1、專業(yè)好文檔復(fù)變函數(shù)課程試卷一、 單項(xiàng)選擇題（每題2分，共20分）1 以下命題正確的是a b零的輻角為零 c d對(duì)任意復(fù)數(shù)有 a 2若，則a bc d d 3設(shè)在區(qū)域內(nèi)解析，則a b c d b 4下列說法正確的是a如果存在，則在處解析 b如果和在區(qū)域內(nèi)可微，則在區(qū)域內(nèi)解析c如果在區(qū)域內(nèi)處處可導(dǎo)，則在區(qū)域內(nèi)解析 d如果在區(qū)域內(nèi)解析，則在區(qū)域內(nèi)一定不解析 c 5下列等式中不正確的是a （為整數(shù)） bc （為整數(shù)） d b 6設(shè)在復(fù)平面內(nèi)處處解析（其中為常數(shù)），則a b c d c 7設(shè)為單位圓周，則積分的值為a bc d d 8級(jí)數(shù)的收斂圓為a bc d a 9是函數(shù)的a一級(jí)零點(diǎn) b二級(jí)零點(diǎn)c三級(jí)

2、零點(diǎn) d四級(jí)零點(diǎn) c 10設(shè)則a bc d d 二、填空題（每空2分，共10分）11 12設(shè)為包圍的任一簡單閉曲線，為整數(shù)，則 或013的主值等于 14函數(shù)在處的主要部分為 ，在處的主要部分為 0二、 解答題15討論函數(shù)在原點(diǎn)的連續(xù)性與可導(dǎo)性。解：令，則因在處連續(xù)，故在處連續(xù)。又，故在處不可導(dǎo)。16設(shè)在區(qū)域內(nèi)解析，且。試證在內(nèi)必為常數(shù)。證：因在內(nèi)解析，故已知等式兩邊分別對(duì)求偏導(dǎo)，并用上式得：同理可得，故均為常數(shù)，進(jìn)一步有在內(nèi)必為常數(shù)。17計(jì)算積分，其中為不過和的任一簡單閉曲線。解：均在的外部，在所圍的閉區(qū)域上解析，故在內(nèi)部，在外部，由高階導(dǎo)數(shù)公式，其中充分小。在外部，在內(nèi)部，則均在的內(nèi)部，由多

3、連通區(qū)域上的復(fù)合閉路定理得18（1）將函數(shù)在圓環(huán)內(nèi)展為laurent級(jí)數(shù)。解：或（2）求出函數(shù)的奇點(diǎn)并判別它們的類型（包含無窮遠(yuǎn)點(diǎn)）。所以為的可去奇點(diǎn)（不含負(fù)冪項(xiàng)），為的的本性奇點(diǎn)（含無窮多正冪項(xiàng)）。19利用留數(shù)計(jì)算實(shí)積分解：故20設(shè)區(qū)域內(nèi)一條正向簡單閉曲線，為內(nèi)一點(diǎn)，如果在內(nèi)解析，且，在內(nèi)無其它零點(diǎn)，試證：證：因以為一級(jí)極點(diǎn)，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

4、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

5、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 s

6、omething 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 taskfo

7、rce, 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 f

8、irst 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

9、 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. sta

10、rting 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

11、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

12、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 di

13、stance, 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

14、 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