复变函数第2章41408new

《复变函数第2章41408new》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、12Ù)Û¼ê2014c323F1)Û¼êVg2¼ê)Û¿‡^‡3мê1.EC¼êꆇ©½Â¼êw=f(z)3:z0,•N(z0)Sk½Â,e4•1.EC¼êꆇ©½Â¼êw=f(z)3:z0,•N(z0)Sk½Â,e4•4wf(z0+4z)f(z0)lim=lim4z!04z4z!04z1.EC¼êꆇ©½Â¼êw=f(z)3:z0,•N(z0)Sk½Â,e4•4wf(z0+4z)f(z0)lim=lim4z!04z4z!04z•3,K¡f(z)3:z0Œ,¿¡d4•Š•f(z)3z0

2、:ê,PŠdw0f(z0)½jz=z0:dzdw0f(z0)½jz=z0:dzÄK,¡f(z)3z0:ØŒ½êØ•3.u´dw0f(z0)½jz=z0:dzÄK,¡f(z)3z0:ØŒ½êØ•3.u´0dwf(z0+4z)f(z0)f(z0)=jz=z0=limdz4z!04zdw0f(z0)½jz=z0:dzÄK,¡f(z)3z0:ØŒ½êØ•3.u´0dwf(z0+4z)f(z0)f(z0)=jz=z0=limdz4z!04z0dwf(z)f(z0)½f(z0)=jz=z0=lim:dzz!z0zz0dw0f(z0)

3、½jz=z0:dzÄK,¡f(z)3z0:ØŒ½êØ•3.u´0dwf(z0+4z)f(z0)f(z0)=jz=z0=limdz4z!04z0dwf(z)f(z0)½f(z0)=jz=z0=lim:dzz!z0zz0ef(z)3«•DS??Œ,K¡f(z)3DSŒ.~¦f(z)=z2ê.~¦f(z)=z2ê.f(z0+4z)f(z0))lim4z!04z(z+4z)2z2=lim4z!04z=lim(2z+4z)4z!0=2z;~¦f(z)=z2ê.f(z0+4z)f(z0))lim4z!04z(z+4z)2z

4、2=lim4z!04z=lim(2z+4z)4z!0=2z;f0(z)=2z:~f(z)=x+2yi´ÄŒ?~f(z)=x+2yi´ÄŒ?f(z0+4z)f(z0))lim4z!04z(x+4x)+2(y+4y)ix2yi=lim4z!04x+i4y4x+2i4y=lim:4z!04x+i4yez+4z÷²1ux¶••ªuz;K4y=0;ez+4z÷²1ux¶••ªuz;K4y=0;4x+2i4y4xlim=lim=1;4z!04x+i4y4z!04xez+4z÷²1ux¶••ªuz;K4y=0;4x+2i4y4xlim=li

5、m=1;4z!04x+i4y4z!04xez+4z÷²1uy¶••ªuz;K4x=0;ez+4z÷²1ux¶••ªuz;K4y=0;4x+2i4y4xlim=lim=1;4z!04x+i4y4z!04xez+4z÷²1uy¶••ªuz;K4x=0;4x+2i4y2i4ylim=lim=2;4z!04x+i4y4z!0i4yez+4z÷²1ux¶••ªuz;K4y=0;4x+2i4y4xlim=lim=1;4z!04x+i4y4z!04xez+4z÷²1uy¶••ªuz;K4x=0;4x+2i4y2i4ylim=lim=2;4z!04x

6、+i4y4z!0i4yf(z)=x+2yiØŒ.ëY†Œ'Xdd~Œ„,ëY¼ê™7Œ.e¼ê3z0Œ,K3z0ëY:ëY†Œ'Xdd~Œ„,ëY¼ê™7Œ.e¼ê3z0Œ,K3z0ëY:‡yëY†Œ'Xdd~Œ„,ëY¼ê™7Œ.e¼ê3z0Œ,K3z0ëY:‡ylim(f(z)f(z0))=0:z!z0ëY†Œ'Xdd~Œ„,ëY¼ê™7Œ.e¼ê3z0Œ,K3z0ëY:‡ylim(f(z)f(z0))=0:z!z0¯¢þëY†Œ'Xdd~Œ„,ëY¼ê™7Œ.e¼ê3z0Œ,K3z0ëY:‡

7、ylim(f(z)f(z0))=0:z!z0¯¢þf(z)f(z0)0lim(zz0)=f(z0)
0:z!z0zz0EC¼ê¦{KI000(1)[f(z)g(z)]=f(z)g(z);EC¼ê¦{KII000(2)[f(z)g(z)]=f(z)g(z)+f(z)g(z);f(z)f0(z)g(z)f(z)g0(z)0(3)[]=;g(z)g2(z)g(z)6=0;EC¼ê¦{KIII000(4)ff[g(z)]g=f(w)g(z);Ù¥w=g(z);10(5)f(z)='0(z)EC¼ê¦{KIVÙ¥w=f(z)

8、†z='(w)•üp•‡¼êüŠ¼ê,…'0(w)6=0:EC¼ê‡©f(z0+4z)f(z0)lim4z!04z4w00=f(z0),f(z