电大《复变函数》作业参考答案

1、专业好文档复变函数作业参考答案一判断题1.对； 2对；3对；4对； 5对； 6对； 7对； 8对； 9对； 10错； 11对； 12对13对14对；15对； 16对；17错；18对；19错；20对；21对； 22错； 23对；24错。25、错 26、对 27、错 28、错 29、对 30、对 31、对 32、错 33、对 34、对 35、对 36、对 37、对 38、对二填空题1；2；3；4； 5整函数； 6亚纯函数。7. ； 8191； 1011；12；13； 14 15160；17、实部，虚部。18.内点集合，边界点集合是。19.解析区域是，20.模：，幅角：21.收敛区域是：，和函数是：

2、。22.是函数的 可去 极点，而在处有 1 阶极点。23.0，024.三计算题12求。31个。4 5。61个。7， 89；101112；13；14. ； 15.16.因为孤立奇点是可去奇点，所以留数等于 0。17. 先将保形变为上半单位圆，再变为第一象限，最后变为上半平面：，所以1819求。201个。21.先将平移的保形变为带形区域：，再将保形变为带形区域：最后利用指数函数保形变为上半平面，所以四证明题1若函数f(z)在z0处可导，则f(z)在z0连续。证明：直接利用定义。2若数列收敛，则与都收敛。证明：利用不等式:即可。3若整函数f(z)将复平面映照为单位圆内部且，则。证明：由于整函数f(z

3、)将复平面映照为单位圆内部且，则整函数f(z)是一个有界整函数，由刘维尔定理知道，。4证明方程在内仅有3个根。证明：在上，由得，在单位圆内只有一个根，在利用在上，由得，在有4个根，所以方程在内仅有3个根。5. 证明：由于等于常数，而函数在区域内解析，所以实部是可微的，并且有 再利用柯西-黎曼条件，得从而其虚部也是常数，故函数恒等于常数。6. 证明：由于等于常数，而函数在区域内解析，所以虚部是可微的，并且有 再利用柯西-黎曼条件，得从而其实部也是常数，故函数恒等于常数。if we dont do that it will go on and go on. we have to stop it;

4、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 ivori

5、an 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 footba

6、ll 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

7、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

8、.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

9、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 a

10、s 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 tropos

11、phere) 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 tropo

12、pause),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, bu

13、t 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 t

14、han 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 te

15、am 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 at mach