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复变函数 第 6 讲. 本文件可从网址 http://math.vip.sina.com 上下载 ( 单击 ppt 讲义后选择‘复变函数 ' 子目录 ). 例 1 设一平面流速场的复势为 f(z)=az(a>0 为实常数 ), 试求该场的速度 , 流函数和势函数. }. 等势线. y. {. 流 线. x. O. - PowerPoint PPT Presentation
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6http://math.vip.sina.com(ppt')
1 f(z)=az(a>0), , .
[]
,
, x.
(x,y)=ay, y=c1;
(x,y)=ax, x=c2.
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2 , div v 0, (div v > 0 , div v < 0). , .[] v, , . , z0v=g(r)r0,r=|z|, r0z, , g(r).
, "". (2.4.6), f(z)c=c1+ic2.
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2.5xyO(N>0)
1
1. C(). C(), C, . CAB, ABC, BAC, C-. , , . P, PP.
w=f(z)D, CDAB. Cn, A=z0,z1,...,zk-1,zk,...,zn=B
zk-1,zk(k=1,2,...,n)k,
, Cxaxb, f(z)=u(x), .
u,v, , n, C, (xk,hk), .
CC1,C2,...,Cn,
1 , C3+4i.[]x=3t, y=4t, 0t1,z=3t+i4t, 0t1.C, z=(3+4i)t, dz=(3+4i)dt.
2 , Cz0, r, n.z0rqz-z0=reiqzOxy
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, . .
3.
- f(z)B, BC:CB
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