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4Â¥: Originally posted by zz3476 at 2014-04-13 19:45:09
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2Â¥2014-04-13 14:23:30
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zz3476: ½ð±Ò+5, ¶Ô£¬ÓеÀÀí¡£ 2014-04-13 20:38:32
Áîu=t*x,v=t*y,
ÒòΪf(t*x,t*y)=f(u,v)=t^n*f(x,y)
Á½±ß¶ÔtÇóÒ»½×ºÍ¶þ½×µ¼Êý£¨×¢Ò⣬½«f[u(t),v(t¿´×÷tµÄ¸´ºÏº¯Êý£©£º
Pf(u,v)/Pu*x+Pf(u,v)/Pv*y=n*t^(n-1)*f(x,y)
ÔٴζÔÁ½±ßÇótµÄµ¼Êý£¨×¢Ò⣬½«Pf[u(t),v(t)]/Pu¡¢Pf[u(t),v(t)]/Pv¿´×÷tµÄ¸´ºÏº¯Êý£©£º
x^2*P^2f(u,v)/Pu^2+2*x*y*P^2f(u,v)/(Pu*Pv)
    +y^2*P^2f(u,v)/Pv^2=n*(n-1)*t^(n-2)*f(x,y)
                                     =n*(n-1)*t^(n-2)*f(u/t,v/t)
                                       =n*(n-1)*t^(n-2)*(1/t)^n*f(u,v)
u^2*P^2f(u,v)/Pu^2+2*u*v*P^2f(u,v)/(Pu*Pv)+
    +v^2*P^2f(u,v)/Pv^2=n*(n-1)*f(u,v)
ÉÏʽ¶ÔÓÚÈκÎu,v¶¼ÊdzÉÁ¢µÄ£¬Òò´Ë£¬Èô½«u¡¢v·Ö±ð»»³Éx¡¢yÒ²Ó¦¸ÃÊdzÉÁ¢µÄ£¬¹ÊÌâÄ¿µÄ½áÂÛ³ÉÁ¢¡£
3Â¥2014-04-13 17:03:55
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