北理工考博数值分析——试卷

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2014年北理工机车学院博士入学考试内容汇总

2014年北京理工大学机械学院博士入学考试内容回顾
一、英语
1、题型、四篇阅读理解，英译汉，汉译英，理解论述题、作文。

2、在网上能找到06、07、08三年的真题。

3、最后一篇阅读理解是08年的原题，词汇量很多，应该有1000多词。

4、英译汉和汉译英都是短文翻译。

5、理解论述题是阅读一篇英文短文，然后用英语写一篇短文（80个词），介绍文章内容以及自己的感悟。

6、作文给你一句话，写200多词的文章。

二、数学（《数值分析》）
1、教材是丁丽娟、程杞元编著的《数值计算方法》，2011年8月版，高等教育出版社。

2、全是大题，题很简单，但需要记很多公式。

3、印象较深的就是考了第四章矩阵特征值与特征向量的计算，推到证明题，较难；还有第七章Romberg求积公式，表7-3。

4、建议整本书都要复习到，不是很难，就是要记忆的内容较多。

三、专业课
1、动力学和汽车理论可以任选一门，其中汽车理论（余志生主编，第五版，机械工业出版社）。

2、题型：简答题、论述题（有的需要画图）、计算题。

3、简答题记不清楚了，论述题记得有个制动过程的分析，114页的
那个图；计算题两个，各20分，第一章的汽车行驶方程式，第六章的汽车平顺性，关于质量系统振动的计算题。

4、专业课注重实际问题的考察，考试内容与能在网上找到的前些年的原题差别很大。

《北京理工大学博士研究生入学考试》

《北京理工大学博士研究生入学考试》北京理工大学博士研究生入学考试英语模拟试题一PART ⅠReading ComprehensionDirections: In this part there are four passages for you to read. After each passage there are five questions, below each of whom there are four answers marked A, B, C and D. Choose the best answer and mark the corresponding letter with a pencil on the Machine-Scoring Answer Sheet with a single line through the center. Questions 1 to 5 are based on the following passage: Many people believe the glare from snow causes snow blindness. Yet, dark glasses or not they find themselves suffering from headaches and watering eyes, and even snowblindness, when exposed to several hours of "snow light".The United States Army has now determined that the glare from snow does not cause snow-blindness in troops in a snow-covered country. Rather, a man's eyes frequently find nothing to focus on in a broad expanse of a snow-covered area So his gaze continually shifts and jumps back and forth over the entire landscape in search of something to look at. Finding nothing, hour after hour, the eyes never stop searching and the eyeballs become sore and the eye muscle aches. Nature balances this annoyance by producing more and more liquid which covers the eyeballs. The liquid covers the eyeballs in increasing quantity until vision blurs. And the result is total, even though temporary, snowblindness.Experiments led the Army to a simple method of overcoming this problem. Scouts ahead of a main body of troops are trained to shake snow from evergreen bushes, creating a dotted line asthey cross completely snow-covered landscape. Even the scouts themselves throw lightweight, dark-colored objects ahead on which they too can focus. The men following can then see something. Their gaze is arrested. Their eyes focus on a bush and having found something to see, stop searching through the snow-blanketed landscape. By focusing their attention on one object at a time, the man can cross the snow without becoming hopelessly snowblind or lost. In this way the problem of crossinga solid white area is overcome.1. The eyeballs become sore and the eye muscles ache because______.A. tears cover the eyeballsB. the eyes are annoyed by blinding sunlightC. the eyes are annoyed by blinding snowD. there is nothing to focus on2. When the eyes are sore, tears are produced to______.A. clear the visionB. remedy snowblindnessC. ease the annoyanceD. loosen the muscles3. Snow-blindness may be avoided by______.A. concentration on the solid white areaB. providing the eyes with something to focus onC. searching for something to look at in snow-covered areasD. covering the eyeballs with liquid4. The first paragraph is mainly concerned with______.A. snow glare and snow blindnessB. the whiteness from snowC. headaches, watering eyes and snowb lindnessD. the need for dark glasses5. A suitable title for this passage would be______.A. Snowblindness and How to Overcome ItB. Nature' s Cure for SnowblindnessC. Soldiers in the SnowD. Snow VisionQuestions 6 to 10 are based on the following passage:There are great careers in which the increasing emphasis is on specialization. You find these careers in engineering, in production, in statistical work, and in teaching. But there is an increasing demand for people who are able to take in a great area at a glance, people who perhaps know too much about any one field. There is, in other words, a demand for people Who are capable of seeing the forest rather than the trees, of making generaljudgments. And these "generalists" are particularly needed for positions in administration, where it is their job to see that other people do the work, where they have to plan for other people, to organize other people' s work, to begin it and judge it.The specialist understands one field; his concern is with technique and tools. He is a "trained" man; and his educational background is properly technical or professional. The generalist-and especially the administrator-deals with people; his concern is with leadership, with planning, and with direction giving. He is an "educated" man; and the humanities are his strongest foundation.V ery rarely is a specialist capable of being an administrator. And very rarely is a good generalist also a good specialist in a particular field. Any organizations need them in different proportions. It is your task to find out, during your training period, into which of the two kinds of jobs you fit, and to plan your career accordingly.Your first job may turn out to be the right job for you-but this is a pure accident. Certainly you should not change jobs constantly or people will become suspicious of your ability to hold any job. At the same time you must not look upon the first job as the final job; it is primarily a training job, an opportunity to understand yourself and your fitness for being an employee.6. There is an increasing demand for______.A. all-round people in their own fieldsB. people whose job is to organize other people' s workC. generalists whose educational background is either technical or professionalD. specialists whose chief concern is to provide administrative guidance to others7. The specialist is______.A. a man whose job is to train other peopleB. a man who has been trained in more than one fieldC. a man who can see the forest rather that the treesD. a man whose concern is mainly with technical or professional matters8. The administrator is______.A. a "trained" man who is more a specialist than a generalistB. a man who sees the tress as well as the forestC. a man who is very strong in the humanitiesD. a man who is an "educated" specialist9. During your training period it is important______.A. to try to be a generalistB. to choose a profitable jobC. to find an organization which fits youD. to decide whether you are fit to be a specialist or a generalist10. A man's first job______.A. is never the right job for himB. should not be regarded as his final jobC. should not be changed or people will become suspicious of his ability to hold any jobD. is primarily an opportunity to fit himself for his final jobQuestions 11 to 15 are based on the following passage:The world's population continues to grow. There now are about 4 billion of us on earth. That could reach 6 billion by the end of the century and 11 billion in another 75 years. Experts long have been concerned about such growth Where will we find the food, water, jobs, houses, schools and health care for all these people?A major new study shows that the situation may be changing.A large and rapid drop in the world's birth rate has taken place during the past 10 years. Families generally are smaller now than they were a few years ago. It is happening in both developing and industrial nations,Researchers said they found a number of reasons for this. More men and women are waiting longer to get married and are using birth control devices and methods to prevent or delay pregnancy. More women are going to school or working at jobs away from their homes instead of having children. And more governments, especially in developing nations, now support family planning programs to reduce population growth. China is one of the nations that has made great progress in reducing its population growth.China has already cut its rate of population growth by about one half since 1970. China now urges each family to have no more than one child. And it hopes to reach zero populationgrowth, the number of births equaling the number of deaths, by the year 2000.Several nations in Europe already have fewer births than deaths. Experts said that these nations could face a serious shortage of workers in the future. And the persons who are working could face much higher taxes to help support the growing number of retired people.11. In Paragraph one, the sentence "Experts Dong have been concerned about such growth", the phrase "concerned about" is similar in meaning to______.A. worried aboutB. related toC. engaged inD. made a study of12. "Family planning programs" means______.A. birth control policy in a countryB. economic policy in a familyC. TV programs designed for a familyD. economic policy in a country13. The world's birth rate has dropped because______.A. people marry at a much later timeB. more birth control devices and methods have been usedC. women would rather go to study or work than have childrenD. all the above reasons are true14. By the year 2000, the number of births and the number of deaths in China will______.A. be greatly differentB. be equal to each otherC. drop a great dealD. become much larger15. Some time in the future, the people who are working in Europe would have to pay much higher taxes because______.A. more and more children will be bornB. fewer and fewer children will be bornC. they will be making a lot of moneyD. the number of retired people will become ever lingerQuestions 16 to 20 are based on the following passage:When I was walking down the street the other day, I happened to notice a small brown leather wallet lying on the sidewalk. I picked it up and opened it to see if I could find out the owner's name. There was nothing inside it except some change and an old photograph-a picture of a woman and a young gift about twelve years old, who looked like the woman's daughter. I put the photograph back and took the wallet to the police station, where I handed it to the desk sergeant. Before I left, the sergeant took down my name and address in case the owner might want to write and thank me.That evening I went to have dinner with my aunt and uncle. They had also invited a young woman so that there would be four people at the table. Her face was familiar. I was quite sure that we had not met before, but I couldn' t remember where I had seen her. In the course of conversation, however, the young woman happened to mention that she had lost her wallet that afternoon. All at once I realized where I had seen her. She was the young girl in the photograph, although she was now much older. She was very surprised, of course, when I was able to describe her wallet to her. Then I explained that I had recognized her from the photograph I had found in the wallet. My uncle insisted on going to the police station immediately to claim the wallet. As thepolice sergeant handed it over, he said that it was amazing that I had not only found the wallet, but also the person who had lost it.16. The wallet which the writer found______.A. was emptyB. had some money in itC. had a few coins and a photograph in itD. had an old photograph in it17. The writer opened the wallet because he wanted to ______ in it.A. find some moneyB. find some goldC. find the owner' s nameD. find the owner' s photograph18. The writer recognized the young woman because______.A. he had met her somewhere beforeB. she was the old woman in the photographC. she often had dinner with his aunt and uncleD. she looked like the young girl in the photograph19. The young woman told of her loss of the wallet______.A. at the beginning of the dinnerB. during the conversationC. as soon as she saw the writerD. after the dinner20. The story was amazing because______.A. the writer found both the wallet and its ownerB. the finder and the loser of the wallet were old friendsC. the finder and the loser of the wallet met at the police stationD. the woman knew the writer and his unclePART ⅡTranslationSection A: Translate the following short paragraphs into Chinese.21. Opinion polls are now beginning to show an unwilling general agreement that, whoever is to blame and whatever happens from now on, high unemployment is probably here to stay. This means we shall have to find ways of sharing the available employment widely.22. But we need to go further. We must ask some fundamental questions about the future work. Should we continue to treat employment as the norm? Should we not rather encourage many other ways for self respecting? Should we not create conditions in which many of us can work for ourselves, rather than for an employer? Should we not aim to revive the household and the neighborhood, as well as the factory and the office as centers of production and work?23. The industrial age has been the only period of human history in which most people's work has taken the form of jobs. The industrial age may now be coming to an end, and some of the changes in work patterns which it brought may have to be reversed. This seems a discouraging thought. But, in fact, it could offer the prospect of a better future for work. Universal employment, as its history shows has not meant economic freedom.24. Employment became widespread when the 17th and 18th centuries made many people dependent on paid work by depriving them of the use of the land, and thus of the means to provide a living for themselves. Then the factory system destroyed the cottage industries and removed work from people's homes. Later, as transport improved, first by rail andthen by road, people traveled longer distances to their places of employment until, eventually, many people's work lost all connection with their home lives and the places in which they lived.Section B :Translate the following paragraph into English.现在，成千上万的美国人沉湎于对身材苗条的追求之中。

北京理工大学2008级数值分析试题及答案

课程编号：12000044 北京理工大学2009-2010学年第二学期2008级计算机学院《数值分析》期末试卷A 卷班级学号姓名成绩注意：① 答题方式为闭卷。

② 可以使用计算器。

请将填空题和选择题的答案直接填在试卷上，计算题答在答题纸上。

一、填空题（每空2分，共30分）1. 设函数f (x )区间[a ，b]内有二阶连续导数，且f (a )f (b )<0, 当时，用双点弦截法产生的解序列收敛到方程f (x )=0的根。

2. n 个求积节点的插值型求积公式的代数精确度至少为______次，n 个求积节点的高斯求积公式的代数精度为。

3. 已知a =3.201，b =0.57是经过四舍五入后得到的近似值，则a ⨯b 有位有效数字，a +b 有位有效数字。

4. 当x =1，-1，2时，对应的函数值分别为f (-1)=0，f (0)=2，f (4)=10，则f (x )的拉格朗日插值多项式是。

5. 设有矩阵⎥⎦⎤⎢⎣⎡-=4032A ，则‖A ‖1＝_______。

6. 要使...472135.420=的近似值的相对误差小于0.2%，至少要取位有效数字。

7. 对任意初始向量0()X 和常数项N ，有迭代公式1()()k k x Mx N +=+产生的向量序列{}()k X 收敛的充分必要条件是。

8. 已知n=3时的牛顿-科特斯系数,83,81)3(1)3(0==C C 则=)4(2C ，=)3(3C 。

9. 三次样条函数是在各个子区间上的次多项式。

10. 用松弛法 (9.0=ω)解方程组⎪⎩⎪⎨⎧=+-=++--=++3103220241225322321321x x x x x x x x x 的迭代公式是。

11. 用牛顿下山法求解方程033=-x x 根的迭代公式是，下山条件是。

二、选择填空（每题2分，共10分）1. 已知数x 1=721 x 2=0.721 x 3=0.700 x 4=7*10-2是由四舍五入得到的，则它们的有效数字的位数应分别为( )。

(完整word版)数值分析试题(word文档良心出品)

一、填空题（每空2分，共20分）1、解非线性方程阿西吧的f(x)=0的牛顿迭代法具有＿＿＿＿＿＿＿收敛2、迭代过程（k=1,2,…）收敛的充要条件是＿＿＿3、已知数 e=2.718281828...,取阿西吧的近似值 x=2.7182,那麽x具有的有效数字是＿＿＿4、高斯--塞尔德迭代法解阿西吧的线性方程组的迭代格式中求阿西吧的＿＿＿＿＿＿＿＿＿＿＿＿＿＿5、通过四个互异节点的插值多项式p(x),只要满足＿＿＿＿＿＿＿，则p(x)是不超过二次的多项式6、对于n+1个节点的插值求积公式至少具有＿＿＿次代数精度.7、插值型求积公式的求积系数之和＿＿＿8、 ,为使A可分解为A=LL T, 其中L为对角线元素为正的下三角形，a的取值范围＿9、若则矩阵A的谱半径(A)=＿＿＿10、解常微分方程初值问题的梯形格式是＿＿＿阶方法二、计算题（每小题15分，共60分）1、用列主元消去法解线性方程组2、已知y=f（x）的数据如下x 0 2 3f（x） 1 3 2求二次插值多项式及f（2.5）3、用牛顿法导出计算的公式，并计算，要求迭代误差不超过。

4、欧拉预报--校正公式求解初值问题取步长k=0.1,计算y(0.1),y(0.2)的近似值,小数点后保留5位.三、证明题（20分每题 10分）1、明定积分近似计算的抛物线公式具有三次代数精度2、若，证明用梯形公式计算积分所得结果比准确值大，并说明这个结论的几何意义。

参考答案：一、填空题1、局部平方收敛2、< 13、 44、5、三阶均差为06、n7、b-a8、9、 1 10、二阶方法二、计算题1、2、3、≈1.25992 (精确到,即保留小数点后5位)4、y(0.2)≈0.01903三、证明题1、证明：当=1时，公式左边：公式右边：左边==右边当=x时左边：右边：左边==右边当时左边：右边：左边==右边当时左边：右边：左边==右边当时左边：右边：故具有三次代数精度A卷一、填空题（本大题共8小题，每小题3分，共9×3＝27分）1、要使11的近似值的相对误差不超过0.1%，应取______________有效数字。

北京理工大学2003年攻读博士学位研究生入学考试试题

北京理工大学2003年攻读博士学位研究生入学考试试题Part II. Vocabulary(20 point, 0.5 point for each)Section ADirections: There are 20 questions in this section. Each question is a sentence with one word or phrase underlined. Below the are four words or phrases marked A, B, C and D. Choose the word or phrase that is closest in meaning to the underlined one. Mark the corresponding letter with a single bar across it on your Answer Sheet.16. The candidate has complied with all the requirements set by the university; this institution, therefore awards herthe degree of Master of Arts.A. permitsB. grantsC. rewardD. forwards17. The argument that Children are no longer an economic asset, but more of a liability, drew more attention of thepublic.A. productivityB. possibilityC. responsibilityD. necessity18. With all his experience abroad he was a major asset company.A. candidateB. applicantC. mangerD. resource19. The team published their report after three-month investigation which triggered off a parliamentary debate.A. shotB. delayedC. startedD. concluded20. The board of directors required that Mr. Brown justify buying the expensive equipment at a time when thecompany was practicing strict ecnomy.A. give reasons forB. verifyC. testifyD. give evidence about21. Today’s college students have ambiguous feelings about the role they should play in the world.A. wonderfulB. unusualC. ambitiousD. doubtful22. Railway services are not yet sound enough economically without government subsidy.A. aidB. chargeC. approvalD. domination23. The Public Broadcasting System is supported by donations from foundations and other sources.A. grantsB.referencesC. accountsD. advertisements24. The merit of a sales tax is that it decreases government reliance on income taxes.A. outcomeB. supplyC. virtueD. balance25. The microscope enables scientists to distinguish an incredible number and variety of bacteria.A. a selectedB. a verifiableC. an unbelievableD. an unavoidable26. Grandpa Wang, a famous painter, spent his life in a tranquil little farming cottage.A. a lovelyB. a peacefulC. an isolatedD. a noisy27. The doctor did not rule out the possibility of food poisoning.A. foreseeB. acceptC. excludeD. foretell28. My colleagues and I were greatly puzzled by our repeated failures in the experiment.A. distressedB. discontentedC. annoyedD. perplexed29. Contestants who do not comply with the regulations will be disqualified.A. cooperate withB. observeC. approveD. submit to30. John boasted that he could finish the job all by himself in no time.A. very rapidlyB. on timeC. in timeD. at any moment31. The Bureau of Public Security has decided to hold an inquiry to find out the cause of the big fire.A. investigationB. researchC. examinationD. inquest32. He was given a present in acknowledgement of his work for the business.A. honorB. realizationC. encouragementD. recognition33. Congressional debate over the passage of this controversial bill is inevitable.A. popularB. personalC. disputedD. beneficial34. The dispute between the faculty and the administration was not resolved until the faculty members got betterworking conditions.A. threatB. argumentC. problemD. discussion35. After being defeated they submitted to the enemy.A. surrenderedB. succeededC. stressedD. submergedSection BDirections: There are 20 questions in this section. Each question is a sentence with something missing. Below each sentence are four words or phrases marked A, B, C and D. Choose one word or phrase that best completes the sentence. Mark the corresponding letter with a single bar across it on your Answer Sheet.36. Waving received strict training in oil painting these artists paint in a _______ and figurative style.A. relevant C. narrativeB. realistic D. sensitive37. Having weighed up all the factors the department finally agreed to receive all the _________ to the committee.A. rejectionB. hypothesesC. nominationsD. resistance38. In the past decade some third countries have suffered from an cycle of drought _______ with flood.A. alteringB. activatingC. nominationsD. alternating39. I am sorry I opened your handbag but I ________ it for mine.A. mistookB. confusedC. recognizedD. imagined40. John and I have _______ to meet at the bus station at 9 o’clock.A. confirmedB. combinedC. appointedD. arranged41. You’re _______ your time trying to persuade him; he’ll never help you.A. wastingB. losing C spending D. missing42. The cyclist was _______ his bike by a truck.A. hit offB. knocked offC. knocked downD. hit down43. ______ the bad weather, we decided to go to the picnic.A. DespiteB. In spiteC. AlthoughD. Though44. The dealer wanted $500, I wanted to pay $400, and we finally agreed to the difference.A. divideB. splitC. dropD. decrease45. Passengers are ________ not to leave their cases and packages here.A. commandedB. informedC. notifiedD. advised46. The new teacher was ________ to the needs of all the children in her care.A. attentiveB. earnestC. carefulD. observant47. You should ________ at least three days for the journey.A. expectB. permitC. acceptD.allow48. Could you possibly ________ me at the next committee meeting?A. stand in forB. make up forC. tall back onD. kee in with49. The customs officer asked me if I had anything to _______.A. sayB. stateC. explainD. declare50. This ticket _______ you to a free meal in our new restaurant.A. givesB. entitiesC. grantsD. credits51. After his long absence from school he found it difficult to ______ up with the rest of his class.A. catchB. takeC. makeD. work52. I asked the tailor to make a small _______ to my trousers because they were too long.A. changeB. variationC. revisionD. alteration53. ______ all of us who are here tonight, I would like to thank Mr. Johnson for his informative talk.A. On behalf ofB. On account ofC. In honor ofD. In terms of54. Tom’s steps had _______ and there was a moment of absolute silence.A. died downB. died fromC. died awayD. died out55. Stressful environments lead to unhealthy behaviors such as poor eating habits, which _______ increase the risk ofheart disease.A. in turnB. in returnC. by chanceD. by turnsPart III. Cloze( 10 points 0.5 for each)Directions: In this section, you are to read a passage with twenty blanks and fill in the blanks with words or phrases given. Choose one suitable word or phrase marked A, B, C or D. for each blank and mark the corresponding letter of your choice with a single bar through the center on your ANSWER SHEET.Years ago, a group of brilliant young men at the University of Wisconsin seemed to have amazing creative literary.talent. They were 56 poets, novelists and essayists. They were extraordinary, in their to put the English language 57 , These 58 young men met regularly to read and critique each other’s work. And critique it they did!These men were merciless 59 one another. They 60 the most minute literary expression 61 a hundred pieces. They were heartless, tough, even mean in their criticism. The sessions became 62 arenas of literary criticism that the members of this exclusive club called themselves “Stranglers.”63 , the women of literary talent in the university were detemllned to start a club of 64 , one comparable to the Stranglers. They called themselves “Wranglers.” They, too, read their works 65 But there was one great difference. The criticism was much softer, more positive, more encouragmg 66 there was 67 criticism at all. Every effort, even the most feeble one, was encouraged.Twenty years later, when an alumnus (男校友) of the university 68 an exhaustive study of his classmates’careers, he noticed a vast difference in the literary 69 of the Stranglers 70 the Wranglers. Of all the bright young men in the Stranglers, not one had made a significant literary accomplishment 71 . From the Wranglers had come six or more successful writers, some of national renown such as Marjorie Kinnan Rawlings. 72 wrote The Yearling.Talent between the two? Probably the same. Level of education? 73 difference. But the Stranglers strangled, while the Wranglers 74 to give each other a life. The Stranglers promoted an atmosphere of contention and self -doubt. The Wranglers 75 the best, not the worst.56 A. would-soon-be B. would-be C. should -soon -be D. should be57 A. to its best use B. for its best C. as its best use D. in its best use58 A. premising B. clever C. promising D. perspective59 A. on B. for C. with D. to60. A. dissected B. reduced C. collapsea D. severed61 A. in B. onto C. into D. within62 A. so B. such C. thus D. that63 A. Not to overdo B. Never overdo C. Not to be outdone D. Never overdoing64 A. themselves’ B. their own’s C. their own D. their65 A. for each other B. to one another’s C. as to one mother D. to one another66 A. Sometimes B. Sometime C. Always D. Usually67 A. hardly no B. almost not C. almost no D. scarcely68 A. carried B. executed C. conducted D. engaged69 A. consequences B. accomplishments C. performances D. results70 A. as opposed B. on the contrary C. as opposed to D. on the objection to71 A. of such kine B. of any kind C. of some kind D. of no kind72 A. who B. that C. which D. the73 A. Not much B. Not such C. No much D. Not at all74 A. were firm B. were determined C. were sure D. were decided75 A. brightened B. highlighted C. enlightened D. demonstratedPart IV. Reading Comprehension (25 points 1 for each)Directions: Each of the passages below is followed by several questions about it. Read the passages carefully and to each question choose the best answer A, B, C or D. Mark your answer on the ANSWER SHEET by blackening the corresponding letter with a pencil.Passage OneOn the first day of my second year at California State University at Sacramento, I saw the most gorgeous guy! He was standing alone in line at the cafeteria and looked out place. Turning to my friends, I said, “I have to meet him!”Challenging my spontaneity, my friends reached into their purses and came up with money for a bet. They then dare me to run up to him, pretend that I knew him and convince him that he knew me. Smiling, I turned and was off to the cutie pie.“Dan, Dan!” I yelled as I ran up to him. “How are you? How’s your mom?” He just stood there looking at me I could tell that he was shy. I liked him immediately.“I’m not Dan,” he said, looking a little confused.“Sure you are!” I countered. “You lived in Sierra Hall last year, third floor! You were Bob’s roommate.”“No I lived off campus last year,” this sweet man replied still not getting it. I turned and started to leave, and he began asking me a series of questions, know you from mom’s allergy clinic? (I hate shots.) “Were you in the parrot class I took last summer?”(I like birds only slight more than shots.) “Do you eat at Taco Bell? I work there.”(Never.)“Well,” he said, “I know I’m not Dan, and I didn’t live in Sierra Hall.” He reached out his hand to mine. My name is Tim, and I’m pleased to meet you anyway.He invited me to his fraternity party that night. I composed myself and informed him that I did not go to fraternity parties. But as I watched him walk away, I had second thoughts. That afternoon, I took the money that I’d won from the bet and bought a black miniskirt. I was going to my first fraternity party.When I arrived there, I was a little nervous. Would he be there? when I got to the front steps of the frat house, I looked up and saw Tim sitting at the top. He looked at me and smiled.“I was hoping you would come. I’ve been waiting for you.” I sat down next to him and we started talking. We talked all that night and for the next three nights until dawn. Four months later, he asked me to marry him. Four years later, we tied the knot. This year, we celebrated the fifteenth anniversary, of the day we met.Some nights when we are snuggling together, I’m reminded that I found my soul mate on a dare. Now and then, my husband asks, “Am I Dan or Tim tonight?” Having a special place in my heart for both of them, I always laugh and reply, “You decide!”76. The narrator in the story said: “I have to meet him!” because ___________.A. she knew the guyB. she enjoyed the guy’s handsome appearanceC. she wanted to satisfy, her curiosityD. she wanted to win the bet77. The verb “tell” in the sentence “I could tell that he was shy” (Paragraph 3) means __________.A. speakB. ascertainC. proveD. vitness78. The sentence “I hate shots.” in the brackets (Paragraph 6) can best be paraphrased as ____________.A. I don’t like to be attacked by a lot of so many unexpected questionsB. I hate the guy for his endless questioning of my storyC. I hate being given an injectionD. I feel extremely shy before the handsome guy79. The narrator had finally decided to attend the fraternity party perhaps because ___________.A. she had fallen in love with him at the first sightB. she changed her mind when the guy had leftC. she felt lucky to win the betD. she was able to buy a black miniskirt with the money she won80. The story you read here can best be titled as ____________.A. A Brave Girl in Making an Important DecisionB. A Girl Daring to Search for Her Love regardless of Social PrejudiceC. God Helps Those Who Help ThemselvesD. A Brave Challenge of Girl’s Usual Shyness Results in a Happy MarriagePassage TwoThe score is tied in the second half of the World Cup finals, and aboard a 747, passengers cheer as they watch the game on their laptops--40,000 feet above Earth. Sound futuristic?Boeing Plans to make this scenario possible with its broadband telecommunications initiative, Connexion by Boeing. This service will allow fliers to surf the Web, send and receive email .access the company intranet, book dinner reserervations trade the honest stock, shop online and watch live TV from any seat in an aircraft. Connexion is already available cn privat jets, and Boeing says that the two-way broadband service will be installed on domestic flights in late 2001. Global coverage is slated to arrive by 2005. Subscribers will be able to access Connexion from their seats using laptops or personal digital assistants, plus a network card and a cable provided by the airline. The cost? Comparable to ground-floor cellular phone service; between $ 6 and $ 25 an hour.One key enabler for this technology is a phased-array antenna, originally developed by Boeing in 1986. Located on the aircraft’s, upper fuselage, the antenna electronically transmits beams to a satellite at 1.5Mb per second and receives them at 5 Mb per second. Thus, every passenger can access Connexion concurrently, securing connection speeds of no less than 56 Kh per second each. The actual bandwidth will be continually upgraded.Boeing ultimately wants to bring the service to markets like cruise ships and oil exploration platforms. Until then, the sky’s the limit.81. What is the main idea of this article?A. In the near future people will be able to watch live soccer matches on a plane.B. The future holds many exciting developments.C. Boeing is currently introducing Internet access on its planes.D. There is a strong demand for web access by Boeing passengers.82. Which of the following will not be used by air passengers to access Connexion?A. Their own portable computers.B. Personal distal assistants.C. The cabled computers on the airliner.D. The cellular phone service.83. Which of the following statements about Connexion is FALSE?A. Boeing planes worldwide will have this service by 2005.B. The service will cost between $ 6 and $ 25 an hour.C. The phased-array antenna is an important aspect· of Boeing’s new service.D. The service on works at speeds of less than 1.5Mb per second.84. According to the article, what does the word “concurrently” (Para. 4) mean?A. At the same time.B. One at a timeC. In orderD. Not currently85. What is true about the Connexion service to cruise ships and oil exploration platforms?A. Boeing is trying to provide them with the service.B. They cannot get the service now because the sky is limited.C. The service is not available to them now as Boeing is busy servicing the fliers.D. They can get the service because they are in the limt the project.Passage ThreeU. S. airlines could slash 70,000 more jobs if there were war with Iraq and the U. S. government did not give the industry, more help, the biggest domestic carriers said on Tuesday.The Air Transport Association, which represents major airlines, said in a report on airline finances that its members would take aggressive steps to counter any sharp drop in travel demand and an increase in costs caused by an Iraqi war.Big airlines are seeking government assistance to stem rising fuel costs and ease taxes that are contributing to losses that soared to more than $ 10 billion in 2002.The industry outlined a “most likely scenario if war broke out, saying that reduced demand and higher cost’s due to a conflict lasting 90 days would cost it $ 4 billion in lost revenue. Without a conflict, losses would still be expected to reach almost $ 7 billion for the year.“The nation’s air carders will continue to do all we can, but we fear that the consequences of this war will be severe,” James May, president and chief executive of the air transport group, told a news conference.May restated the industry’s belief that war could prompt more bankruptcies or force some financially fragile carder into liquidation. Recovery would take several years and ticket prices would have to fall further to spur demand.US Airways Group Inc. and UAL Corp’s United Airlines are in Chapter 11 bankruptcy protection, and some industry experts believe that AMR Corp’s American Airlines, the world’s biggest carrier could follow later this year. Airlines expect overall traffic volume during a second Gulf conflict would fall more sharply than it did during the 1991 war, when it declined 8 percent after fighting began. The airlines based their assessment on a slide of more than 20 percent in advance bookings for overseas travel after the U. S. government elevated its domestic terror alert status from yellow to orange in early February.Jet fuel has more than doubled in price from a year ago to $ 1.30 a gallon recently. Fuel is the second-largest expense after labor for an airline. An increase of one penny a gallon costs the industry an estimated $ 180 millionannually.86. U. S. airlines would have to suffer the following losses if there were war with Iraq except that __________.A. the industry would have to lose $ 180 million revenue each year with one gallon of jet fuel increasing onepenny on saleB. the overall traffic volume is expected to drop at least over eight percent, which took place during the first gulfwarC. the U. S. government refuses to give the main airline companies any essential financial support once the warbroke outD. it would take a few years to get the prewar ticket prices resumed and then to spur the passengers’rivingdemand87. The countermeasures the nation’s main air carriers would take to prevent any sharp drop in travel demand mayinclude ________________.I. seeking government financial assistanceII asking for low tax rateШ promoting more bankruptcies and forcing some weak airline companies into liquidationA. I onlyB. I and IIC. I and ШD. II and Ш88. The sentence “... AMR, Corp’s American Airlines, the world’s biggest carrier, could follow later this year”(Paragraph 7) can best restated as __________.A. it would also seek bankruptoy protectionB. it would have to spur its passengers’ steps demand for ticketsC. it would have to take aggressive steps to avoid bankruptcyD. it would call for more financial subsidy from the government for its survival89. The phrase “force some financially fragile carries into liquidation” (Paragraph 6) may probably mean _______.A. compel them to reduce flightB. make them do nothing but to declare bankruptcyC. push them to be destroyedD. bring them into luquid state90. From the passage we can conclude that ___________.A. the writer intends to show his strong anti-war positionB. the writer tells what the American air transportation industry would have to worry about in facing the waragainst IraqC. the writer shows deep sympathy for the sufferings the war would bring to Iraqi peopleD. the writer wants to show indignation against George Bush’s position on Iraqi problemPassage FourA half hour before test time, I was afraid to look in the mirror. But I had to assess the damages. After all, there were cute guys in this class. Granted, they would be worrying more about the final than what I looked like, and that was my hope at this point.The first things I saw were my own bloodshot eyes. Where was that Visine? My hair looked like Attila the Hun ad spent the night camping in it. Well, I’d pull it back into a ponytail and take the tangles out later.And then I saw it. It was a huge swelling on the front of my chin that had to be the size of a small golf ball. Surely I was hallucinating from lack of sleep. I had never seen anything like that before,I’d heard of people getting hives from nerves. But a single hive, on the front of my face? I gingerly touched it. A hard swelling met my curious fingertips. What had caused this? The pizza I’d consumed at midnight or the mountain Dew I’d consumed at two and four and six in the morning? Perhaps it was the Cap’s Crunch at three or the candy bar at five. My stomach had a strict policy. If I was going to keep it up all night, it insisted on being fed.How was I going to cover this up? I rummaged through all my toiletries until I found my lone bandage, put there for emergencies. Well, this qualified as one, Oh no, that looked really stupid. How embarrassing. Oh well, no time to do anything else about it now. My philosophy final was waiting for me. My beleaguered brain had tried all night to grasp the arguments of different philosophies so that I could write them down on the essay test this morning.I loved to hear our philosophy professor in class. I could follow the arguments when he discussed them, but trying to formulate them on my own just wasn’t happening. Perhaps the bump was the result of stress. I had to pass thisfinal or I would fail the class. And I couldn’t fail the class, or I would have to take the college’s summer school sessions. And I couldn’t go to summer school because I needed to work to help pay for next fall’s tuition. Swallowing the last gulp of fiat Mountain Dew, I headed for class. I picked a seat that didn’t directly face the clock. That would only make me more nervous, and cod knew I had already used up my adrenaline(肾上腺素) supply, Dr. Wennberg passed out the essay books while explaining the roles. We would have exactly one hour. My two pencils in hand, I waited for the signal.“Begin.”I closed my eyes took a deep breath and said a prayer “Please, God , help me remember all that I’ve studied for this test.”I looked over the questions. I could do this. I had to do this. I began writing.Twenty minutes had gone by. I had been writing as fast as I could before I forgot the infonnation. So far so good . But my eyes were so tired. They hurt so badly. They felt so heavy. I’d just rest them for a minute. I leaned my puffy chin on my hand.Someone sneezed. I came to with a start. What?! I’d fallen asleep? I’d never done that before in a final! Oh no! Fearfully, I looked at the clock.Only ten minutes left?! I’d slept a half hour? Oh no!I thought I’d used up all my adrenaline, but I was wrong. I broke out in a cold sweat. What could I do in ten minutes? Think, I must think. I need a plan. I’m doomed. No, think. I began writing as fast as I could to finish the questions. I stared at the last blank page of the essay test booklet with its nearly ruled lines. Dare I? I had nothing to lose. I still had two minutes. I wrote Dr. Wennberg. I told him how sorry I was. How I’d stayed awake all night to study because this was important to me, only to fall asleep during the exam. How I’d really wanted to do better I asked for mercy.One week later, I stood in front of the test board where the results would be posted. The mysterious swelling on my chin had gone away with sleep, but I touched my fingers to my chin nervously, It wasn’t coming back, was it?I stood awaiting my fate. The secretary came out and pinned a pape to the board. I scanned down the list of names, looking for my final class grade. There it was; a C--minus. Tears filled my eyes. I looked again. I had passed, I was sure I hadn’t deserved that. But I wasn’t about to argue! Dr. Wennberg had shown mercy. It was one philosophy lesson I’ve never forgotten.91. Why does the writer say “I was afraid to look in the mirror” in the first sentence of the first paragraph of the text?A. Perhaps because he didn't like his own appearance.B. Perhaps because he didn't prepare enough for the test.C. Perhaps because he was afraid to look at his utterly battled look for the previous sleepless night.D. Perhaps because he had too many worries about the damages brought to his health due to his busy preparationfor the test.92. When the writer says “ and that was my hope at this point” (Paragraph 1) “my hope” may be used I to mean thatA. he hoped all the other guys would fail in the test.B. he hoped that all the others shared the same worries with him.C. he hadn’t wished to see that all his classmates would have the same worries as his.D. he would be glad to see his classmates would have more worries than he had.93. When the writer says “I’d heard of people getting hives from nerves,” the phrase of “getting hives from nerves”( Paragraph 3 ) most probably means __________.A. getting overexcited and overjoyed when facing unexpected situationsB. feeling so nervous and bewildered as not to be able to do things regularlyC. feeling uncomfortable or itching due to a bee-stingingD. becoming red and swelling with a scar or a wound94. The proper noun Mountain Dew “(Paragraph 3) can be used in the context to mean ___________.A. the morning dew in a summer mornmgB. the dew that one often sees after a rainy dayC. a brand of drinkD. a gush of sweat as is seen after a gust of hard work95. The following phrasal verbs can he taken as the synonyms of the verb" rummage through" in the context except_________.A. fumble throughB. search throughC. delve intoD. carry through96. The writer says that he had to pass the philosophy final (Paragraph 5) because _______________.I . if not, he would have had to attend the college’s summer schoolII otherwise he would have been able to continue his study in the classШif he had failed the philosophy final, he would have been able to find time to work to earn money for next-term tuitionA. I onlyB. I and IIC. I andШD. I, II and Ш97. The incomplete sentence of" So far so good" (Paragraph 10) can probably be used to mean _____________.A. I t is goode as long as I can do itB. Until now things have gone wellC. Though until now things have gone well, I still hope to do it betterD. Though I am not so sure if all my answers are correct, I still fell OK98. Why someone sneezed the writer( Paragraph 11)?A. Perhaps he wanted the writer to give him a hint.B. Perhaps the man wanted to give the writer a hint on some point.C. Perhaps the writer had fallen asleep during the examD. Perhaps the man wanted to remind the writer of little time to be left99. The whole paragraph 13 from “I thought I’d used up all my adrenaline to answering the questions” is used to_________.A. describe the writer’s reflection of what he should have done before the examB. describe the depressed feeling of the write when knowing he failed in the examC. describe worrying mood in the exan and contradictory thoughts over his work at his philosophical classD. describe how sorry the writer was feeling for his not having been working enough for his philosophical class 100. The writer believed he had passed the exam _____________.A. as the result of his hard workB. as the result of his professor’s showing mercy to himC. mainly due to his tireless revision in the night before the examD. out of his expectationPart V. Writing and Translation (30 points, 15 points for each)Section A: Writing(15 points for each)Directions: Write an essay, in no less than 180 words according to the following demands. Remember to write your composition on your ANSWER SHEET.Title: The Future Prosperity of Our Country and the Peasant ProblemOutline: A. e encouraging economic situation of our country and the low-income level of our peasantsB. The core of our peasant problem and the way-out for our peasantsC. Measures to be taken to speed up the reform in our countryside to increase the income of our peasants Section B: Translation(15 points for each)Directions: Put the following passage into English and remember to write down your translation on your ANSWER SHEET.人们可以对欧元的贬值或美元的走强，提供很多的解释，这是问题的另一面。

北理工数值计算方法试题及答案

数值计算方法试题一一、填空题（每空1分，共17分）1、如果用二分法求方程043=-+x x 在区间]2,1[内的根精确到三位小数，需对分（）次。

2、迭代格式)2(21-+=+k k k x x x α局部收敛的充分条件是α取值在（）。

3、已知⎪⎩⎪⎨⎧≤≤+-+-+-≤≤=31)1()1()1(2110)(233x c x b x a x x x x S 是三次样条函数，则a =( )，b =（），c =（）。

4、)(,),(),(10x l x l x l n 是以整数点n x x x ,,,10 为节点的Lagrange 插值基函数，则∑==nk kx l0)(( )，∑==nk k jk x lx 0)(( )，当2≥n 时=++∑=)()3(204x l x xk k n k k( )。

5、设1326)(247+++=x x x x f 和节点,,2,1,0,2/ ==k k x k 则=],,,[10n x x x f 和=∆07f。

6、5个节点的牛顿-柯特斯求积公式的代数精度为，5个节点的求积公式最高代数精度为。

7、{}∞=0)(k kx ϕ是区间]1,0[上权函数x x =)(ρ的最高项系数为1的正交多项式族，其中1)(0=x ϕ，则⎰=14)(dx x x ϕ 。

8、给定方程组⎩⎨⎧=+-=-221121b x ax b ax x ，a 为实数，当a 满足，且20<<ω时，SOR 迭代法收敛。

9、解初值问题00(,)()y f x y y x y '=⎧⎨=⎩的改进欧拉法⎪⎩⎪⎨⎧++=+=++++)],(),([2),(]0[111]0[1n n n n n n n n n n y x f y x f h y y y x hf y y 是阶方法。

10、设⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=11001a a a a A ，当∈a （）时，必有分解式T LL A =，其中L 为下三角阵，当其对角线元素)3,2,1(=i l ii 满足（）条件时，这种分解是唯一的。

北京理工大学考博英语真题及其解析

北京理工大学考博英语真题及其解析SectionⅠUse of EnglishDirections:Read the following text.Choose the best word(s)for each numbered blank and mark A,B,C or D on ANSWER SHEET1.(10points) As former colonists of Great Britain,the Founding Fathers of the United States adopted much of the legal system of Great Britain.We have a“common law”,or law made by courts1a monarch or other central governmental2like a legislature.The jury,a3of ordinary citizens chosen to decide a case,is an4part of our common-law system.Use of juries to decide cases is a5feature of the American legal system.Few other countries in the world use juries as we do in the United States.6the centuries,many people have believed that juries in most cases reach a fairer and more just result7would be obtained using a judge8,as many countries do.9a jury decides cases after “10”，or discussions among a group of people,the jury’s decision is likely to have the11from many different people from different backgrounds,who must as a group decide what is right.Geng duo yuan xiao zhen ti ji qi jie xi qing lian xi quan guo mian fei zi xun dian hua:si ling ling liu liu ba liu jiu qi ba,huo jia zi xun qq:qi qi er liu qi ba wu san qi.Juries are used in both civil cases,which decide12among13 citizens,and criminal cases,which decide cases brought by the government14that individuals have committed crimes.Juries areselected from the U.S.citizens and15.Jurors,consisting of16 numbers,are called for each case requiring a jury.The judge17to the case18the selection of jurors to serve as the jury for that case.In some states,19jurors are questioned by the judge;in others,they are questioned by the lawyers representing the20under rules dictated by state law.1.[A]other than[B]rather than[C]more than[D]or rather2.[A]agency[B]organization[C]institution[D]authority3.[A]panel[B]crew[C]band[D]flock4.[A]innate[B]intact[C]integral[D]integrated5.[A]discriminating[B]distinguishing[C]determining[D]diminishing6.[A]In[B]By[C]After[D]Over7.[A]that[B]which[C]than[D]as8.[A]alike[B]alone[C]altogether[D]apart9.[A]Although[B]Because[C]If[D]While10.[A]deliberations[B]meditations[C]reflections[D]speculations11.[A]outline[B]outcome[C]input[D]intake12.[A]arguments[B]controversies[C]disputes[D]hostilities13.[A]fellow[B]individual[C]personal[D]private14.[A]asserting[B]alleging[C]maintaining[D]testifying15.[A]summoned[B]evoked[C]rallied[D]assembled16.[A]set[B]exact[C]given[D]placed17.[A]allocated[B]allotted[C]appointed[D]assigned18.[A]administers[B]manages[C]oversees[D]presides19.[A]inspective[B]irrespective[C]perspective[D]prospective20.[A]bodies[B]parties[C]sides[D]unitsSectionⅡReading ComprehensionPart ADirections:Read the following four texts.Answer the questions below each text by choosing A,B,C or D.Mark your answers on ANSWER SHEET 1.(40points)Text OneIt’s plain common sense—the more happiness you feel,the less unhappiness you experience.It’s plain common sense,but it’s not true.Recent research reveals that happiness and unhappiness are not really two sides of the same emotion.They are two distinct feelings that,coexisting,rise and fall independently.People might think that the higher a person’s level of unhappiness,the lower their level of happiness and vice versa.But when researchers measure people’s average levels of happiness and unhappiness,they often find little relationship between the two.The recognition that feelings of happiness and unhappiness can co-exist much like love and hate in a close relationship may offer valuable clues on how to lead a happier life.It suggests,for example, that changing or avoiding things that make you miserable may well make you less miserable,but probably won’t make you any happier.Thatadvice is backed up by an extraordinary series of studies which indicate that a genetic predisposition for unhappiness may run in certain families.On the other hand,researchers have found happiness doesn’t appear to be anyone’s heritage.The capacity for joy is a talent you develop largely for yourself.Psychologists have settled on a working definition of the feeling—happiness is a sense of subjective well-being.They have also begun to find out who’s happy,who isn’t and why.To date,the research hasn’t found a simple formula for a happy life,but it has discovered some of the actions and attitudes that seem to bring people closer to that most desired of feelings.Why is unhappiness less influenced by environment?When we are happy,we are more responsive to people and keep up connections better than when we are feeling sad.This doesn’t mean,however,that some people are born to be sad and that’s that.Genes may predispose one to unhappiness,but disposition can be influenced by personal choice. You can increase your happiness through your own actions.21.According to the text,it is true that[A]unhappiness is more inherited than affected by environment.[B]happiness and unhappiness are mutually conditional.[C]unhappiness is subject to external more than internal factors.[D]happiness is an uncontrollable subjective feeling.22.The author argues that one can achieve happiness by[A]maintaining it at an average level.[B]escaping miserable occurrences in life.[C]pursuing it with one’s painstaking effort.[D]realizing its coexistence with unhappiness.23.The phrase“To date”(Para.4)can be best replaced by[A]As a result.[B]In addition.[C]At present.[D]Until now.24.What do you think the author believes about happiness and unhappiness?[A]One feels unhappy owing to his miserable origin.[B]They are independent but existing concurrently[C]One feels happy by participating in more activities.[D]They are actions and attitudes taken by human beings.25.The sentence“That’s that”(Para.5)probably means:Some people are born to be sad[A]and the situation cannot be altered.[B]and happiness remains inaccessible.[C]but they don’t think much about it.[D]but they remain unconscious of it.Text TwoWhat are the characteristics of a mediator?Foremost,the mediator needs to be seen as a respected neutral,objective thirdparty who is capable of weighing out fairness in the resolution of a conflict.The mediator must be trusted by both parties to come up with a solution that will protect them from shame.While the central issue is justice,the outcome needs to be win-win,no losers.The abilities to listen impartially,suspend judgment,and accurately gather and assess information are other important characteristics. Finally,to function effectively the mediator must have power (financial,status,position),so that both parties will take seriously and abide by the mediator’s judgment.If one party refused to cooperate,he or she should fear the possibility of being shamed and losing face before the mediator and the whole community.If that real possibility does not enter the minds of both parties,the mediator will be ineffective.In several countries mediators are still used to find a bride for a ually this is a job for the parents,and they in turn employ the services of a mediator.Because this event takes much planning, the parents will try to identify the mediator well in advance.Since these services sometimes require reward,money must be saved.Or in some cases parents try to do a number of favors for the mediator so that he or she will feel indebtedness and perform the service as a kind of repayment.The parents will try to get the most influential mediator possible, to boost their chances of being approved by the potential bride’s parents.The young woman’s parents will not want to risk shame byturning down a request from such an important person—so the reasoning goes.Of course,the higher-ranked the mediator,the higher the cost of the services.Complicating the process is the fact that turning down the mediator is also a slight of the potential groom and his parents,which will likely generate conflict between the families.If the parties are not careful,the entire community can take sides.One way to alleviate this eventuality is for the young woman’s family to identify a flaw that would make her a less desirable prospect.They might say,“She is sickly.”or“She may not be able to bear children.”Although none of these statements may be true,and probably everyone knows they aren’t,they do provide a way for the young man’s parents to withdraw their request for a perfectly legitimate reason.Everyone saves face,at least at the surface,and peace is preserved.26.The characteristics of a mediator include all of the following except[A]unbiased judgment of arguments.[B]hard prudence in decision-making.[C]impartial treatment to a conflict.[D]remarkable insight into controversies.27.The author deems it important for a mediator[A]to be quite wealthy and considerate.[B]to be powerful to shame either party.[C]to justify the solution of a conflict.[D]to have high status to fear arguers.28.In some courtiers,young people’s marriage[A]is independent of their parents’will.[B]needs careful valuation in advance.[C]costs a small fortune of their family.[D]is usually facilitated by a mediator.29.The request of the groom’s parents may be turned down unless[A]they manage to hire a qualified mediator.[B]they make their best choice at all risks.[C]the young woman’s parents want to lose face.D]the bride’s parents dare to offend the mediator.30.It may be the best way to resolve a conflict for[A]the entire community to offer support.[B]a mediator to be identified by both sides.[C]the outcome of mediation to be acceptable.[D]a valid excuse to spare both sides’blushes.Text ThreeThe Internet,like its network predecessors,has turned out to be far more social than television,and in this respect,the impact of the Internet may be more like that of the telephone than of TV. Our research has shown that interpersonal communication is the dominant use of the Internet at home.That people use the Internet mainly for interpersonal communication,however,does not imply thattheir social interactions and relationships on the Internet are the same as their traditional social interactions and relationships,or that their social uses of the Internet will have effects comparable to traditional social activity.Whether social uses of the Internet have positive or negative effects may depend on how the Internet shapes the balance of strong and weak network ties that people maintain.Strong ties are relationships associated with frequent contact,deep feelings of affection and obligation,whereas weak ties are relationships with superficial and easily broken bonds,infrequent contact,and narrow focus.Strong and weak ties alike provide people with social support. Weak ties including weak online ties,are especially useful for linking people to information and social resources unavailable in people’s closest,local groups.Nonetheless,strong social ties are the relationships that generally buffer people from life’s stresses and that lead to better social and psychological outcomes.People receive most of their social support from people with whom they are in most frequent contact,and bigger favors come from those with stronger ties.Generally,strong personal ties are supported by physical proximity.The Internet potentially reduces the importance of physical proximity in creating and maintaining networks of strong social ties.Unlike face-to-face interaction or even the telephone, the Internet offers opportunities for social interactions that do notdepend on the distance between parties.People often use the Internet to keep up with those with whom they have preexisting relationships. But they also develop new relationships on-line.Most of these new relationships are weak.MUDs,newsgroups,and chat rooms put people in contact with a pool of new groups,but these on-line“mixers”are typically organized around specific topics,or activities,and rarely revolve around local community and close family and friends.Whether a typical relationship developed on-line becomes as strong as a typical traditional relationship and whether having on-line relationships changes the number or quality of a person’s total social involvements are open questions.Empirical evidence about the impact of the Internet on relationships and social involvement is sparse.Many authors have debated whether the Internet will promote community or undercut it.Much of this discussion has been speculative and anecdotal,or is based on cross-sectional data with small samples.31.The text is mainly about[A]the dominance of interpersonal communication.[B]strong and weak personal ties over the Internet.[C]the difference between old and modern relationships.[D]an empirical research on the Internet and its impact.32.It is implied in the text that[A]the Internet interactions can rival traditional ones.[B]television is inferior to telephone in social effect.[C]strong links are far more valid than weak ones.[D]the Internet features every home and community.33.The word“buffer”(Para.2)can probably be replaced by[A]deviate.[B]alleviate.[C]shield.[D]distract.34.According to the author,the Internet can[A]eliminate the hindrance of the distance.[B]weaken the intimate feelings among people.[C]provide people with close physical contacts.[D]enhance our ability to remove social stresses.35.From the text we can infer that[A]the evidence for the effect of the Internet seems abundant.[B]the social impact of the Internet has been barely studied enough.[C]some discussions are conclusive about the function of the Internet.[D]random samples have witnessed the positive influence of the Internet.Text FourLeadership is hardly a new area of research,of course.For years, academics have debated whether leaders are born or made,whether a person who lacks charisma(capacity to inspire devotion and enthusiasm)can become a leader,and what makes leaders fail.Warren G.Bennis,possibly the possibly the world’s foremost expert on leading,has,together with his co-author,written two best-sellerson the topic.Generally,researchers have found that you can’t explain leadership by way of intelligence,birth order,family wealth or stability,level of education,race,or sex.From one leader to the next,there’s enormous variance in every one of those factors.The authors’research led to a new and telling discovery:that every leader,regardless of age,had undergone at least one intense, transformational experience—what the authors call a“crucible”(severe test).These events can either make you or break you.For emerging leaders,they do more making than breaking,providing key lessons to help a person move ahead confidently.If a crucible helps a person to become leader,there are four essential qualities that allow someone to remain one,according to the authors.They are:an“adaptive capacity”that lets people not only survive inevitable setbacks,heartbreaks,and difficulties but also learn from them;an ability to engage others through shared meaning or a common vision;a distinctive and compelling voice that communicates one’s conviction and desire to do the right thing;and a sense of integrity that allows a leader to distinguish between good and evil.That sounds obvious enough to be commonplace,until you look at some recent failures that show how valid these dictums(formal statements of opinion)are.The authors believe that former Coca-Cola Co.Chairman M.Douglas Ivester lasted just28months because“his grasp of context was sorrowful.”Among other things,Ivesterdegraded Coke’s highest-ranking African-American even as the company was losing a$200million class action brought by black employees.Procter&Gamble Co.ex-CEO Durk Jager lost his job because he failed to communicate the urgent need for the sweeping changes he was making.It’s striking,too,that the authors found their geezers(whose formative period,as the authors define them,was1945to1954,and who were shaped by World War II)sharing what they believed to be a critical trait—the sense of possibility and wonder more often associated with childhood.“Unlike those defeated by time and age,our geezers have remained much like our geeks (who came of age between1991and2000,and grew up“virtual,visual, and digital”)—open,willing to take risks,hungry for knowledge and experience,courageous,and eager to see what the new day brings”, the authors write.36.The text indicates that leadership research[A]has been a controversial study for years.[B]predicts how a leader comes to be.[C]defines the likelihood to be a leader.[D]probes the mysteries of leadership.37.According to Bennis,the trait shared by leaders consists of[A]top levels of intelligence and education and devotion.[B]remarkable ability to encourage people with loyalty and hope.[C]striking qualities of going through serious trials andsufferings.[D]strong personalities that arouse admiration and confidence.38.The favorable effect of a crucible depends on whether a leader[A]proves himself/herself to be a newly emergent one.[B]accepts it as a useful experience for progress.[C]shrinks back from tiring and trying experiences.[D]draws important lessons for his/her followers.39.A leader can hardly maintain his/her position unless he/she[A]fulfils all necessary quality requirements.[B]helps people to prevent defeats and sorrows.[C]fails to attract people with common concerns.[D]lacks appealing and strength of character.40.The authors’dictums can be justified by the fact that[A]Douglas Ivester defeated a highest-ranking black employee in a suit.[B]Durk Jager was dismissed owing to his poor communicating ability.[C]Geezers couldn’t erase the brands stamped in childhood.[D]Geeks are sensible enough to meet dangers and challenges.Part BDirections:You are going to read a list of headings and a text. Choose the most suitable heading from the list A-F for each numbered paragraph(41-45).The first and last paragraphs of the text are not numbered.There is one extra heading which you do not need to use.Mark your answers on ANSWER SHEET 1.(10points)[A]Physical Changes[B]Low Self-Esteem[C]Emerging Independence and Search for Identity[D]Emotional Turbulence[E]Interest in the Opposite Sex[F]Peer Pressure and ConformityThe transition to adulthood is difficult.Rapid physical growth begins in early adolescence—typically between the ages of9and 13—and thought processes start to take on adult characteristics. Many youngsters find these changes distressing because they do not fully understand what is happening to them.Fears and anxieties can be put to rest by simply keeping an open line of communication and preparing for change before it occurs.The main issues that arise during adolescence are:(41)__________A child’s self worth is particularly fragile during adolescence. Teenagers often struggle with an overwhelming sense that nobody likes them,that they’re not as good as other people,that they are failures, losers,ugly or unintelligent.(42)__________Some form of bodily dissatisfaction is common among pre-teens. If dissatisfaction is great,it may cause them to become shy or very easily embarrassed.In other cases,teens may act the opposite—loudand angry—in an effort to compensate for feelings ofself-consciousness and inferiority.As alarming as these bodily changes can be,adolescents may find it equally distressing to not experience the changes at the same time as their te maturation can cause feelings of inferiority and awkwardness.(43)__________Young people feel more strongly about everything during adolescence.Fears become more frightening,pleasures become more exciting,irritations become more distressing and frustrations become more intolerable.Every experience appears king-sized during adolescence.Youngsters having a difficult adolescence may become seriously depressed and/or engage in self-destructive behavior. Often,the first clue that a teenager needs professional help is a deep-rooted shift in attitude and behavior.Parents should be alert to the warning signs of personality change indicating that a teenager needs help.They include repeated school absences,slumping grades, use of alcohol or illegal substances,hostile or dangerous behavior and extreme withdrawal and reclusiveness.(44)__________There is tremendous pressure on adolescents to conform to the standards of their peers.This pressure toward conformity can be dangerous in that it applies not only to clothing and hairstyles;it may lead them to do things that they know are wrong.(45)__________Adolescence marks a period of increasing independence that often leads to conflict between teenagers and parents.This tension is a normal part of growing up—and for parents,a normal part of the letting-go process.Another normal part of adolescence is confusion over values and beliefs.This time of questioning is important as young people examine the values they have been taught and begin to embrace their own beliefs.Though they may adopt the same beliefs as their parents,discovering them on their own enables the young person to develop a sense of integrity.Although adolescence will present challenges for young people and their parents,awareness and communication can help pave the way for a smooth transition into this exciting phase of life.Part CDirections:Read the following text carefully and then translate the underlined segments into Chinese.Your translation should be written clearly on ANSWER SHEET 2.(10points)Culture shock might be called an occupational disease of people who have been suddenly transplanted abroad.Like most ailments,it has its own symptoms and cure.Culture shock is precipitated by the anxiety that results from losing all our familiar signs and symbols of social intercourse.Those signs or cues include the thousand and one ways in which we orient ourselves to the situation of daily life:when to shake hands and what to say when we meet people,when and how to give tips,how to makepurchases,when to accept and when to refuse invitations,when to take statements seriously and when not.46)These cues,which may be words, gestures,facial expressions,customs,or norms,are acquired by all of us in the course of growing up and are as much a part of our culture as the language we speak or the beliefs we accept.47)All of us depend for our peace of mind and our efficiency on hundreds of these cues, most of which we do not carry on the level of conscious awareness.Now when an individual enters a strange culture,all or most of these familiar cues are removed.He or she is like a fish out of water.48)No matter how broad-minded or full of goodwill you may be,a series of props(支柱)have been knocked from under you,followed by a feeling of frustration and anxiety.People react to the frustration in much the same way.First they reject the environment which causes the discomfort.“The ways of the host country are bad because they make us feel bad.”49)When foreigners in a strange land get together to grouse about the host country and its people,you can be sure they are suffering from culture shock.Another phase of culture shock is regression.The home environment suddenly assumes a tremendous importance.To the foreigner everything becomes irrationally glorified.All the difficulties and problems are forgotten and only the good things back home are remembered.It usually takes trip home to bring one back to reality.Individuals differ greatly in the degree in which culture shock affects them.Although not common,there are individuals who cannotlive in foreign countries.Those who have seen people go through a serious case of culture shock and on to a satisfactory adjustment can discern steps in the process.During the first few weeks most individuals are fascinated by the new.They stay in hotels and associate with nationals who speak their language and are polite and gracious to foreigners.This honeymoon stage may last from a few days or weeks to six months depending on circumstances.50)If one is a very important person he or she will be taken to the show places,will be pampered and petted,and in a press interview will speak glowingly about progress,goodwill,and international friendship.If he returns home may well write a book about his pleasant if superficial experience abroad.SectionⅢWriting51.Directions:Study the following drawing carefully and write an essay to1)describe the drawing,2)deduce the purpose of the painter of the drawing,and3)suggest counter-measures.You should write about160—200words neatly ANSWER SHEET2.(20 points)答案详解：Section I答案及解析答案详解1.【解析】[B]逻辑衔接题。

北京理工大学数学专业数学分析Ⅱ试题(MTH17002)

2011级数学专业数学分析Ⅱ阶段测验一试题1.设(),,ln arctanyxf x y z x y z z =++，O 为坐标原点。

（1）求f 在()2,1,2P -点沿方向PO的方向导数；（2）求f 在()2,1,2P -点沿方向PM的方向导数为0的点M 的轨迹方程。

2.设(),z z x y =是由方程()2222,0f x z y x --=确定的可微的隐函数，其中(),f u v 具有连续的一阶偏导函数，求z zyx x y∂∂+∂∂并化为最简形式。

3.设()22,2z f xy x y =-，其中f 有二阶连续偏导数。

又。

求2,,z z zx y x y∂∂∂∂∂∂∂。

4.设(),f x y =，求()()0,0,0,0x y f f ''。

又问：f 在()0,0点是否可微？5.设函数(),z z x y =有连续的二阶偏导数且满足方程2222220u u x y x y ∂∂-=∂∂，做变换,xxy yξη==。

设()(),,z x y ϕξη=，试求函数ϕ满足的方程。

6.设()()22,22ln z f x y x xy y y x ==-++-，求f 在()1,2点邻域内带Peano 型余项的二阶Taylor 公式。

7.设()20,,,0s x t a u x t e ds x t -=∈> ，求222u u a t x ∂∂-∂∂。

8.设f 在)},|,x y a x b c y d Ω=<<<<内有定义，f 关于y 的偏导函数y f '在Ω内存在且有界，又设对每个固定的()0,y c d ∈，()0,f x y 关于x 在(),a b 内连续，求证：f 在Ω内连续。

9.设f 在平面区域(){},01,01x y x y Ω=<<<<内定义。

（1）叙述f 在Ω内一致连续的严格含义；（2）叙述极限()0lim ,x y f x y →+→+存在的Cauchy 收敛准则；（3）设f 在区域Ω内一致连续，求证：极限()00lim ,x y f x y →+→+必存在；（4）求证：(),xf x y y =在区域Ω内不一致连续。

北理工考博数值分析——试卷

一、填空题：(共20分)1.非奇异矩阵的条件数为，条件数的大小反映了方程组的。

2.的相对误差和的相对误差之间的关系是。

3．给出一个求解对任意初值都收敛的迭代公式，说明如何获得及收敛理由。

4. 设为互异节点，为对应节点上的拉格朗日插值基函数，则, 。

5．设互异，则当时，；。

6．数值积分公式的代数精确度是，____Gauss型求积公式。

二、（10分）设阶矩阵对称正定，用迭代公式求解。

问实数取何值时迭代收敛？三、（13分）设有线性方程组， (1)将系数矩阵A分解为，求；(2)求解方程组。

四、（10分）用最小二乘法确定中的参数和，使该函数曲线拟合于下列形式的数据（推导满足的正则方程组）。

五、（10分）求四次插值多项式，使其满足条件，并写出插值余项。

六、（10分）设，考虑方程，证明求解该方程的牛顿法产生的序列（其中）是收敛的；并求，使得。

七、（15分）对于积分，当要求误差小于时，用复化梯形公式及复化抛物线公式计算近似值时，所需节点数及步长分别为多少？计算满足精度要求的近似值。

八、（12分）试求系数，使3步公式的阶数尽可能高，并写出其局部截断误差的主项。

一、（12分）设有线性方程组，（1）将系数矩阵A分解为L和U的乘积，其中L是单位下三角阵，U是上三角阵；（2）解线性方程组。

二、（18分）（1）已知数据：试分别用线性及二次插值计算的近似值，并估计误差。

（2）设，试求三次插值多项式使得,并对任一写出误差估计式。

三、（20分）（1）设线性方程组的系数矩阵试写出收敛的迭代计算公式；（2）若线性方程组的系数矩阵，用表示迭代法和迭代法收敛的充分必要条件。

四、（15分）（1）若用复化梯形、复化辛普森公式计算积分的近似值，要求计算结果有5位有效数字，分别应取多大？（2）选一复化求积公式计算积分的近似值，要求截断误差小于。

五、（10）确定，使求积公式的代数精确度尽可能高，并指出是否是型求积公式。

六、（15分）试用法推导出求近似值的迭代格式, 并用导出的公式计算的近似值，要求误差不超过。

北京理工大学人文与社会科学学院考博参考书-考博分数线-专业课真题

北京理工大学人文与社会科学学院考博参考书-考博分数线-专业课真题一、专业的设置北京理工大学人文与社会科学学院共招生2人，下设思想文化教育与社会发展专业，研究方向为心理发展与健康教育，导师是贾晓明和李林英。

二、考试的科目学院、专业、研究方向代码及名称招生计划指导教师复试要求及相关说明外国语业务课一业务课二人文与社会科学学院(022)2思想文化教育与社会发展(0401Z1)202.心理发展与健康教育贾晓明1001英语2032心理与教育研究方法3083社会性与人格发展面试：1、科研能力评估2、综合素质3、外语听力与口语水平测试李林英三、导师介绍贾晓明，北京理工大学人文社会科学学院社会工作与心理学系教授。

1991年至2001年任学生心理咨询中心主任，从2002年开始担任中心督导。

作为高级访问学者于1998到1999年在加拿大大布局列颠哥伦比亚大学咨询心理学系学习研究。

自20世纪80年代末开始从事心理咨询工作。

李林英，生于1963年5月，北京理工大学马克思主义理论教研部副主任、教授，发展与教育心理学硕士生导师，所在学科为思想政治教育、心理学。

讲授的硕士生核心课程有《人生发展与心理健康教育》；本科生课程有《思想道德修养与法律基础》、《人类行为与社会环境》、《社会心理学》等。

近年来承担北京市、福特基金会等9项课题，研究成果获北京市和校级教学成果奖4项，出版教材和专著10本，在国内外重要学术刊物上发表论文30余篇。

育明教育考博分校解析：考博如果能够提前联系导师的话，不论是在备考信息的获取，还是在复试的过程中，都会有极大的帮助，甚至是决定性的帮助。

育明教育考博分校经过这些年的积淀可以协助学员考生联系以上导师。

四、参考书目《心理与教育研究方法》（修订版）；董奇著，北京2032心理与教育研究方法师范大学出版社2004年版《社会性与人格发展》（第五版）；戴维.谢弗，陈会3083社会性与人格发展昌等译，人民邮电出版社，2012年6月出版五、北理考博英语北理的考博英语满分100分，题型有阅读、翻译和写作等。

北京理工大学法学院考博参考书-考博分数线-专业课真题

资料来源：
考博就找育明教育考博分校
考专题的讲解，是对一一轮和深化和凝练，第三轮是针对真题的难度深度广度灵
活度和缜密度以及出题老师的特点，就出题老师的学科背景，研究重点，上课的
笔记讲稿，论文，研究课题成果等进行深度讲解，第四轮是就最新的理论前沿和
学科热点结合现实的热点进行拔高应用性讲解，最后一轮是模拟练习，教会考生
曲三强，北京理工大学法学院院长、教授、博士生导师；北京大学法学院教
授、博士生导师；中关村知识产权法律保护研究院院长；中国知识产权法学研究
会副会长。曲三强教授在刑法学和知识产权法学两个领域均颇有建树，被誉为法
学界难得的“复合型人才”。在刑法学领域，其具有代表性的论著有《经济犯罪
学》、《犯罪与刑罚新论》等。
4
杨成铭韩君玲曲三强张艳丽徐昕李寿平罗丽
张景瑞
2031 法学 3082 法学 1001 英语
基础理论前沿问题
2031 法学 3082 法学 1001 英语
基础理论前沿问题
2031 法学 3082 法学 1、专业英语；2、法学
1001 英语基础理论
前沿问题
基础理论；3、经济学基
2031 法学 3082 法学础知识。 1001 英语
资料来源：
考博就找育明教育考博分校
北京理工大学法学院考博参考书-考博分数线-专业课真题
一、专业的设置
北京理工大学法学院招收博士生 4 名，下设法律经济学、空间活动与法律专
业。
其中法律经济学专业下设 4 个方向，分别是杨成铭、韩君玲的法律经济学理
论；曲三强的民商法经济学；张艳丽、徐昕的诉讼法经济学；李寿平、罗丽的国
基础理论前沿问题
1001 英语 2031 法学 3082 法学

北京理工大学数值分析总复习

北京理工大学数值分析总复习2012
考试时带计算器
• 上机题请在11月30日晚9:30之前交，交打印稿。
• 答疑时间：11月28，29, 30（即星期3, 4， 5）晚上7:30—9:30，上机作业也在答疑时间交。
• 答疑地点：中教816。
2
第一章误差
绝对（相对）误差 ( 限 ) 有效数字
(2) H H '((xx ii)) yyii,', (i0,1, ,n).
24
➢ H ( x ) y 0 h 0 ( x ) y 1 h 1 ( x ) y n h n ( x ) y 0 ' H 0 ( x ) y 1 ' H 1 ( x ) y n ' H n ( x )
(i 1 ,2 , ,n )
12
➢ 迭代法收敛的充分必要条件
x(k1) Mx(k) g,
x(0) 任意
收敛
(M)1.
➢ 迭代法收敛的充分条件
若i迭代法和Gauss-Seidel迭代法均收敛.
若A为对称正定阵, 则求解Ax=b的Gauss-Seidel迭代法收敛.
复化梯形公式复化Simpson公式 Romberg算法 Gauss型求积公式代数精确度截断误差
33
代数精确度
设有求积公式
b
n
f(x)dx
a
Akf(xk)
k0
若它对 f (x)=1, x, x2,…, xm 都能精确成立(即上式等
号成立), 但对 f (x)=xm+1 上式等号不成立, 则称该求
hi (x)
xi x0
(2n+1)次多项式
x i x n 1
h i ( x ) 1 2 l i ' ( x ) x ( x i ) l i 2 ( x ),

北理工数值分析大作业

数值分析上机作业第 1 章1.1计算积分，n=9。

（要求计算结果具有6位有效数字）程序：n=1:19;I=zeros(1,19);I(19)=1/2*((exp(-1)/20)+(1/20));I(18)=1/2*((exp(-1)/19)+(1/19));for i=2:10I(19-i)=1/(20-i)*(1-I(20-i));endformat longdisp(I(1:19))结果截图及分析：在MATLAB中运行以上代码，得到结果如下图所示：当计算到数列的第10项时，所得的结果即为n=9时的准确积分值。

取6位有效数字可得.1.2分别将区间[-10.10]分为100,200,400等份，利用mesh或surf命令画出二元函数z=的三维图形。

程序：>> x = -10:0.1:10;y = -10:0.1:10;[X,Y] = meshgrid(x,y);Z = exp(-abs(X))+cos(X+Y)+1./(X.^2+Y.^2+1);subplot(2,2,1);mesh(X,Y,Z);title('步长0.1')>> x = -10:0.2:10;y = -10:0.2:10;[X,Y] = meshgrid(x,y);Z = exp(-abs(X))+cos(X+Y)+1./(X.^2+Y.^2+1);subplot(2,2,1);mesh(X,Y,Z);title('步长0.2')>>x = -10:0.05:10;y = -10:0.05:10;[X,Y] = meshgrid(x,y);Z = exp(-abs(X))+cos(X+Y)+1./(X.^2+Y.^2+1);subplot(2,2,1);mesh(X,Y,Z);title('步长0.05')结果截图及分析：由图可知，步长越小时，绘得的图形越精确。

北京理工大学数学专业数值计算方法Ⅰ期末试题2013级B卷,2015级A卷(MTH17170)

北京理工大学2014-2015学年第二学期2013级数值代数与数值分析期末试题B 卷一、（1031.953=有5位有效数字，试求方程233204x x -+=的两个根，使它们至少有4位有效数字。

二、（10分）已知矩阵100024024A ⎛⎫ ⎪= ⎪ ⎪-⎝⎭，求A 的1-范数，∞-范数，F-范数，2-范数。

三、（15分）用LU 分解求解方程组12321374321261513x x x ⎛⎫⎛⎫⎛⎫ ⎪⎪ ⎪= ⎪⎪ ⎪ ⎪⎪ ⎪⎝⎭⎝⎭⎝⎭，要求写出LU 矩阵。

四、（15分）用迭代公式()1,0,1,k k k x x Ax b k α+=+-=求解方程组12323121x x ⎛⎫⎛⎫⎛⎫= ⎪ ⎪ ⎪-⎝⎭⎝⎭⎝⎭，求α的范围使迭代收敛。

五、（10分）用插值多项式理论证明：00n ni k k i x k x i i k ==≠⎛⎫- ⎪= ⎪- ⎪⎝⎭∑∏。

六、（10分）已知下面的数据表，写出用最小二乘法求形如2y a bx =+的经验公式的正则方程组。

七、（15分）已知方程1552sin 0x x -+=在03x =附近有根，试构造一种收敛的迭代格式，并说明理由。

八、（3次的插值多项式，建立导数型插值误差公式，并证明。

注：本课程自2014级起改为大二上学期必修和大三上学期选修两部分，名称分别为数值计算方法Ⅰ和数值计算方法Ⅱ。

北京理工大学2016-2017学年第一学期2015级数值计算方法Ⅰ期末试题A 卷一、（1030.952=有5位有效数字，试求方程233104x x -+=的两个根，使它们至少有4位有效数字。

二、（10分）已知矩阵100024024A ⎛⎫ ⎪= ⎪ ⎪-⎝⎭，求A 的1-范数，2-范数，1-条件数，2-条件数。

三、（15分）用LU 分解求解方程组123212124312261526x x x ⎛⎫⎛⎫⎛⎫ ⎪⎪ ⎪= ⎪⎪ ⎪ ⎪⎪ ⎪⎝⎭⎝⎭⎝⎭，要求写出LU 矩阵。

北理工数值分析考试卷-2013级数值分析考试习题

2013——2014年《数值分析》考试习题一、（15分）设2101202a a ⎡⎤⎢⎥A =⎢⎥⎢⎥⎣⎦ ，123x x x x ⎡⎤⎢⎥=⎢⎥⎢⎥⎣⎦ ，331b ⎡⎤⎢⎥=⎢⎥⎢⎥⎣⎦（1）求出当a 满足何条件时可以对A 进行cholesky 分解（即T LL 分解，L 为非奇异下三角矩阵）（2）若a=1时利用T LL 分解对方程组Ax=b 进行求解（保留两位小数）二、（10分）求证：111a a a a a a ⎡⎤⎢⎥A =⎢⎥⎢⎥⎣⎦，只有当1122a -<< 时用Jacobi 迭代法求解方程组Ax=b 才收敛三、（15分）（1）已知i x1 3 4 6 ()i f x-75814对其进行3次插值，并求出()2f 的值（2）给定函数组i x0 1 2 ()i f x 1 4 15 ()'i f x6对其进行3次Hermite 插值多项式3H 并求出余项()()f x H x - 的表达式四、（15分）利用最小二乘法，求形如2y a bx =+ 的拟合i x 1 2 3 4 5 i y0.12.98.114.924.1五、（15分）（1）选择合适的数值积分方法，对210x e dx ⎰ 进行积分，使其具有2位有效数字（2）根据（1）中选取的数值积分方法，编写Matlab 源程序代码六、（15分）（1）构造迭代格式求解40x x e --= 的根，使其具有4位有效数字（2）从理论上证明你所构造的迭代格式是收敛的七、（15分）对常微分方程初值问题()()'00,y f x y y x y ⎧=⎪⎨=⎪⎩ ，证明其二步公式111(58)12n n n n n hy y f f f ++-=++- 是三阶精度的迭代公式，并求出该二步公式的局部截断误差主项。

北京理工大学 2006级数值分析期末试题(B)

8x1 x2 x3 1 性方程组 2x1 10x2 x3 4 一定收敛。
6 x1 x2 ax3 3
8. 向量 X=(1,-2,3)，Y=(3,4,0)，则向量 X 的 1-范数||X||1=
范数|||Y||2=
。
9.
已知
n=4
时的牛顿-科特斯系数则
C (4) 0
7 90
,
C
(4 3
时
，上述两类误差分配最为合理。
2. 已知 a=3.201，b=0.57 是经过四舍五入后得到的近似值，则 ab 的结果的计算误差
大约为
，a+b 的结果的计算误差大约为
。
3. 用双点弦截法求解方程 x 4 2x 4 0 在 [1,2] 之间的根的迭代公式
是
。
4.
)
16 45
,
C (4) .1
C (4) 2
。
I
10. 用复化辛卜生公式求积分
1 dx
0 1 x
的近似值时，至少需
函数值，才能保证所求积分近似值的误差不超过 10－5。
，向量 Y 的 2，
个节点处的
11. 当 x=1,-1,2 时， f(x)=0,-3,4 ，则 f(x) 的拉格朗日插值多项式
6. 用 Euler 法、隐式欧拉法、梯形法求解初值问题, 取 h＝0.1,计算到 x=0.5，要求计算结果保留小数点后 5 位。
y y
' y2 (0)
, 1
0 x 0.5
2
3.
设方程组
0x.14
0.4x2 x1 x2
0.4 x 3 0.8 x 3