复变函数与积分变换试题A卷答案.doc

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1、复变函数与积分变换参考答案及评分标准一、单项选择题。（每小题3分，共15分）1、B2、D3、A4、B5、C二、填空题。（每小题3分，共15分）6、7、28、09、10、.三、计算下列积分。（本大题共4小题，每小题6分，共18分）11、设C为正向圆周，计算积分.解：····································（4分）·····················································（6分）12、设C为正向圆周，计算积分.解：由于有两个一级极点1,-1，而这两个极点都在内所以·············

2、···················（2分）由规则I，得因此，················（6分）13、利用留数计算积分和.解：由于函数在上半平面内只有一个极点···························（1分）故··························（3分）················································································（5分）所以，，·······················（6分）四、解答题。（本大题共3小题，每题6分，共18分）

3、14、已知调和函数，求解析函数使.解：由C-R条件，有，················（1分）则·····························（3分）∴·························（5分）又∵∴故································（6分）15、求函数f(z)=的全部孤立奇点.若为极点，则指出其级数.解：及方程的根，均为函数的奇点··········（3分）又为的一级零点，且当时。这样为函数的三级零点。····································（5分）故为三级极点，为一级

4、极点。·················（6分）16、设C为正向圆周，()，求.解：··············（3分）··························（5分）······························（6分）五、(本大题12分)17、将在圆环域（1）；（2）内展开成洛朗级数.解：当时·················（3分）···························（6分）当时，····························（9分）···················（12分）六、（本大题共3小题，第

5、18、19题各7分，第20题8分，共22分）18、求函数的Laplace逆变换.解：···················（3分）故··········19、若F，利用Fourier变换的性质，求函数的Fourier变换.解：由线性性质及象函数的微分性质，有FFFF···································20、利用Laplace变换，求解微分积分方程：，.解：原方程可写为，·············两边取Laplace变换，，即，························从而方程的解为.·····················

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