当C是分段光滑曲线,C=C1+C2+…+Cn时,有 f(a)d f(2)dz+/f(2)d f(e)dz
C ´©ã1w, C = C1 + C2 + · · · + Cn , k Z C f(z)dz = Z C1 f(z)dz + Z C2 f(z)dz + · · · + Z Cn f(z)dz. 10/127
总结起来,计算沿光滑曲线的复变函数积分的方法有 化为两要实二元函数的线积分来计算
• o(å5, O÷1wEC¼êÈ©{k: 1. zǑü¢¼êÈ©5O. Z C f(z)dz = Z C udx − vdy + i Z C vdx + udy. 2. Ñ C ëê§: z = z(t) = x(t) + iy(t), , Z C f(z)dz = Z β α f[z(t)]z ′ (t)dt. 11/127
总结起来,计算沿光滑曲线的复变函数积分的方法有 1.化为两个实二元函数的线积分来计算 f(a)dz= ud -vdy+i/ udar+udy 2.写出C的参数方程 f=(1)=(t)d
• o(å5, O÷1wEC¼êÈ©{k: 1. zǑü¢¼êÈ©5O. Z C f(z)dz = Z C udx − vdy + i Z C vdx + udy. 2. Ñ C ëê§: z = z(t) = x(t) + iy(t), , Z C f(z)dz = Z β α f[z(t)]z ′ (t)dt. 11/127
总结起来,计算沿光滑曲线的复变函数积分的方法有 1.化为两个实二元函数的线积分来计算 f(a)dz= ud -vdy+i/ udar+udy 2.写出C的参数方程:z=z(1)=x()+iy(t),然后求 f(2)d2=/f()()d
• o(å5, O÷1wEC¼êÈ©{k: 1. zǑü¢¼êÈ©5O. Z C f(z)dz = Z C udx − vdy + i Z C vdx + udy. 2. Ñ C ëê§: z = z(t) = x(t) + iy(t), , Z C f(z)dz = Z β α f[z(t)]z ′ (t)dt. 11/127
3.积分的性质 1)/f(a)dx f(edz 2)/kf(2)d=k/f(=)d;(k为常数) 3)/[f(x)±g(z)]dz=/f(2)d2±/g(=)dz
3. È©5 1) Z C f(z)dz = − Z C− f(z)dz; 2) Z C kf(z)dz = k Z C f(z)dz; (kǑ~ê) 3) Z C [f(z) ± g(z)]dz = Z C f(z)dz ± Z C g(z)dz. 12/127