Complex Integration: Fundamental Properties 复变积分的基本性质 0若积分/(2)d=,/(x,…,/f(2都 存在,则 (2)+1(2)+…+f(2) f(2)z+/f(2d 2+…+ e若C=C1+C2+…+Cn,则 f(2)dz+/f()dz+…+/.f()d f(z)d
Complex Integration Cauchy Integral Theorems Two Useful Lemmas Complex Integration: Definition Complex Integration: Fundamental Properties ECÈ©Ä 5 ❶ eÈ© Z C f1(z)dz, Z C f2(z)dz, · · · , Z C fn(z)dzÑ Z 3§K C h f1(z) + f2(z) + · · · + fn(z) i dz = Z C f1(z)dz + Z C f2(z)dz + · · · + Z C fn(z)dz ❷ Z eC = C1 + C2 + · · · + Cn§K C1 f(z)dz + Z C2 f(z)dz + · · · + Z Cn f(z)dz = Z C f(z)dz C. S. Wu 1où ECÈ©()
Complex Integration: Fundamental Properties 复变积分的基本性质 3/ f(adz f(z)dz,其中C-表示C的 逆向 0af(2)d==a/f(2)d=,其中a为常数
Complex Integration Cauchy Integral Theorems Two Useful Lemmas Complex Integration: Definition Complex Integration: Fundamental Properties ECÈ©Ä 5 ❸ Z C− f(z)dz = − Z C f(z) dz§Ù¥C −L«C _ ❹ Z C af(z) dz = a Z C f(z) dz§Ù¥a~ê ❺ Z C f(z)dz ≤ Z C |f(z)||dz| C. S. Wu 1où ECÈ©()
Complex Integration: Fundamental Properties 复变积分的基本性质 3/ f(adz f(z)dz,其中C-表示C的 逆向 o/af(e)d ∫(z)dz,其中a为常数 f(=)d
Complex Integration Cauchy Integral Theorems Two Useful Lemmas Complex Integration: Definition Complex Integration: Fundamental Properties ECÈ©Ä 5 ❸ Z C− f(z)dz = − Z C f(z) dz§Ù¥C −L«C _ ❹ Z C af(z) dz = a Z C f(z) dz§Ù¥a~ê ❺ Z C f(z)dz ≤ Z C |f(z)||dz| C. S. Wu 1où ECÈ©()
Complex Integration: Fundamental Properties 复变积分的基本性质 3/ f(adz f(z)dz,其中C表示C的 逆向 e/af(a)dz=a/f()d,其中a为常数 6/f(=)dz|≤/|f(=)川|d
Complex Integration Cauchy Integral Theorems Two Useful Lemmas Complex Integration: Definition Complex Integration: Fundamental Properties ECÈ©Ä 5 ❸ Z C− f(z)dz = − Z C f(z) dz§Ù¥C −L«C _ ❹ Z C af(z) dz = a Z C f(z) dz§Ù¥a~ê ❺ Z C f(z)dz ≤ Z C |f(z)||dz| C. S. Wu 1où ECÈ©()
Complex Integration: Fundamental Properties 复变积分的基本性质 0|/(地15M,其中M为(在C上的 上界,l为C的长度
Complex Integration Cauchy Integral Theorems Two Useful Lemmas Complex Integration: Definition Complex Integration: Fundamental Properties ECÈ©Ä 5 ❻ Z C f(z)dz ≤ Ml§ Ù¥M f(z) 3Cþ þ.§lCÝ C. S. Wu 1où ECÈ©()