第十三章向量分析 x=x(1) (a≤t≤B) 2 ==(x(0),y) 5X(xy,=+(x,y)= ∫(x(x(y()=()y)x()+(x(y()(c()y)()址 5X(x,y=(x,y)+(x,y:(x,y) 「z0:x()+=;y(0)h=于z÷+2=d 5x(xy.+(xy,地b+2(xy d x(x, y =(x, y)kr+r(x, =(x, y)dy+z= ar+Z,dy f(x(xy:(x,)+z:)+((x,)+2= +2=y)a(X+Z ar_ax dxdy dxdy +ze dodi a(y( z(x, y, 2)ldx dy or aY azaZ alkte-ildrdvsa(r(x,3, 2)+=' Z(x,y, 2)2dxdy 第十三章向量分析第十三章 向量分析 第十三章 向量分析 ( )      = = = ( ( ), ( )) ( ) z z x t y t y y t x x t , (  t   ) X(x y z)dx Y(x y z)dy L , , + , ,  = = (X(x(t) y(t) z(x(t) y(t)))x (t) Y(x(t) y(t) z(x(t) y(t)))y (t))dt   +    , , , , , , = X(x y z(x y))dx Y(x y z(x y))dy L , , , + , , ,  ( ) ( ( ) ( ) ( ( ) ( ) ( ( ) ( )))) ( )   =    Z x y z dz Z x t y t z x t y t z x t y t z t dt L , , , , , , , = ( )( ( ) ( ))     +   =  +   L Z t z x x t z y y t dt Z z x dx Z z y dy   X(x y z)dx Y(x y z)dy Z(x y z)dz L , , + , , + , ,  = X(x y z(x y))dx Y(x y z(x y))dy L , , , + , , ,   +  +   L Z z x dx Z z y dy = (X(x y z(x y)) Z z )dx (Y(x y z(x y)) Z z )dy y L x +  + +   , , , , , , = ( ) ( ) dxdy y X Z z x Y Z z Dxy y x            +  −   +  **=                    −     +        −    −           −   − Dxy x y dxdy y X x Y z x X z Z z z Y y Z = ( )    Dxy F n dxdy   = ( )    S F dS   . ** ⚫ ( ) dxdy x Y Z z y   +  = ( ) dxdy x Y x y z z Z x y z y   ( , , ) +  ( , , ) = = z Z z dxdy z Z x Z z z z Y x Y x y x x y          +          +    +          +   ; ⚫ ( ) dxdy y X Z z x   +  = ( ) dxdy y X x y z z Z x y z x   ( , , ) +  ( , , ) =