电大数学与应用数学复变函数练习小抄参考

1、 一、单项选择题 1.设，则可用表示为（）(a) (b) (c) (d) 2.若，则上半平面可表示为（）(a) (b) (c) (d) 3.（）(a)(b) (c) (d) 4.函数在复平面上可表示为（）(a) (b) (c) (d) 5.设，则为的（）(a) 一级零点 (b) 二级零点(c) 三级零点 (d) 四级零点 二、填空题 1.设为实数，称形如的为复数 2.设，则称 为指数函数，其中“”为自然对数的底 3.若存在某个，使得 ，则称点为函数的解析点 4.函数在点展成罗朗级数，即在 内展成罗朗级数 5.若映射在区域内是 ，则称此映射为区域内的保形映射 三、计算题1.设，试求解析函数，使得

2、，且满足2.设，试将在点展成幂级数3.计算积分四、证明题试证：一、单项选择题 1.b 2.c 3.d 4.b 5.a二、填空题1. 有序数对2. 3. 在内处处可导4. 5. 单叶且保角的三、计算题 1.解：由cr条件有，所以 又因为，得，所以 所以由此得 由得，故 经验证 或即为所求 2. 解：在内可展成幂级数，有 ， 5. 解：积分路径即为，而被积函数共有两个奇点1与位于内部，所以 而 故 四、证明题证：令 于是 故 if we dont do that it will go on and go on. we have to stop it; we need the courage to

3、do it.his comments came hours after fifa vice-president jeffrey webb - also in london for the fas celebrations - said he wanted to meet ivory coast international toure to discuss his complaint.cska general director roman babaev says the matter has been exaggerated by the ivorian and the british medi

4、a.blatter, 77, said: it has been decided by the fifa congress that it is a nonsense for racism to be dealt with with fines. you can always find money from somebody to pay them.it is a nonsense to have matches played without spectators because it is against the spirit of football and against the visi

5、ting team. it is all nonsense.we can do something better to fight racism and discrimination.this is one of the villains we have today in our game. but it is only with harsh sanctions that racism and discrimination can be washed out of football.the (lack of) air up there watch mcayman islands-based w

6、ebb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how h

7、e felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation

8、 into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska.baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather pla

9、ys an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to

10、-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a l

11、ot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.below, the earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. still,

12、hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. it will be like he is diving into the shallow end.skydiver preps for the big jumpwhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. like hi

13、tting the top of the water, he will begin to slow as he approaches the more dense air closer to earth. but this will not be enough to stop him completely.if he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. his team hopes its not needed

14、. instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).in order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). he will have a reserve parachute that will open automatically if he loses consciousness at mach speed