2014年电大复变函数试题及答案小抄参考.doc

专业好文档复变函数课程试卷一、 单项选择题（每题2分，共20分）1 以下命题正确的是a b零的辐角为零 c d对任意复数有 a 2若，则a bc d d 3设在区域内解析，则a b c d b 4下列说法正确的是a如果存在，则在处解析 b如果和在区域内可微，则在区域内解析c如果在区域内处处可导，则在区域内解析 d如果在区域内解析，则在区域内一定不解析 c 5下列等式中不正确的是a （为整数） bc （为整数） d b 6设在复平面内处处解析（其中为常数），则a b c d c 7设为单位圆周，则积分的值为a bc d d 8级数的收敛圆为a bc d a 9是函数的a一级零点 b二级零点c三级零点 d四级零点 c 10设则a bc d d 二、填空题（每空2分，共10分）11 12设为包围的任一简单闭曲线，为整数，则 或013的主值等于 14函数在处的主要部分为 ，在处的主要部分为 0二、 解答题15讨论函数在原点的连续性与可导性。解：令，则因在处连续，故在处连续。又，故在处不可导。16设在区域内解析，且。试证在内必为常数。证：因在内解析，故已知等式两边分别对求偏导，并用上式得：同理可得，故均为常数，进一步有在内必为常数。17计算积分，其中为不过和的任一简单闭曲线。解：均在的外部，在所围的闭区域上解析，故在内部，在外部，由高阶导数公式，其中充分小。在外部，在内部，则均在的内部，由多连通区域上的复合闭路定理得18（1）将函数在圆环内展为laurent级数。解：或（2）求出函数的奇点并判别它们的类型（包含无穷远点）。所以为的可去奇点（不含负幂项），为的的本性奇点（含无穷多正幂项）。19利用留数计算实积分解：故20设区域内一条正向简单闭曲线，为内一点，如果在内解析，且，在内无其它零点，试证：证：因以为一级极点，故，在解析，故if we dont do that it will go on and go on. we have to stop it; we need the courage to 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 media.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 visiting 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 webb, 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 he 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 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 plays 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-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 lot 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, 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 hitting 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. 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