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1、專業(yè)好文檔 中國(guó)海洋大學(xué) 2008-2009學(xué)年 第一學(xué)期 期末考試試卷 學(xué)院《常微分方程》課程試題(A卷) 優(yōu)選專業(yè)年級(jí) 信息與計(jì)算科學(xué) 06級(jí) 學(xué)號(hào) 姓名 　 授課教師 高存臣 座號(hào) ----------------裝----------------訂----------------線---------------- 共 ３ 頁(yè) 第 1 頁(yè) 考試說(shuō)明：本課程為閉卷考試，可攜帶 計(jì)算器、圓規(guī)、直尺、半圓儀 文具，滿分為：

2、100分。 題號(hào) 一 二 三 四 五 總分 得分 一、選擇題（本題共10分） 1、微分方程的( )稱之為微分方程的積分曲線． (A)斜率； (B)解曲線； (C) 的微分； (D) (A)(B)(C)都不對(duì)． 2、方程有只與有關(guān)的積分因子的充要條件為下面哪一個(gè)( )． (A) ； (B) ； (C) ； (D). 3、對(duì)于一階微分方程，=，．作皮卡序列 , 決定一致收斂的條件是( ) (A) 在R上連續(xù)； (B)在R上關(guān)于y滿足李普希

3、茨條件； (C)在R上關(guān)于x滿足李普希茨條件；(D)在R上關(guān)于y連續(xù)． 4、方程的通解為（ ）. （A）； （B）； （C）；　(D). 5、給定常系數(shù)線性微分方程組，如果A的特征值的實(shí)部都是負(fù)的，則它的任一解當(dāng)時(shí)，都趨于（ ）． (A) 零；　　 (B) 一個(gè)固定的常數(shù)； (C) 無(wú)窮大； 　(D)　保持有界．　 二、判斷題（本題共10分） 1、形式為的方程稱為n階常微分方程．( ) 2、方程可化為變量分離方程．( ) 3、若函數(shù)在區(qū)間，上關(guān)偏導(dǎo)數(shù)連續(xù)，則在R上必關(guān)于滿足李普希茨條

4、件.( ) 4、若函數(shù)在區(qū)間上線性相關(guān)，則在上它們的伏朗斯基行列式恒等于零．（　　　?。? 5、方程組一定存在個(gè)線性無(wú)關(guān)的解．( ) 三、填空題（本題共10分） 1、如果函數(shù)代入方程后，能使它變?yōu)楹愕仁? )，則稱( )為方程的解． 2、形如( )的方程稱為齊次方程，其中（ ）函數(shù)． 3、方程的解的存在且唯一的區(qū)域?yàn)椋? ）. 4、方程的通解為（　　　　　　　　　　　　　?。? 5、的（　　　　　　　　?。┓Q為的一個(gè)基本解組.

5、　顯然，具有（　　　　　　?。﹤€(gè)不同的基本解組． 四、簡(jiǎn)答題（本題共40分） 1、求方程的積分因子，并求解方程． 2、已知在上連續(xù)，且關(guān)于y滿足李普希茲條件．又　　　 當(dāng)時(shí)連續(xù)．求證：在上一致收斂． 3、求方程的通解. 4、設(shè)是方程的個(gè)線性無(wú)關(guān)解，其中，，求證方程組的任何解恒可表示成 ① 其中是常數(shù)，且滿足關(guān)系式 ② 反之，滿足②式的函數(shù)①也必是方程組的解． 五、綜合題（本題共30分） 1．火車沿水平的道路運(yùn)動(dòng)，火車的重量是，機(jī)車的牽引力是F，運(yùn)

6、動(dòng)時(shí)的阻力，其中是常數(shù)，而是火車的速度；s是走過(guò)的路程．試確定火車的運(yùn)動(dòng)規(guī)律，設(shè)時(shí)，，． 2. 求方程組的解，其中， ，． 授課教師命題教師或命題負(fù)責(zé)人簽字 年 月 日 院系負(fù)責(zé)人簽字 年 月 日 共 ３ 頁(yè) 第 ３ 頁(yè) "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 We

7、bb - 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 congr

8、ess 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 be

9、tter 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 tas

10、kforce, 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 spea

11、k 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 actio

12、ns. 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 import

13、ant 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 weathe

14、r 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 turbu

15、lence. 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. St

16、ill, 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 -- 690 mph (1,110 kph) -- in less than 40 secon

17、ds. 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

18、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 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