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1、專業(yè)好文檔 《復(fù)變函數(shù)》作業(yè)參考答案 一．判斷題 1.對； 2．對；3．對；；4．對； 5．對； 6．對； 7．對； 8．對； 9．對； 10錯； 11．對； 12．對 13．對14．對；15．對； 16．對；17．錯；18．對；19．錯；20．對；21．對； 22．錯； 23．對；24．錯。 25、錯 26、對 27、錯 28、錯 29、對 30、對 31、對 32、錯 33、對 34、對 35、對 36、對 37、對 38、對 二．填空題 1．； 2．； 3．； 4．； 5．整函數(shù)； 6．亞純函數(shù)。 7. ； 8．1 9．1；

2、 10． 11．； 12．； 13．； 14． 15． 16．0； 17、實部，虛部。 18.內(nèi)點集合，邊界點集合是。 19.解析區(qū)域是， 20.模：，幅角： 21.收斂區(qū)域是：，和函數(shù)是：。 22.是函數(shù)的 可去 極點，而在處有 1 階極點。 23.0，0． 24. 三．計算題 1． 2．求。 3．1個。 4． 5．。 6．1個。 7．， 8． 9．； 10． 11． 12．； 13．； 14. ； 15. 16.因為孤立奇點是可去奇點，所以留數(shù)等于 0。 17. 先將保形變?yōu)樯习雴挝粓A，再

3、變?yōu)榈谝幌笙?，最后變?yōu)樯习肫矫妫? ， ， ， 所以 18． 19．求。 20．1個。 21.先將平移的保形變?yōu)閹螀^(qū)域：， 再將保形變?yōu)閹螀^(qū)域： 最后利用指數(shù)函數(shù)保形變?yōu)樯习肫矫妫? 四．證明題 1．若函數(shù)f(z)在z0處可導(dǎo)，則f(z)在z0連續(xù)。 證明：直接利用定義。 2．若數(shù)列收斂，則與都收斂。 證明：利用不等式: 即可。 3．若整函數(shù)f(z)將復(fù)平面映照為單位圓內(nèi)部且，則。 證明：由于整函數(shù)f(z)將復(fù)平面映照為單位圓內(nèi)部且，則整函數(shù)f(z)是一個有界整函數(shù)，由劉維爾定理知道，。 4．證明方程在內(nèi)僅有3個根。 證明：在上，由得

4、，在單位圓內(nèi)只有一個根，在利用在上，由得，在有4個根，所以方程在內(nèi)僅有3個根。 5. 證明：由于等于常數(shù)，而函數(shù)在區(qū)域內(nèi)解析，所以實部是可微的，并且有 再利用柯西-黎曼條件，得 從而其虛部也是常數(shù)，故函數(shù)恒等于常數(shù)。 6. 證明：由于等于常數(shù)，而函數(shù)在區(qū)域內(nèi)解析，所以虛部是可微的，并且有 再利用柯西-黎曼條件，得 從而其實部也是常數(shù)，故函數(shù)恒等于常數(shù)。 "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

5、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, 7

6、7, 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 tea

7、m. 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 Island

8、s-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

9、 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

10、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

11、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 atmospher

12、e (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 (cal

13、led 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

14、 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 jump When he jumps, he is expected to reach the speed of sound

15、-- 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 ca

16、n 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 reser

17、ve parachute that will open automatically if he loses consciousness at mach speeds. Even if everything goes as planned, it wont. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters). cause there 第 6 頁 共 6 頁