当x<-1/2 当-1/2<x<l 当x>l/2 当x≠0 lim d()= 当x=0 若记lm6(x)=6(x),6(x)什么意义?(公 →0
Dirac δ function Green Functions of ODE Possible Symmetric Properties of GF’s Density Distribution of A Point Source Basic Operation Rules 2D & 3D δ functions δl(x) = 0 x < −l/2 1 l −l/2 < x < l/2 0 x > l/2 lim l→0 δl(x) = ( 0 x 6= 0 ∞ x = 0 eP lim l→0 δl(x) = δ(x)§δ(x)ko¿Âº C. S. Wu 1Êù δ¼ê
6(x)的意义 对于任意一个在-/2<x<l/2内连续的函 数f(x),根据中值定理,有 f(x)b(x)dx=f(6)-1/2≤6≤1/2 取极限一0,对于任意一个在=0,点连续的函 数f(x),有 f()o()dr=f(o)
Dirac δ function Green Functions of ODE Possible Symmetric Properties of GF’s Density Distribution of A Point Source Basic Operation Rules 2D & 3D δ functions δ(x)¿Â éu?¿3−l/2 < x < l/2SëY¼ êf(x)§ ⥽n§k Z ∞ −∞ f(x)δl(x)dx = f(θl) − 1/2 ≤ θ ≤ 1/2 4l → 0§éu?¿3x = 0:ëY¼ êf(x)§k Z ∞ −∞ f(x)δ(x)dx = f(0) AO´ Z ∞ −∞ δ(x)dx = 1 C. S. Wu 1Êù δ¼ê
6(x)的意义 对于任意一个在-/2<x<l/2内连续的函 数f(x),根据中值定理,有 f(x)b(x)dx=f(6)-1/2≤b≤1/2 取极限l→0,对于任意一个在x=0点连续的函 数f(x),有 f(a)8(a)dx=f(O) 特别是
Dirac δ function Green Functions of ODE Possible Symmetric Properties of GF’s Density Distribution of A Point Source Basic Operation Rules 2D & 3D δ functions δ(x)¿Â éu?¿3−l/2 < x < l/2SëY¼ êf(x)§ ⥽n§k Z ∞ −∞ f(x)δl(x)dx = f(θl) − 1/2 ≤ θ ≤ 1/2 4l → 0§éu?¿3x = 0:ëY¼ êf(x)§k Z ∞ −∞ f(x)δ(x)dx = f(0) AO´ Z ∞ −∞ δ(x)dx = 1 C. S. Wu 1Êù δ¼ê
6(x)的意义 对于任意一个在-/2<x<l/2内连续的函 数f(x),根据中值定理,有 f(x)b(x)dx=f(6)-1/2≤b≤1/2 取极限l→0,对于任意一个在x=0点连续的函 数f(x),有 f(a)8(a)d.c=f( 特别是 6(x)dx=1
Dirac δ function Green Functions of ODE Possible Symmetric Properties of GF’s Density Distribution of A Point Source Basic Operation Rules 2D & 3D δ functions δ(x)¿Â éu?¿3−l/2 < x < l/2SëY¼ êf(x)§ ⥽n§k Z ∞ −∞ f(x)δl(x)dx = f(θl) − 1/2 ≤ θ ≤ 1/2 4l → 0§éu?¿3x = 0:ëY¼ êf(x)§k Z ∞ −∞ f(x)δ(x)dx = f(0) AO´ Z ∞ −∞ δ(x)dx = 1 C. S. Wu 1Êù δ¼ê
/f(x)(x)dx=f(0)才是6函数的定义 严格说来,f()应当满足:(1)任意阶导数均 存在,(2)具有有限支集
Dirac δ function Green Functions of ODE Possible Symmetric Properties of GF’s Density Distribution of A Point Source Basic Operation Rules 2D & 3D δ functions Z ∞ −∞ f(x)δ(x)dx = f(0)â´δ¼ê½Â î`5§f(x)A÷vµ(1) ?¿ êþ 3§(2) äkk|8 ȩؽ´±∞©f(x)|8á u(a, b)§Òk Z b a f(x)δ(x)dx = f(0) δ¼êáu2¼ê(generalized function§½ distribution) C. S. Wu 1Êù δ¼ê