2复变函数往年考试题

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1、一、选择题(每小题3分,共30分)请将答案填在下面表格内！题号12345678910答案1.=（）(A)是整数(B)是整数(C)是整数(D)是整数2.积分（）.（A）（B）（C）（D）3.有关初等函数的说法正确的是（）.（A）与都是复平面上的无界函数.(B)复指数函数是周期函数而复双曲正弦函数不是周期函数.(C)幂函数只有当为虚数时才是多值函数.(D）在复数范围内负数是没有对数的.4.下列说法不正确的是（）（A）在区域内可导当且仅当在区域内解析.（B）若在区域内解析,则区域内有任意阶导数.（C）若在点可导,则在点

2、解析.（D）若在点解析,则在点的某个邻域内解析.考生答题不得过此线··················密······························封························线···························院系专业　　　　年级班级　姓名学号··················装······························订························线···························第5页共5

3、页5.=（）（A）（B）（C）（D）6.（）(A)(B)(C)(D)7.级数的收敛半径（）(A)(B)(C)(D)8.是的().（A）可去奇点(B)极点(C)本性奇点(D)非孤立奇点9.下列说法正确的是()（A）若,则级数收敛.（B）函数在区域内满足柯西－黎曼方程是指在区域内.（C）若是函数的可去奇点,则.（D）若有限点是函数的可去奇点,则.10.级数（）（A）条件收敛（B）绝对收敛（C）发散（D）敛散性不确定二、计算题(每小题7分，共70分)1.判断函数的可导性与解析性2.设函数，求使为解析函数，并求其导数.考

4、生答题不得过此线··················密······························封························线···························院系专业　　　　年级班级　姓名学号··················装······························订························线···························第5页共5页3.将函数展开成的幂级数.4.设,(1)将在内展

5、开为洛朗级数.(2)将在内展开为洛朗级数.5.在扩充复平面上找出函数的孤立奇点并加以分类,若是极点指出其阶数.6.已知函数为调和函数,求函数，使得函数解析.考生答题不得过此线··················密······························封························线···························院系专业　　　　年级班级　姓名学号··················装······························订···

6、·····················线···························第5页共5页7.计算，其中是（1）从点到的直线段；（2）从点到的直线段，再从点到的直线段所连结成的折线段.8.计算积分,其中为正向圆周：.9.计算积分,其中为正向圆周：.10.计算积分,其中为正向圆周：.考生答题不得过此线··················密······························封························线························

7、···院系专业　　　　年级班级　姓名学号··················装······························订························线···························第5页共5页考生答题不得过此线··················密······························封························线···························院系专业　　　　年级班级　姓名学号···

8、···············装······························订························线···························第5页共5页