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复变函数习题答案第3章习题详解.pdf

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1、精品文档学习交流第三章习题详解1沿下列路线计算积分idzz302。1)自原点至i3的直线段；解：连接自原点至i3的直线段的参数方程为：tiz310tdtidz31031033233023313313itidttidzzi2)自原点沿实轴至3，再由3铅直向上至i3；解：连接自原点沿实轴至3的参数方程为：tz10tdtdz330330230233131tdttdzz连接自3铅直向上至i3的参数方程为：itz310tidtdz331031023323313313313iitidtitdzzi33331023023023313313313313iiidtitdttdzzi3)自原点沿虚轴至i，再由i沿

2、水平方向向右至i3。解：连接自原点沿虚轴至i的参数方程为：itz10tidtdz3103102023131iitidtitdzzi连接自i沿水平方向向右至i3的参数方程为：itz10tdtdz33103102323113131iiitdtitdzzii333332023021313113131iiiidzzdzzdzziiii2分别沿xy与2xy算出积分idziyx102的值。解：xyixxiyx22dxidz1-第 1 页，共 16 页精品p d f 资料可编辑资料-精品文档学习交流iixixidxixxidziyxi2131121311110231021022xy22221xiixxiy

3、xdxxidz2110104321022131142311211iixixidxxixidziyxi而iiiii656121213131213113设zf在单连通域B内处处解析，C为B内任何一条正向简单闭曲线。问0CdzzfRe，0CdzzfIm是否成立？如果成立，给出证明；如果不成立，举例说明。解：不成立。例如：zzf，iezC：，0iiddzzfCsincoscosRe20sincossinImiddzzfC204利用在单位圆上zz1的性质，及柯西积分公式说明idzzC2，其中C为正向单位圆周1z。解：011zzzifdzzdzzCC202015计算积分Cdzzz的值，其中C为正向圆周：1

4、)2z；解：在2z上，iez2iiidededzzziiC4222222020202)4z-第 2 页，共 16 页精品p d f 资料可编辑资料-文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:

5、CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8

6、R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 Z

7、R8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10

8、N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10

9、 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R

10、9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文

11、档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10精品文档学习交流解：在4z上，iez4iiidededzzziiC8444442020206试用观察法得出下列积分的值，并说明观察时所依据的是什么？C是正向的圆周1z。1)Czdz2解：21zzf在C内解析，根据柯西古萨定理，02Czdz2)Czzdz422解：2221421zzzzf在C内解析，根据柯西古萨定理，0422Czzdz3)Czdzcos解：zzfcos1在C内解析，根据柯西古萨定理，0Czd

12、zcos4)Czdz21解：1zf在C内解析，210z在C内，iifzdzC2212215)Czdzze解：zzezf在C内解析，根据柯西古萨定理，0Czdzze6)Czizdz22解：21zzf在C内解析，20iz在C内，22122222iiiifzizdzC-第 3 页，共 16 页精品p d f 资料可编辑资料-文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX

13、5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R1

14、0文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8

15、I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3

16、B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 H

17、O10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V

18、5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编

19、码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10精品文档学习交流7沿指定曲线的正向计算下列各积分：1)Czdzze2，C：12z解：2z在C内，zezf在C解析，根据柯西积分公式：222iedzzeCz2)Cazdz22，C：aaz解：az在C内，azzf1在C解析，根据柯西积分公式：

20、idzazazazdzCC222213)Cizdzze12，C：232iz解：iz在C内，izezfiz在C解析，根据柯西积分公式：CizCizedzizizedzze124)Cdzzz3，C：2z解：3z不在C内，3zzzf在C解析，根据柯西古萨定理：03Cdzzz5)Czzdz1132，C：1rz解：11132zzzf在C解析，根据柯西古萨定理：01132Czzdz6)Czdzz cos3，C：为包围0z的闭曲线解：zzzfcos3在C解析，根据柯西古萨定理：03Czdzz cos7)Czzdz4122，C：23z-第 4 页，共 16 页精品p d f 资料可编辑资料-

21、文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I

22、9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B

23、5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO

24、10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5

25、Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码

26、:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O

27、8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8

28、ZR8I9Z1O8R10精品文档学习交流解：iz在C内，412zizzf在C解析，根据柯西积分公式：Czzdz41228)Cdzzzsin，C：1z解：0z在C内，zzfsin在C解析，根据柯西积分公式：002sinsinidzzzC9)Cdzzz22sin，C：2z解：2z在C内，zzfsin在C解析，根据高阶导数公式：02222sinsinidzzzC10)Czdzze5，C：1z解：0z在C内，zezf在C解析，根据高阶导数公式：!4204245ifidzzeCz8计算下列各题：1)iizdze32解：02121263232iiiiziiz

29、eeedze2)063izdzch；解：3203133130606iishzshzdzchii-第 5 页，共 16 页精品p d f 资料可编辑资料-文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编

30、码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1

31、O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8

32、 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I

33、10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W

34、10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX

35、5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R1

36、0文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10精品文档学习交流3)iizdz2sin；解：222412212212shiizidzzzdziiiiiisincossin4)10zdzzsin；解：1010101011sincoscoscoscossinzdzzzzzdzdzz5)izdzeiz0；解：iiiizizizizieeeidzeeizdeizdzeiz100006)idzztgz121cos（沿1到i的直线段）。解：12112121112212112tg

37、tgitgtgiztgtgzdtgztgzdzztgziiicos9计算下列积分：1)Cdzizz2314，（其中C：4z为正向）；解：iidzizdzzdzizzCCC14342231423142)Cdzzi122，（其中C：61z为正向）；解：0222222122izizCCCCiziiziidzizizidzizizidzizizidzzi3)213CCCdzzzcos，（其中1C：2z为正向，2C：3z为负向）；解：3zzzfcos在所给区域是解析的，根据复合闭路定理：0213CCCdzzzcos4)Cizdz，C：1z（其中C为以21，i56为顶点的正向菱形）；解：在所给区域内，iz

38、zf1有一孤立奇点，由柯西积分公式：iizdzC2-第 6 页，共 16 页精品p d f 资料可编辑资料-文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10

39、N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10

40、 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R

41、9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文

42、档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9

43、Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5

44、R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO1

45、0I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10精品文档学习交流5)Czdzaze3，（其中a为1a的任何复数，C：1z为正向）。解：当az，3azezfz在所给区域内解析，根据柯西古萨基本定理：03Czdzaze当az，zezf在所给区域内解析，根据高阶导数公式：ieeidzazeaaCz!22310证明：当C为任何不通过原点的简单闭曲线时，012Cdzz。证明：当C所围成的区域不含原点时，根据柯西古萨基本定理：012Cdzz；当C所围成的区域含原点时，根据

46、高阶导数公式：00212ifdzzC；11下列两个积分的值是否相等？积分2)的值能否利用闭路变形原理从 1)的值得到？为什么？1)2zdzzz2)4zdzzz解：1）0222202dieeedzzziiiz；2）0444204dieeedzzziiiz由此可见，1）和 2）的积分值相等。但2）的值不能利用闭路变形原理从 1）得到。因为zzzf在复平面上处处不解析。-第 7 页，共 16 页精品p d f 资料可编辑资料-文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z

47、1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R

48、8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10

49、I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6

50、W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:CX5R9V5Y6W10 HO10I10N3B5R8 ZR8I9Z1O8R10文档编码:C

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