2022年《复变函数与积分变换A》期末考试题A-A参考答案 .pdf

北京交通大学2008-2009 学年第一学期复变函数与积分变换B期末考试试卷A 学院_ 专业_ 班级 _ 学号_ 姓名_ 题号一二三四五六七八九十11 12 总分得分阅卷人一填空题（本题满分 16 分，每空 1 分），请将合适的答案填在空中.1 复 数iiiz2)52)(43(，则)Re(z-27；)Im(z-13；|z2925；)arg(z26arctan()7；复数 z的三角表达式为529(cos(arg()sin(arg()2ziz指数表达式为a r g()5292ize.2612622cossin,0,1,2,3,4,566kikkeik3ii(2)2kekZ4.)1(Ln(21)kikZ5函数zarg在复平面上的连续性为除去原点和负实轴上的点外都连续。6幂级数12nnnnz的收敛半径为 _2_.7映射zew将带形域2)Im(0z映照成除去正实轴（包含原点）的全平面.8幂函数3zw，把角形域6)arg(0z映照为 w平面的 第一象限.90,Re1zes1.10变换52zw在iz1的旋转角为4，伸缩率为2 2二判断下列命题的真假（本题满分 10 分，每道小题 1 分），对的填“”，错的填“”.1zikzee2.()2当 z 为复数时，1|sin|z仍然成立.()30z是zzf1sin1)(的孤立奇.()4如果)(0zf存在，则)(zf在0z 解析.()5 解 析 函 数 一 定 是 调 和 函 数，但 调 和 函 数 不 一 定 是 解 析 函 数()6当 C 是一条不通过原点的简单闭曲线时，积分Cdzz01.()7每一个幂级数的和函数在收敛圆内可能有奇点.()8LnzLnz22.()9如 果 幂 级 数0)2(nnnzc在0z收 敛，则 在3z也 收 敛.()10映射2zw在 z 平面上每一点都具有伸缩率和旋转角的不变性.()文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2三（本题满分 6 分）讨论函数)Re()(zzzf的连续性、可导性、解析性.解：22,()(),2,0,0,0,()Re()0zxiyf zxiy xxixyuxvxyuuxxyvvyxxyuvuvxyxyyxf zzzz设则又设则时，在复平面内连续，在可导，但在复平面内任一点都不解析。四（本题满分 6 分）将函数11zz在10z展成泰勒级数，并求出泰勒级数的收敛半径.解：111222122zzzzzzzzzz11(1)()111 11 111设即1时，2 分22312112221222nnnnnzzzzzzzzz-1-1-1z-1=(-1)-1-1-1-1=(-1)-2 分收敛半径2R2 分文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2五（本题满分 8 分）在扩充复平面上找出函数442)(sin)2)(1()(zzzzf的孤立奇点并加以分类，若是极点，指出其级数.解：4sincos0,1,2,0,1,2,sinsin112zzzzzzf z在都不为零是的一级零点，从而是的四级零点，这些点中除去，外都是的四级极点。3 分24242422242404111132,122limlimlim1sinsin1lim21sin3zzzzzzzfzzzzzfzzzz又是的 级极点,至于因为42641221121,sin111;122,2112010nnnzfzzfnnznznfnnfzfz是的可去奇点关于因为可知=0，使分母为零，当时，=1,即当时，即这两点上面已讨论过，当时，为的极点，当时，不是的孤立奇点，即不是的孤立奇点。5 分文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2六（本题满分 18分）1分别沿xy与2xy计算积分idziyx2202)(（6 分）；解：（1）沿xy，原式iiiixixiixxdixx238142381|23120232023 分（2）沿2xy原式iidxixxidxxiixixxdixx83812121120322022220223 分2 计算积分Cndzzz10)(1，其中C为包含0z 的任意一条正向简单闭曲线，n为整数.（6 分）；解：根据闭路变形原理，原式0,00,21010nnidzzzrzzn3已知调和函数yxu)1(2，求解析函数ivuzf)(，且if)2(.（6 分）解：yxuxyu2,12，由RC条件2212xxyuxV。2 分设yxxV22，则CyyyxuyyV22，2分所 以CyxxV222，Cyxxyxzf22212，有 已 知if 2，则izfyx,0,2，iCiCf0442，所 以iyxxyxzf21222 分文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2七（本题满分6 分）将函数)2()1(1)(zzzf分别在圆环1|1|0z与|2|1z内展成洛朗级数.解：（1）在110z，内2111211111111111111111111111nnnnzzzzzzzzzzzzf3 分（2）在21z内nnzzzzzzzzzf21121211212111211212112223 分八（本题满分 6 分）计算dzzzzz3|34215)2)(1(.解：原式=0,11Re2,Re22,Re,Re,Re,Re,Re224321zzfsizfsizfszzfszzfszzfszzfsi4 分因为10,11Re2zzfs。所以原式2 i2 分文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2九（本题满分 6 分）计算)0(,sin1022ada.解：原式012212220202,Re21122221121cos1222cos2121zzfsizazdziizdzzzaxadxxadzz令4 分其中1212220aaaz，所以原式=11412222aaaaii2 分十（本题满分 6 分）计算)0,0(,cos022amdxxamx解：原式aeaieiaizaesidxxaedxxamxamammixmix222Re21,Re2Re21Re21cos21222222十一.（本题满分 6 分）讨论在映射izw2下，以1,1,321zziz为顶点的三角形被映成什么图形.解：因为izeizw222为旋转变换（旋转角为2）且02iw，2分所以它将1,1,321zziz为顶点的三角形映射为以iwiww2,2,2321为文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9T7 HP4G7Z7I1G10 ZN1P7H3S6J2文档编码:CL3F2N6B9