∫(x)(x)dx=∫(0)才是6函数的定义 严格说来,∫(x)应当满足:(1)任意阶导数均 存在,(2)具有有限支集 积分限不一定是 只要f(x)的支集属 于(a.b),就有
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
∫(x)(x)dx=∫(0)才是6函数的定义 严格说来,∫(x)应当满足:(1)任意阶导数均 存在,(2)具有有限支集 积分限不一定是士∞.只要∫(x)的支集属 于(a,b),就有 f(r)s(a)d.c= f(o) 画数属于广义函数(0h,“类 distribution
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
∫(x)(x)dx=∫(0)才是6函数的定义 严格说来,∫(x)应当满足:(1)任意阶导数均 存在,(2)具有有限支集 积分限不一定是士∞.只要f(x)的支集属 于(a,b),就有 f(a)8(ad x= f( 6函数属于广义函数( (generalized function,或 distribution)
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
函数,并不是通常意义下的函数:它并没有 给出函数与自变量之间的对应关系 它给出的对应关系 当x≠0 在通常意义下是没有意义的
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 δ¼ê§¿Ø´Ï~¿Âe¼êµ§¿vk ѼêgCþméA'X §ÑéA'X δ(x) = ( 0 x 6= 0 ∞ x = 0 3Ï~¿Âe´vk¿Â §¤Ñ/¼ê0´3È©$¥â k¿Â Z ∞ −∞ f(x)δ(x)dx = f(0) C. S. Wu 1Êù δ¼ê
●6函数,并不是通常意义下的函数:它并没有 给出函数与自变量之间的对应关系 它给出的对应关系 当x≠0 6(x) 当x=0 在通常意义下是没有意义的 它所给出的“函数值”只是在积分运算中才 有意义
Dirac δ function Green Functions of ODE Possible Symmetric Properties of GF’s Density Distribution of A Point Source Basic Operation Rules 2D & 3D δ functions δ¼ê§¿Ø´Ï~¿Âe¼êµ§¿vk ѼêgCþméA'X §ÑéA'X δ(x) = ( 0 x 6= 0 ∞ x = 0 3Ï~¿Âe´vk¿Â §¤Ñ/¼ê0´3È©$¥â k¿Â Z ∞ −∞ f(x)δ(x)dx = f(0) C. S. Wu 1Êù δ¼ê