《复变函数论》试题(B)
2. If a point is a pole of order of ,then is a zero of order of .( )
3. An entire function which maps the plane into the unite disk must be
a constant.( )
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2. Show that if , then is a polynomial of order .
3. Show that , where is the circle centered at with radius .
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评卷 Ⅰ. Cloze Tests( Points)
人 1. If ,then
.
2. If denotes the circle centered at positively oriented and is a positive
integer,then .
3. The radius of the power series is
5. If a function is continuous on the plane and 0 for every simple
closed contour , then is an entire function. ( )
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评卷 Ⅲ. Computations ( Points)
人 1. Find .
2. Find the value of .
3. Let ,find the Laurent expansion of on the annulus . 4. Given ,where ,find .
5. Given ,find .
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评卷 Ⅳ. Verifications ( Points)
人 1. Show that the function
.
9. The definition of is
.
10. Log=
.
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评卷 Ⅱ. True or False Questions ( Points)
人 1. If a function is differentiable at a point ,then it is
continuous at .( )
4. A function is differentiable at a point if and only if whose real and
imaginary parts are differentiable at and the Cauchy Riemann
conditions hold there.( )
.
4. The singular points of the function are
.
5. , where is a positive integer.
6.
.
7. The main argument and the modulus of the number are .
8. The square roots of 1+ are
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复变函数论(B)
题号 一 二 三 四 五 六 七 八 九 十 总分 分数
答卷注意事项: 1、学生必须用蓝色(或黑色)钢笔、圆珠笔或签字笔直接在试题卷上答题。 2、答卷前请将密封线内的项目填写清楚。 3、字迹要清楚、工整,不宜过大,以防试卷不够使用。 4、本卷共 4 大题,总分为100分。