资源描述：
《校级课题申请书(2013年新版)》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、成都理工大学《复变函数》模拟考试试题（一）参考答案大 题一二三四总 分得 分一填空题(每题4分，共5题20分)1，则i。2三角形三个顶点复数为，则重心处的复数是。3函数的奇点是全体复数（任意复数）。4=-e。5
2、z
3、=1，化简=0。二计算题(每题6分，共4题24分)6求Ln(1+)的全体值。解：原式=···················3分=·····················3分7求的全体值。解：原式==····························3分15==[]·············3分8计算。解：
4、原式=············3分==·············3分9计算，C：的正向。解：原式=，C内只包围奇点a,····3分===··········································3分三解答题(每题6分，共4题24分)10u(x,y)=，求函数v(x,y)，使u(x,y)+iv(x,y)是解析函数。解：由C-R方程，，····3分由，得15由，）=0，所以）=C。·····································3分11求级数的收敛域。解：，半径R=.······
5、·······3分圆心为。收敛域·······························3分12求映射在z=i处的伸缩率和转动角。解：,·························3分。伸缩率为2，转动角。·······3分13在映射w=(1+i)下，z平面上的图形
6、z-i
7、<1被映射成w平面上的什么图形。解：共轭表示以实轴为对称轴上下翻，映射为
8、z+i
9、<1·····3分，乘以(1+i)表示旋转，再以原点为基准向外膨胀为倍的圆。15圆心是，膨胀到1-i。半径从1膨胀到。最后图形是
10、w-(1-i)
11、<。······
12、······················3分四计算题(每题8分，共4题32分)14计算，L是连接(0,0)与(，0)的曲线，(0,0)为起点。解：原式=··············定义2分=·····展开2分=·············代路径2分=·······································分部积分2分15把函数在区域1<
13、z
14、<2展开成洛朗级数。解：原式=····拆项2分其中·····················2分···························2分15···
15、·····················2分16判断函数的所有有限奇点与无穷远奇点的类型，并计算每个奇点的留数。解：有限奇点有z=0,z=2,分别是一级极点。··············2分因为，所以z=是可去奇点。······2分`········两个有限奇点的留数2分留数定理2：·····2分17求将下半平面Im(z)<0映射成单位圆
16、w-i
17、<2的分式线性映射。解：下半平面取任一复数。映射到0，映射到。，·········································2分当z=1,
18、w
19、=1,所以
20、k
21、
22、=1.下半平面映射到单位圆内，··········································2分扩大为半径为2的圆内15··········································2分往上平移至圆心为i.+i·········································2分15成都理工大学《复变函数》模拟考试试题（二）附参考答案大 题一二三四总 分得 分一．判断题（每题2分，共6题，总分12分）1.若是和的一个奇点，则也是和的奇点(╳)2.若函数点解析，则在该
23、点连续。(√)3. (√)4.，，则是解析函数(╳)5.若存在，则与有相同的收敛半径(√)6.是的孤立奇点(╳)二．填空题（每题3分，共8题，总分24分）1.设，则2.设，则的指数形式表示为3.函数将平面上的曲线变为平面上的曲线的方程是（用u,v表示）。4.151.-12.，则。3.映射在z=i处转动角是0，伸缩率是ch14.函数的奇点是所有纯虚数，（y轴上除0以外的所有点）一．解答题（每题6分，共8题，总分48分）1.证明：解：左边=····················
24、2分······················2分·····················2分2.解方程解：·····················2分·······································2分··················
