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1、-1-_数学与应用数学专业一、填空题（每小题2 分）1、复数i 212的指数形式是2、函数w=z1将ZS上的曲线1122yx变成WS(ivuw)上的曲线是3、若01ze,则z4、ii1=5、积分idzz2222=6、积分1sin21zdzzzi7、幂级数01nnnzi的收敛半径 R=8、0z是函数zez111的奇点9、1Re21zeszz10、将点,i,0分别变成 0,i,的分式线性变换w二、单选题（每小题2 分）1、设为任意实数，则 1=（）A 无意义 B等于 1 C是复数其实部等于1 D是复数其模等于 12、下列命题正确的是（）A ii2 B 零的辐角是零 C 仅存在一个数 z,使得zz1
2、 D izzi13、下列命题正确的是（）A函数zzf在z平面上处处连续B 如果af存在,那么zf在a解析 C 每一个幂级数在它的收敛圆周上处处收敛 D 如果 v 是 u 的共轭调和函数,则 u 也是 v 的共轭调和函数4、根式31的值之一是（）A i2321 B 223i C 223i Di23215、下列函数在0z的去心邻域内可展成洛朗级数的是（）A z1sin1 B z1cos C zctge1 D Lnz6、下列积分之值不等于0 的是()A 123zzdzB 121zzdzC1242zzzdzD 1coszzdz7、函数zzfarctan在0z处的泰勒展式为（）A 02121nnnnz（
3、z 1）B 01221nnnnz（z 1）C012121nnnnz（z 1）D 0221nnnnz（z 1）8、幂级数nnnz201)1(在1z内的和函数是（）A 211zB 211zC 112zD 211z9、设 ai，C：iz=1，则dziazzC2cos（）-2-_A 0 B e2i C 2ie D icosi 10、将单位圆1z共形映射成单位圆外部1w的分式线性变换是（）A)1(1azaazewi B)1(1azaazewiC)1(aazazewi D)1(aazazewi三、判断题（每小题2 分）1、（）对任何复数 z,22zz成立2、（）若a是zf和zg的一个奇点,则a也是zgzf
4、的奇点3、（）方程01237zz的根全在圆环21z内4、（）z=是函数zf251zz的三阶极点5、（）解析函数的零点是孤立的四、计算题（每小题6 分）1、已知)(2222ydxycxibyaxyxzf在zS上解析,求 a,b,c,d的值2、计算积分22)1(25zdzzzz3、将函数11zzzf在1z的邻域内展成泰勒级数,并指出收敛范围4、计算实积分 I=0222)4)(1(dxxxx5、求211)(zzf在指定圆环iz2内的洛朗展式6、求将上半平面0Imz共形映射成单位圆1w的分式线性变换zLw，使符合条件0iL，0iL五、证明题（每小题7 分）1、设（1）函数)(zf在区域 D 内解析（2
5、）在某一点Dz0有0)(0)(zfn，（,2,1n）证明：)(zf在 D 内必为常数2、证明方程015nzze在单位圆1z内有n个根一填空题（每小题2 分，视答题情况可酌情给1 分，共 20 分）1 ie654，2 21u，3(2k+1)i,(k=0,2,1)，4 kiee242ln(k=0,2,1)5 3i,6 0,7 21,8 可去，9 2e，10 z1二 单选题（每小题 2 分，共 20 分）1 D 2 D 3 A 4 A 5 B 6 B 7 C 8 D 9 A 10 A 三 判断题（每小题 2 分，共 10 分）1 2 3 4 5 四 计算题（每小题 6 分，共 36 分）1 解：22
6、byaxyxu,22ydxycxv3分yxvuydxayx22xyvudycxbyax225 分解得:1,2cbda6分2 解：被积函数在圆周的2z内部只有一阶极点 z=0 及二阶极点 z=1 2分2)1(25)(Re020zzzzzfs文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E
7、9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8
8、E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ
9、8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:C
10、Z8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:
11、CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码
12、:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编
13、码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10-3-_2225)(Re1211zzzzzzzfs分522)1(25zdzzzz=2i(-2+2)=0 6分3 解：11zzzf=nnnzzz12112111112104 分（1z2）6分4 解:被积函数为偶函数在上半z 平面有两个一阶极点 i,2i 1 分 I=dxxxx)4)(1(212222 分 =)(Re)(Re2212zsfzfsiiziz3 分=izizizzzzizzi22222)2)(1()4)(5 分 =66 分
14、5 解：)(1)(izizzf1 分 =iziiz211)(123 分 =02)()2()1()(1nnnniziiziz26 分6 解:w=L(i)=kiziz2分2)(2izikw3 分0)(iLwik4 分iziziw6 分五 证明题（每小题 7 分，共 14 分）1 证明:设)(:0DkRzzk)(zf在0z解析由泰勒定理000)()(!)()(nnnzznzfzf)(Dkz2 分由题设0)(0)(zfn)()(0zfzf，)(Dkz4 分由唯一性定理)()(0zfzf)(Dz7 分2 证明：令nzzf5)(，1)(zez2分 (1）zf及z在1z解析(2）1z上，55nzzf1111
15、eeeezzzz54分故在1z上zzf，由儒歇定理在1z内nzzfNzzzfN)1,()1,(7 分一、填空题（每小题2 分）1、323sin3cos5sin5cosii的指数形式是2、ii=3、若 0r1，则积分rzdzz1ln4、若v是u的共轭调和函数，那么v的共轭调和函数是文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1
16、ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1
17、 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A
18、1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4
19、A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P
20、4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10
21、P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z1
22、0P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10-4-_5、设0z为函数)(zf=33sin zz的 m阶零点，则 m=6、设az为函数zf的 n 阶极点，那么zfzfsazRe=7、幂级数0!nnnz的收敛半径 R=8、0z是函数zz1sin5的奇点9、方程01237zz的根全在圆环内10、将点,i,0分别变成 0,i,的分式线性变换w二、单选题（每小题2 分）1、若函数zf在区域 D内解析，则函数zf在区域 D内（）A在有限个点可导
23、 B存在任意阶导数C 在无穷多个点可导 D存在有限个点不可导2、使22zz成立的复数是（）A 不存在 B 唯一的 C 纯虚数 D实数3、22)1(coszdzzz（）A i sin1 B i sin1 C 2 i sin1 D 2i sin14、根式3i的值之一是（）A 223i B 223i C i Di5、z是zzsin的（）A 可去奇点 B 一阶极点 C 一阶零点 D 本质奇点6、函数411zzzzf，在以0z为中心的圆环内的洛朗展式有 m 个，则 m=()A 1 B 2 C 3 D 4 7、下列函数是解析函数的为（）A xyiyx222B xyix2C)2()1(222xxyiyxD
24、33iyx8、在下列函数中，0Re0zfsz的是（）A 21zezfz B zzzzf1sinC zzzzfcossin D zezfz1119、设 ai，C：iz=1，则dziazzC2cos（）A 0 B e2i C 2ie D icosi 10、将单位圆1z共形映射成单位圆外部1w的分式线性变换是（）A)1(1azaazewi B)1(1azaazewiC)1(aazazewi D)1(aazazewi三、判断题（每小题2 分）1、（）幂级数0nnz在 z 1 内一致收敛2、（）z=是函数2cos1zz的可去奇点3、（）在柯西积分公式中，如果Da，即 a 在D之外，其它条件不变，则积分d
25、zazzfiC210，Dz满分10 得分文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T
26、5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10
27、T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP1
28、0T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP
29、10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 H
30、P10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4
31、HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10-5-_4、（）函数zfzctg
32、e1在0z的去心邻域内可展成洛朗级数5、（）解析函数的零点是孤立的四、计算题（每小题6 分）1、计算积分Cdzixyx2，C：i1+i 的直线段2、求函数211 zzzzf在所有孤立奇点（包括）处的留数3、将函数izizzf11在iz的去心邻域内展成洛朗级数,并指出收敛域4、计算积分Czzdz122,C:1222yyx，5、计算实积分 I=20cosad)1(a6、求将单位圆1z共形映射成单位圆1w的分式线性变换zLw使符合条件021L，11L五、证明题（每小题7 分）1、设函数zf在区域 D 内解析，证明：函数zfi也在 D 内解析2、证明：在0z解析，且满足的nnf21121，nnf212
33、1（2,1n）的函数zf不存在一填空题（每小题2 分，视答题情况可酌情给1 分，共 20 分）1 19ie，2 ke22(k=0,)，3 0，4 u，5 9 6 n，7，8 本质，9 21z，10 z1二 单选题（每小题 2 分，共 20 分）1 B 2 D 3 C 4 D 5 A 6 C 7 C 8 D 9 A 10 A 三 判断题（每小题 2 分，共 10 分）1 2 3 4 5 四 计算题（每小题 6 分，共 36 分）1 解：C 的参数方程为：z=i+t,01t dz=dt 3分Cdzixyx21021dtitt=321i6分2 解:1z为zf一阶极点1分1z为zf二阶极点2分411R
34、e11zzzzzfs3分411Re121zzzzzfs5分0Rezfsz6 分3 解：izizzf11=iiziiz2112112分 =10211nnnniiziz5 分（0iz0，则 z0是)(zf的_零点.6.函数 ez的周期为 _.7.方程083235zzz在单位圆内的零点个数为 _.8.设211)(zzf，则)(zf的孤立奇点有 _.9.函数|)(zzf的不解析点之集为 _.10._)1,1(Res4zz.三.计算题.(40 分)1.求函数)2sin(3z的幂级数展开式.2.在复平面上取上半虚轴作割线.试在所得的区域内取定函数z在正实轴取正实值的一个解析分支，并求它在上半虚轴左沿的点及
35、右沿的点iz处的值.3.计算积分：iizzId|，积分路径为（1）单位圆（1|z）的右半圆.文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M
36、5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1
37、M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S
38、1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7
39、S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A
40、7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9
41、A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ
42、9A7S1M5D10-8-_4.求dzzzz22)2(sin.四.证明题.(20 分)1.设函数 f(z)在区域 D 内解析，试证：f(z)在 D 内为常数的充要条件是)(zf在 D 内解析.2.试用儒歇定理证明代数基本定理.复变函数考试试题（三）二.填空题.(20分)1.设11)(2zzf，则 f(z)的定义域为 _.2.函数 ez的周期为 _.3.若nnninnz)11(12，则nznlim_.4.zz22cossin_.5.1|00)(zznzzdz_.（n为自然数）6.幂级数0nnnx的收敛半径为 _.7.设11)(2zzf，则 f(z)的孤立奇点有 _.8.设1ze，则_z.9.若0
43、z是)(zf的极点，则_)(lim0zfzz.10._)0,(Resnzze.三.计算题.(40分)1.将函数12()zf zz e在圆环域 0z内展为 Laurent 级数.2.试求幂级数nnnznn!的收敛半径.3.算下列积分：Czzzze)9(d22，其中C是1|z.4.求0282269zzzz在|z|1 内根的个数.四.证明题.(20分)1.函数)(zf在区域D内解析.证明：如果|)(|zf在D内为常数，那么它在D内为常数.2.设)(zf是一整函数，并且假定存在着一个正整数n，以及两个正数 R及 M，使得当Rz|时nzMzf|)(|，证明)(zf是一个至多n次的多项式或一常数。复变函数
44、考试试题（四）二.填空题.(20 分)1.设iz11，则_Im_,Rezz.2.若nnzlim，则nzzznn.lim21_.3.函数 ez的周期为 _.4.函数211)(zzf的幂级数展开式为 _ 5.若函数 f(z)在复平面上处处解析，则称它是_.6.若函数f(z)在区域D 内除去有限个极点之外处处解析，则称它是D 内的_.文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:C
45、Z8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:
46、CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码
47、:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编
48、码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档
49、编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文
50、档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10文档编码:CZ8E9M3H4T4 HP10T5Z10P4A1 ZZ9A7S1M5D10