电大《常微分方程》课程试题(A卷)小抄参考

1、专业好文档中国海洋大学 2008-2009学年 第一学期 期末考试试卷 学院常微分方程课程试题(a卷)优选专业年级 信息与计算科学 06级 学号 姓名 授课教师 高存臣 座号 -装-订-线- 共 页 第 1 页考试说明：本课程为闭卷考试，可携带 计算器、圆规、直尺、半圆仪 文具，满分为：100分。 题号一二三四五总分得分一、选择题（本题共10分） 1、微分方程的( )称之为微分方程的积分曲线(a)斜率； (b)解曲线；(c) 的微分； (d) (a)(b)(c)都不对 2、方程有只与有关的积分因子的充要条件为下面哪一个( )(a) ； (b) ； (c) ； (d). 3、对于一阶微分方程，=

2、，作皮卡序列,决定一致收敛的条件是( )(a) 在r上连续； (b)在r上关于y满足李普希茨条件；(c)在r上关于x满足李普希茨条件；(d)在r上关于y连续 4、方程的通解为（ ）.（a）； （b）；（c）；(d). 5、给定常系数线性微分方程组，如果a的特征值的实部都是负的，则它的任一解当时，都趋于（ ）(a) 零； (b) 一个固定的常数； (c) 无穷大； (d)保持有界二、判断题（本题共10分） 1、形式为的方程称为n阶常微分方程( ) 2、方程可化为变量分离方程( ) 3、若函数在区间，上关偏导数连续，则在r上必关于满足李普希茨条件.( ) 4、若函数在区间上线性相关，则在上它们的伏

3、朗斯基行列式恒等于零（） 5、方程组一定存在个线性无关的解( )三、填空题（本题共10分） 1、如果函数代入方程后，能使它变为恒等式( )，则称( )为方程的解 2、形如( )的方程称为齐次方程，其中（ ）函数 3、方程的解的存在且唯一的区域为（ ）. 4、方程的通解为（） 5、的（）称为的一个基本解组.显然，具有（）个不同的基本解组四、简答题（本题共40分） 1、求方程的积分因子，并求解方程 2、已知在上连续，且关于y满足李普希兹条件又当时连续求证：在上一致收敛 3、求方程的通解. 4、设是方程的个线性无关解，其中，求证方程组的任何解恒可表示成 其中是常数，且满足关系式 反之，满足式的函数也

4、必是方程组的解五、综合题（本题共30分） 1火车沿水平的道路运动，火车的重量是，机车的牵引力是f，运动时的阻力，其中是常数，而是火车的速度；s是走过的路程试确定火车的运动规律，设时， 2. 求方程组的解，其中，授课教师命题教师或命题负责人签字 年 月 日院系负责人签字年 月 日共 页 第 页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 web

5、b - 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

6、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 r

7、acism 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

8、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

9、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 disapp

10、ointed 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, condi

11、tions 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 ever

12、est (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

13、 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 lik

14、e 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

15、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