Re p > 0 ùp^Re p > 0´ yÈ©Âñ§ ½ö`§´LaplaceC3^ C. S. Wu 1où LaplaceC