推导:设光滑曲线C的参数方程 z=z(t)=x(t)+iy(t),a≤t≤ 正方向为参数增加的方向,参数a及对应于起点A及 终点B,并且z2(t)≠0,a<t<B 如果f(x)=u(x,y)+i(x,y)在D内处处连续, 设(k=5k+imk,由于 Azk= 2k-2k-1=k+iyk-(ak-1+iyk-1 =xk-xk-1+i(k-yk-1)=△xk+i△k,í: 1w­‚ C ëꐧ z = z(t) = x(t) + iy(t), α 6 t 6 ⠐•ǑëêO\•, ëê α 9 β éAuå: A 9 ª: B, ¿… z ′ (t) 6= 0, α < t < β. XJ f(z) = u(x, y) + iv(x, y) 3 D S??ëY,  ζk = ξk + iηk, du △zk = zk − zk−1 = xk + iyk − (xk−1 + iyk−1) = xk − xk−1 + i(yk − yk−1) = △xk + i△yk, 7/127