2015年广东海洋大学考博真题3701数学物理方法
广东海洋大学研究生入学考试真题2015级博士研究生入学英语考试试题
广东海洋大学2015级博士研究生入学英语考试试题Part Ⅰ: Reading Comprehension (30%) Direction: In this part, there are four passages. Read each passage carefully, and then choose the best answer from the four choices given below. Passage 1 Humans are forever forgetting that they can't control nature. Exactly 20 years ago, a Time magazine cover story announced that "scientists are on the verge of being able to predict the time, place and even the size of earthquakes". The people of quake-ruined Kobelearned last week how wrong that assertion was. None of the methods raised two decades ago have succeeded. Even now, scientists have yet to discover a uniform warning signal that precedes all quakes, let alone any sign that would tell whether the coming quake is mild or a killer. Earthquake formation can be triggered by many factors, says Hiroo Kanamori, a seismologist at the California Institute of Technology. So, finding one all-purpose warning sign is impossible. One reason: Quakes start deep in the earth, so scientists can't study them directly.If a quake precursor were found, it would still be impossible to warn humans in advance of all dangerous quakes. Places like Japan and California are filled with hundreds, if not thousands, of minor faults . It is impossible to place monitoring instruments on all of them. And these inconspicuous sites can be just as deadly as their better-known cousins like the San Andreas . Both the Kobe and the 1994 Northridge quakes occurred on small faults. Prediction would be less important if scientists could easily build structures to withstand tremors. While seismic engineering has improved dramatically in the past 10 to 15 years, every new quake reveals unexpected weaknesses in "quake-resistant" structures, says Terry Tullis, a geophysicist at Brown University. In Kobe, for example, a highway that opened only last year was damaged. In the Northridge earthquake, on the other hand, well-built structures generally did not collapse. But engineers have since found hidden problems in 120 steel-frame buildings that survived. Such structures are supposed to sway with the earth rather than crumple. They may have swayed, but the quake also unexpectedly weakened the joints in their steelskeletons. If the shaking had been longer or stronger, the buildings might have collapsed.A recent report in Science adds yet more anxiety about life on the fault lines. Researchers ran computer simulations to see how quake-resistant buildings would fare in a moderate-size tremor, taking into account that much of a quake's energy travels in a large "pulse" of focused shaking. The results: both steel-frame buildings and buildings that sit on班级：姓名： 学号：试题共页加白纸张密封线GDOU-B-11-302insulating rubber pads suffered severe damage.More research will help experts design stronger structures and possibly find quake precursors. But it is still a certainty that the next earthquake will prove once again that every fault cannot be monitored and every highway cannot be completely quake-proofed. Questions 1 to 5 are based on the passage 11. Which of the following statements is true about Kobe -------- ?A. Last week's quake occurred on small faults.B. People there believe in scientists' ability to predict earthquakes.C. Buildings there swayed with the quake rather than crumpledD. It can be expected that every fault can be monitored as a result of more research.2. The author's focus in Para. 3 is on --------A. the need for more researchB. the impossibility to predict earthquakesC. the designing of stronger structures and the finding of quake precursorsD. the impossibility of building completely quake-proofed structures3. It's impossible to avoid damages in earthquakes because --------A. scientists can't study quakes that occur deep in the earth directlyB. it's hard to build perfect "quake-resistant" structuresC. instruments cannot be placed on all of the minor faultsD. all of the above4. It is implied in the passage that --------A. well-erected structures do not collapseB. steel-frame buildings survive any earthquakeC. buildings in Northridge will probably collapse in a stronger earthquakeD. seismic engineering has improved enough for structures to resist quakes5. The best title for this passage could be --------A. Nature Is beyond Human ControlB. Earthquakes: Can We Bring Them under Control?C. New Methods and Stronger Structures to Predict and Withhold QuakesD. Can't We Predict Earthquakes?Passage 2Systematic efforts at national nutrition planning in developing countries go back barely a decade. During that brief time there has been considerable progress in establishing the extent and causes of malnutrition and what can be done to reduce it.Ten years ago, malnutrition was often thought to reflect primarily a shortage of protein (and in some cases, vitamins or minerals). Most nutrition programs concentrated on providing high-protein food to children, usually in schools. The emphasis today is different. There is now a wide measure of agreement on several broad propositions.Serious and extensive nutritional deficiencies occur in virtually all developing countries, though they are worst in low-income countries. They are usually caused by undernourishment—a shortage of food—not by an imbalance between calories and protein. There may often be shortage of specific micronutrients and of protein, especially among young children. But given the typical composition of the diets of the poor, to the extent that calorie requirements (as estimated by the FAO and the WHO) are met, it is likely that other nutritional needs will also be satisfied.Malnutririon affects old and young, male and female, urban and rural dwellers; particularly prevalent among children under five, it reduces their resistance to diseases and is a major cause of their death. In many societies, girls suffer more than boys.Malnutrition is largely a reflection of poverty; people do not have enough income for food. Given the slow income growth that is likely for poverty-stricken people in the forseeable future, large numbers will remain malnourished for decades to come.Poor nutritional practices and the inequitable distribution of food within families are also causes of malnutrition.The most effective long-term policies are those that raise the incomes of the poor, and those that raise food production per person. Other relevant policies include food subsidies, nutrition education, adding minerals or vitamins to salt and other processed foods, and increasing emphasis on producing foods typically consumed by the poor.These points will be amplified in the following discussion.Questions 6 to 10 are based on the passage 26. During the past 10 years developing countries ----------.A. have made considerable attempts to plan about nutrition on a nation-wide scaleB. have started nutrition programs that aim at providing high-protein food…tochildren in schoolC. have taken effective measures to reduce malnutrition everywhereD. have reached an agreement to fight malnutrition by combining efforts7. Which one of the following is NOT mentioned as a cause of malnutrition?A. PovertyB. Poor nutritional practiceC. Inequitable distribution of foodD. Inadequate nutrition education8. With regard to the future, the author tends to believe that ----------.A. malnutrition will be largely eliminated in some developing countries in the nextfew yearsB. the developed countries are planning to offer some help to reduce malnutritionC. many people still have to suffer from malnutrition in the near futureD. people’s income in developing countries will grow rapidly in the foreseeablefuture9. “Nutrition education” is mentioned in the passage as ----------A. one of the most effective policies to reduce malnutrition in the long termB. one of the secondary measures of reducing malnutritionC. one of the ways to improve education in developing countriesD. one of the efforts that has been made during the past 10 years10. It can be predicted from the last sentence of the passage that the author is going totalk in detail about ----------.A. policies for reducing malnutritionB. the causes for malnutritionC. how to raise the incomes of the poorD. producing foods typically consumed by the poorPassage 3The chief purpose of work is not to produce things but to build the man. It is not so important what shape or form our work may take; what is vitally important is our attitude toward that work.Even if the particular duty is one which doesn’t seem worth doing, if you must do it, it is important to do it right. Even if no one else will ever know whether you did it right or not, you will know. By making a commitment to quality work, you make a commitment to yourself to develop your abilities and self-respect, to do the best you can do and be the best you can be. When you do as little as possible or just enough to get by, you are not merely cheating your employer, your customers, your clients and your co-workers, but most importantly, you cheat yourself. To cheat yourself out of an opportunity to develop pride and self-worth. You cheat yourself out of an opportunity to meet a challenge and develop your own inner powers and abilities. You may be able to get away with cheating others, but you never get away with cheating yourself.Thus, the key is a commitment to yourself to use every possible opportunity for self-development and treat every work assignment, no matter how small or boring, as a challenge that can be used in your development.Work is a projection of self. Consciousness can regard any job as a potential opportunity for self-expression, for play, for creativity, for the furtherance of social objectives, and it can arrange the factors in the job so that they form a means of self-expression.Most jobs contain at least some limited options for creativity. To the extent that any job can be done in different ways, the job presents you with an opportunity to project your unique abilities and values into that job. Any type of communication, written or spoken, presents a significant opportunity for creative expression. Even if your efforts are reviewed and must be toned down to fit into the mold of your organization, there is always a slight opening through which you can project your unique personality. Use these opportunities to express and confirm your existence.Questions 11 to 15 are based on the passage 311. The most important thing about work is _________.A. to produce thingsB. the shape one’s work takesC. the amount of money it makesD. one’s attitude towards the work12. If the work doesn’t seem worth doing, you should _________.A. give it upB. tell others to do itC. stop in the middleD. perform it carefully13. What can work assignments offer people?A. An opportunity to develop oneselfB. A chance to get away with cheating themselvesC. Few options for creativity.D. A way to get rid of your unique personality.14. Which of the following statements is not true?A. Sometimes you have to adjust yourself to your workB. There is space for you to show your creativity.C. Work must be done in one way in order to be the most efficient.D. You may never cheat yourself.15. The main idea of the passage is _________.A. how to improve your creativityB. the importance of projecting your values into your jobC. when to express yourselfD. how to change one’s personalityPassage 4The study of genetics has given rise to a profitable new industry called biotechnology. As the name suggests, it blends biology and modern technology through such techniques as genetic engineering. Some of the new bi0tech companies, as they are called, specialize in agriculture and are working enthusiastically to patent seeds that give a high yield, that resist disease drought and frost, and that reduce the need for hazardous chemicals. If such goals could be achieved, it would be most beneficial. But some have raised concerns about genetically engineered crops.“In nature, genetic diversity is created within certain limits,” says the book Genetic Engineering, Food, and Our Environment. “A rose can be crossed with a different kind of rose, but a rose will never cross with a potato.... Genetic engineering, on the other hand, usually involves taking genes from one species and inserting them into another in an attempt to transfer a desired property or character. This could mean, for example, selectinga gene which leads to the production of a chemical with antifreeze properties from an arctic fish, and joining it into a potato or strawberry to make it frost-resistant. It is now possible for plants to be engineered with genes taken from bacteria, viruses, insects, animals or even humans.” In essence, then, biotechnology allows humans to break the genetic walls that separate species.Like the green revolution, what some call the gene revolution contributes to the problem of genetic uniformity-- some say even more so because geneticists can employ techniques such as cloning and tissue culture, processes that produce perfectly identical copies, or clones. Concerns about the erosion of biodiversity, therefore, remain. Genetically altered plants, however, raise new issues, such as the effects that they may have on us and the environment. “We a re flying blindly into a new era of agricultural biotechnology with high hopes, few constraints, and little idea of the potential outcomes,” said science writer Jeremy Rifkin.Questions 16 to 20 are based on the passage 416. According to the author, biotech companies are _________.A. mostly specialized in agricultureB. those producing seeds of better propertiesC. mainly concerned about the genetically engineered cropsD. likely to have big returns in their business17. Now biotech products are made _________.A. within the limits of natural geneticsB. by violating laws of natural geneticsC. without the interference of humansD. safer than those without the use of biotechnology18. In nature, genetic diversity is created _________.A. by mixing different speciesB. within the species itselfC. through natural selectionD. through selection or contest19. According to the author, with the development of biotechnology _________.A. the species of creatures will be reducedB. our living environment will be better than it is nowC. humans will pay for its side effectD. we will suffer from fewer and fewer diseases20. The author's attitude towards genetic engineering can best be described as _________.A. optimisticB. PessimisticC. concernedD. suspiciousPassage 5Computers have been taught to play not only checkers, but also championship chess, which is a fairly accurate yardstick for measuring the computer’s progress in the ability to learn from experie nce. Because the game requires logical reasoning, chess would seem to be perfectly suited to the computer .all a programmer has to do is give the computer a program evaluating the consequences of every possible response to every possible move, and the computer will win every time. In theory this is a sensible approach; in practice it is impossible. Today, a powerful computer can analyze 40 000 moves a second. That is an impressive speed. But there are an astronomical number of possible moves in chess—literally trillions. Even if such a program were written (and in theory it could be ,given enough people and enough time), there is no computer capable of holding that much data. Therefore, if the computer is to compete at championship levels, it must be programmed to function with less than complete data. It must be able to learn from experience, to modify its own programm, to deal with a relatively unstructured situation—in a word, to “think” for itself . In fact, this can be done. Chess-playing computers have yet to defeat world champion chess players, but several have beaten human players of only slightly lower ranks. The computers have had programs to carry them through the early, mechanical stages of their chess games. But they have gone on from there to reason and learn, and sometimes to win the game.There are other proofs that computers can be programmed to learn, but this example is sufficient to demonstrate the point. Granted , winning a game of chess is not an earthshaking event even when a computer does it . But there are many serious human problems which ban be fruitfully approached as games. The Defense Department uses computers to play war games and work out strategies for dealing with international tensions. Other problems—international and interpersonal relations , ecology and economics , and the ever-increasing threat of world famine—can perhaps be solved by the joint efforts of human beings and truly intelligent computers .Questions 21 to 25 are based on the passage 521.T he purpose of creating chess-playing computers is __________A to win the world chess championB to pave the way for further intelligent computersC to work out strategies for international warsD to find an accurate yardstick for measuring computer progress22 .Today , a chess-playing computer can be programmed to ________A give trillions of reponses in a second to each possible move and win the gameB function with complete data and beat the best playersC learn from chess-playing in the early stage and go on to win the gameD evaluate every possible move but may fail to give the right response each time23. For a computer to “think” , it is necessary to ________A mange to process as much data as possible in a secondB program it so that it can learn from its experiencesC prepare it for chess-playing firstD enable it to deal with unstructured situations24 .The author’s attitude towards the Defense Department is____A criticalB unconcernedC positiveD negative25. In the author’s opinion,______A winning a chess game is an unimportant eventB serious human problems shouldn’t be regarded as playing a gameC ecological problems are more urgent to be solvedD there is hope for more intelligent computersPassage 6The wor ld has become so complicated that we’ve lost confidence in our ability to understand and deal with it. But common sense is useful now as it ever was. No amount of expertise substitutes for an intimate knowledge of a person or a situation. At times you just have to trust your own judgement. It almost cost me my life to learn that. I was reading a book one day, idly scratching the back of my head, when I noticed that, in one particular spot, the scratching echoed inside my head like fingernailson an empty ca rdboard carton, I rushed off to my doctor.“Got a hole in your head, have you?” he teased. “It’s nothing—just one of those little scalp nerves sounding off.”Two years and four doctors later, I was still being told it was nothing. To the fifth doctor. I said, almost in desperation,”But I live in tis body. I know something’s different.”“If you won’t take my word for it,I’ll take an X-ray and prove it to you,” he said.Well, there it was, of course, the tumor that had made a hole as big as an eye socket in the back of my skull. After the operation, a young resident paused by my bed. ”It’s a good thing you’re so smart,” he said.” Most patient die of these tumors because we don’t know they’re there until it is too late.”I’m really not so smart. And I’m too docile i n the face of authority. I should have been more aggressive with those first four doctors. It’s hard to question opinions delivered with absolute certainty. Experts always sound so sure. Nevile Chamberlain, the British prime minister, was positive, just before the start of World War II, that there would be “peace for our time.” Producer Irving Thalberg did not hesitate to advise Louis B. Mayer against buying the rights to Gone With the Wind because “no Civil War picture ever made a nickel.” Even Abraham Lin coln surely believed it when he said in his Gettysburg Address:” The world will little note, nor long remember, what we say here…”We should not, therefore, be intimidated by experts. When it’s an area we really know about—our bodies, our families, our houses—let’s listen to what the experts say, then make up our own minds.Questions 26 to 30 are based on the passage 61. We have to trust our own judgement since ____A. not all of us have acquired reliable expertiseB. experts often lose their common senseC. experts may sometimes fail to give good adviceD. intimate knowledge of a person is not to be substituted for by expertise2. While reading one day, the author______A. found a hole at the back of his headB. heard a scratching sound from a cartonC. noticed some echo from his head where he was scratchingD. noticed a sound coming out from his head28 “tease” in paragraph 3 means______A. to make fun ofB. to comfortC. to replyD. to disbelieve29 The author didn’t think he was smart(para.7)because____A. he had already suffered for two yearsB. he had not been able to put up with the painC. he had believed too much in expertiseD. he had formed too strong an opinion of himself30 .It happens that the examples given by the author_____A. all concern with warsB. are taken from modern American historyC. have become popular themes in moviesD. have American Civil War as the backgroundPart Ⅱ Multiple Choice (15%)Direction: In this part, there are 30 statements. Below each statement are four words or phrases marked A, B, C and D. Choose one word or phrase that best completesthe statement.31.As a teacher you should not show -------- towards any of your students.A. pleasureB. favorC. preferenceD. inclination32. Traffic is -------- by police at every intersection.A. enforcedB. imposedC. limitedD. regulated33. The classroom is 30 feet -------- and 20 feet in breadth.A. at lengthB. in lengthC. as for lengthD. to length34. Theodore Roosevelt was a -------- man; he was successful as a statesman, soldier,sportsman, explorer, and author.A. ableB. capableC. skilfulD. versatile35. If you are to be accepted as a member of the club you must -------- by its rules.A. agreeB. abideC. confirmD. conform36. He gave a -------- account of what has happened.A. discomfortedB. distortedC. dismissedD. discovered37. The speaker was a long way --------.A. on the trackB. in the trackC. of the trackD. off the track38. If the body is robbed this way for too long, vital organs --------.A. break downB. break outC. break awayD. break in39. My pencil is -------- to a stump.A. wornB. worn downC. worn offD. worn out40. After 10 years’ efforts, the farmers have ------- the waste land -------- paddy fields.A. turned … outB. turned … overC. turned … intoD. turned … down41. What you say now is not -------- with what you said last week.A. consistentB. persistentC. permanentD. insistent42. They have decided to -------- physical punishment in all local school.A. put awayB. break away fromC. do away withD. pass away43. The price of the coal will vary according to how far it has to be transported and howexpensive the freight -------- are.A. paymentsB. chargesC. fundsD. prices44. Professor Hawking is -------- as one of the world’s greatest living physicists.A. dignifiedB. clarifiedC. acknowledgedD. illustrated45.Individual sports are run by over 370 independent governing bodies whose functionsusually include -------- rules, holding events, selecting national teams and promoting international links.A. drawing onB. drawing inC. drawing upD. drawing down46. Within seconds, the experienced instructor -------- the situation and decided to attemptrescue.A. assumedB. assuredC. assessedD. affirmed47. The captain of the ship -------- the passengers that there was no danger.A. securedB. ensuredC. assuredD. guaranteed48. A very large cat was watching us intently from the top of a -------- car.A. movelessB. stationeryC. motionlessD. stationary49. The police are -------- a war against crime in the city.A. committingB. breakingC. undertakingD. waging50. Black Death was -------- in England in the summer of 1348 without any warning and,most importantly, without any cure.A. currentB. circulatingC. prevailingD. universal51. He -------- the level of unemployment in China.A. concernsB. has concernedC. is concerning aboutD. is concerned about52. Computer software -------- some 70 percent of our range of products.A. accounts forB. accounts outC. counts onD. counts for53. They tried to ------- the project from being destroyed for shortage of money.A. get inB. leave offC. head offD. bring about54. He spoke clearly and -------- and we could understand every word he said.A. distinguishedB. distinguishableC. distinctlyD. distinctively55. The Bank of England has taken further steps to -------- control over the value of thepound.A. resumeB. resurrectC. retainD. retard56. Except for some colleges --------- by the Catholic church, all colleges and universitiesin the United States, public and private, are governed by a board of trustees composed primarily of laymen.A. elevatedB. grantedC. patentedD. sponsored57. Today, household chores have been made much easier by electrical --------.A. facilitiesB. equipmentC. appliancesD. utilities58. Boys who try to -------- a teacher are not sincere.A. make in forB. make up forC. make up toD. make on to59. Doctors are often caught in a -------- because they have to decide whether they shouldtell their patients the truth or not.A. puzzleB. perplexityC. dilemmaD. bewilderment60. the fits aliving67 68is to send it into space, to the sun, 69 it would be burned. Other scientists suggest that this polluting material be buried thousands of meters under the earth’s surface. Such underground areas must be free of possible earthquakes.Advances are being made. But it may still be many years 70 this problem could be finally settled.61. A．on B．with C．to D．in62. A．drained B．dumped C．discharged D．disposed63. A．drops off B．gives off C．puts off D．breaks off64. A．deadly B．unfavourable C．painful D．efficient65. A．reasonably B．rationally C．regularly D．safely66. A．scattering B．preserving C．conserving D．discarding67. A．in B．with C．against D．on68. A．remove B．deliver C．transport D．spread69. A．where B．when C．there D．now that70. A．until B．when C．before D．afterPart Ⅳ: Translation (30%)Directions: T ranslate the following English paragraph into Chinese.Born inland in rivers and streams, pacific salmons swim for thousands of kilometers to reach the open ocean, only to return years later to the same freshwater sites where they spawn and then die. Now scientists have further evidence that the earth's magnetic field is helping the fish to make this epic migration. A team from the US found exposing the fish to different magnetic fields make them change the direction they were swimming in. The researchers say, this is because the Earth's magnetic field different intensity and angle depending on new position on the planets, and the salmon are using this information to establish where they are and where they need to go.Directions: T ranslate the following Chinese paragraph into English.对全球变暖后果的研究结果表明，全世界鱼的数量在未来50年可以会急剧下降。
2015年广东海洋大学博士英语考试试题考博真题试题
第 1 页 共 18 页广东海洋大学2015级博士研究生入学英语考试试题题 号 一 二 三 四 五 总分 阅卷教师 各题分数 30 15 10 30 15 实得分数 Part Ⅰ: Reading Comprehension (30%) Direction: In this part, there are four passages. Read each passage carefully, and then choose the best answer from the four choices given below. Passage 1 Humans are forever forgetting that they can't control nature. Exactly 20 years ago, a Time magazine cover story announced that "scientists are on the verge of being able to predict the time, place and even the size of earthquakes". The people of quake-ruined Kobe learned last week how wrong that assertion was. None of the methods raised two decades ago have succeeded. Even now, scientists have yet to discover a uniform warning signal that precedes all quakes, let alone any sign that would tell whether the coming quake is mild or a killer. Earthquake formation can be triggered by many factors, says Hiroo Kanamori, a seismologist at the California Institute of Technology. So, finding one all-purpose warning sign is impossible. One reason: Quakes start deep in the earth, so scientists can't study them directly.If a quake precursor were found, it would still be impossible to warn humans in advance of all dangerous quakes. Places like Japan and California are filled with hundreds, if not thousands, of minor faults . It is impossible to place monitoring instruments on all of them. And these inconspicuous sites can be just as deadly as their better-known cousins like the San Andreas . Both the Kobe and the 1994 Northridge quakes occurred on small faults. Prediction would be less important if scientists could easily build structures to withstand tremors. While seismic engineering has improved dramatically in the past 10 to 15 years, every new quake reveals unexpected weaknesses in "quake-resistant" structures, says Terry Tullis, a geophysicist at Brown University. In Kobe, for example, a highway that opened only last year was damaged. In the Northridge earthquake, on the other hand, well-built structures generally did not collapse. But engineers have since found hidden problems in 120 steel-frame buildings that survived. Such structures are supposed to sway with the earth rather than crumple. Theymay have swayed, but the quake also unexpectedly weakened the joints in their steel skeletons. If the shaking had been longer or stronger, the buildings might have collapsed.A recent report in Science adds yet more anxiety about life on the fault lines. Researchers ran computer simulations to see how quake-resistant buildings would fare in a moderate-size tremor, taking into account that much of a quake's energy travels in a large "pulse" of focused shaking. The results: both steel-frame buildings and buildings that sit on班级：姓名：学号：试题共页加白纸张 密封线GDOU-B-11-302。
中国海洋大学数学物理方法(数物)考试重点
重点内容第一章● 复数的模与幅角；● 复数的代数、三角及指数表示方法； Euler 公式cos sin i e i θθθ=+12111112(),()Arg z z Argz Argz z Arg Argz Argz z =+=-方根公式：arg 22,0,1,, 1.iArgz z k k iinnnek n πθπ++===-● 复函数的连续性, 极限 (罗必达法则仍成立) ● 区域：连通的开集；单（多）连通区域。
● 函数可导的判定, 解析的概念， 柯西-黎曼条件（,x y y x u v u v ==-）， ● 调和函数的定义，如何求共轭调和函数， 共轭对:223223,23,3cos ,sin x x x y xy x xy x y y e y e y--- ● 初等解析函数（特殊的性质，如正、余弦函数无界；指数函数是以2i π为周期的）(cos sin ),sin ,cos 22iz iz iz izzxe e e e e e y i y z z i ---+=+==，ln ,b bLna Lnz z iArgz a e =+=● 函数()f z u iv =+在单连通区域D 上解析⇔,u v 在D 上可微且处处满足柯西黎曼条件⇔,u v 在D 上调和且处处满足柯西黎曼条件（或v 是u 的共轭调和函数）⇔f 在D 上连续且沿任意简单曲线C D ⊂的积分为零⇔f 在D 上任意点z 处有幂级数展式● 沿给定路线的积分：直线段或圆弧。
此时函数一般不解析，如解析就求原函数直线段的参数方程：12()(1),[0,1]z t t z tz t =-+∈，其中12,z z 分别为起点与终点圆弧的参数方程：(),[,],i z re a θθθαβ=+∈其中,r a 分别为半径与弧心。
● 柯西定理:函数f 在围线C 上连续，C 内部解析，则0Cfdz =⎰。
判定是否解析？● 复围线柯西积分定理iC Cfdz fdz =∑⎰⎰● 柯西积分公式：f 在围线C 内部解析，a 在C 内部，则()()1()2()()2()!C n n C f z dz if a z a f z i dz f a n z a ππ+=-=-⎰⎰ ● 最大模原理:非常函数的解析函数的最大模不能在内部取得刘维尔定理：有界的整函数必是常函数● 收敛半径：通项的绝对值不超过1；条件收敛点必在收敛圆周上● 泰勒、洛朗展式 必考1,()11()n n f f z f z ∞==<-∑ (),!nf z n f en ∞==∑sin ,cos z z● 解析函数的零点是孤立的；零点的阶数, (加减乘除复合) 1阶 sin 1tan z z z e z -2阶21cos 2z z - ; 3阶3sin 6z z z - ● 解析函数具有唯一性，即不可能有两个不同的解析函数在一列有极限的点列上的取值一样。
广东海洋大学大学物理试卷
一、判断对错题（每小题1分，共6分）1）当刚体所受合外力为零时，一定处于平衡状态.2）处于静电平衡状态下的实心导体，内部电场强度处处为零. 3）电场一定是保守场. 4）磁感线一定是闭合曲线.5）回路中通过的电流越强，产生的自感电动势越大.6）狭义相对论不适用于低速运动的物体.二、填空题（每小题2分，共20分）1）一质量为m 的物体，原来以速率v 向北运动，它突然受到外力打击，变为向西运动，速率仍为v ，则外力冲量的大小为（ ）. 2）人造卫星在万有引力作用下，以地球中心为焦点做椭圆运动.相对于地心而言，卫星的（ ）守恒.（选填动量或角动量）3）要想用小电容组合成大电容，应将电容器（ ）.（选填串联或并联） 4）电容器两极板间的电势差增大一倍时，电场能增大到原来的（ ）倍. 5）将一带正电荷的导体球A 移近另一个不带电的导体球B ，则电势较高的球是（ ）.（选填A 或B ）6）位移电流密度的实质是变化的（ ）.（选填电场或磁场）7）一半径为R 的平面圆形导体线圈通有电流I ，放在均匀磁场B中，所受到的最大磁力矩是（ ）.8）根据狭义相对论的基本原理，得到惯性系之间的坐标变换，称为（ ）.（选填伽里略变换或洛仑兹变换）9）当粒子的动能等于它的静止能量时，它的运动速度为（ ）.（光速为c ） 10）在xOy 平面内有一运动的质点，其运动方程为r=10cos5t i +10sin5t j(SI )，则t 时刻其切向加速度的大小为（ ）.三、单选题（每小题3分，共24分） 1）一物体作圆周运动，则（ ）A 、加速度方向必定指向圆心；B 、切向加速度必定为零；C 、法向加速度必等于零；D 、加速度必不为零。
2）一力学系统由两个质点组成，它们之间只有引力作用， 若两质点所受外力的矢量和为零，则此系统( )A 、动量、机械能以及对一轴的角动量守恒；B 、动量、机械能守恒，但角动量是否守恒不能确定；C 、动量守恒、但机械能和角动量是否守恒不能确定；D 、动量和角动量守恒、但机械能是否守恒不能确定。
广东海洋大学=数学物理方法期末复习-名词解释
第一章1.定解条件：边界条件和初始条件统称为定解条件。
边界条件又有Dirichlet 边界条件（也称第一类边界条件）、Neumann 条件,也称第二类边界条件、Robin 边界条件，第三类边界条件。
P3-42.定解问题：一个微分方程（组）和相对应的定解条件合在一起就构成了一个定界问题。
又分有初始问题（Cauchy 问题），只有初始条件没有边界条件的定界问题；边值问题，只有边界条件没有初始条件的定解问题；混合问题，两者都有。
对于边值问题，根据边界条件不同，又可以分为第一、第二和第三边值问题。
P113.定解问题的适定性从数学上看，判断一个定解问题是否合理，即是否能够完全描述给定的物理状态，一般来说有一下三个标准：⑴解的存在性：所给定的定解问题至少存在一个解。
⑵解的惟一性：所给定的定解问题至多存在一个解。
⑶解的稳定性：当给定条件以及方程中的系数有微小变动时，相应的解也只有微小变动。
定解问题解的存在性、惟一性和稳定性统称为定解问题的适定性。
P124.Dirichlet 、Neumann 定解问题定解条件只有Dirichlet 条件没有初始条件的定解问题叫做Dirichlet 定解问题。
定解条件只有Neumann 条件没有初始条件的定解问题叫做Neumann 定解问题。
5.热传导Fourier 定律：热量以传导形式传递时，单位时间内通过单位面积所传递的热量与当地温度梯度成正比。
对于一维问题，可表示为:Φ＝-λA(dt/dx)其中Φ为导热量，单位为W,λ为导热系数,A 为传热面积，单位为m2, t 为温度，单位为K, x 为在导热面上的坐标。
6.Hooke 弹性定律：在弹性限度内，物体的形变跟引起形变的外力成正比。
χχεσE =7.发展方程：所描述的物理过程随时间而演变,如:波动方程、热传导方程等8.在热传导方程中，如果温度分布稳定，即0u t =，则三维热传导方程f u a u 2t +∆=变为 0f u =+∆，此方程为Poisson 方程。
广东海洋大学2015-2016学年第二学期《大学物理》课程试题
第 1 页 共 10 页广东海洋大学2015——2016学年第二学期《大学物理》课程试题课程号：1910003x1☑ 考试 □ A 卷☑ 闭卷□ 考查□ B 卷□ 开卷① 题号中标有（力）的，学质点力学的学生必做；标有（热）的学热学的学生必做；未标有（力）和（热）的，所有学生必做。
② 在无特别说明时，均使用国际单位制。
③ 物理常数视为已知，且必须用与教材一致的符号来表示。
一、 选择题（单选题，每题3分，共30分）1．（力）一质点沿x 轴运动，其运动方程为x=3t 2-2t 3(SI)，当质点的加速度为零时，其速度大小为[ ] A 、12m.s -1； B 、6 m.s -1； C 、3 m.s -1；D 、1.5 m.s -1 1．（热）以理想气体为工作物质的卡诺热机，设其高、低温热源的温度分别为1T 和2T ，则卡诺热机的效率为[ ]。
A 、121T T T -； B 、221T T T -； C 、21T T ； D 、12T T。
2．（力）在一只半径为R 的半球形光滑碗内,有一粒质量为m班级：姓名：学号：试题共页加白纸张密封线GDOU-B-11-302第 2 页 共 10 页的小钢球,当小球以角速度ω在水平面内沿碗内壁作匀速圆周运动时,它距碗底的高度H 为[ ] A 、2ωgR -；B 、2ωgR +； C 、ωgR -； D 、ωg R +2．（热）设p v 、v 和rms v 分别为处于平衡态时某气体分子的最概然速率、平均速率和方均根速率。
则[ ]。
A 、p v >v >rms v ；B 、v >rms v >p v ；C 、rms v >p v >v ；D 、rms v >v >p v 。
3．（力）一质点受力i x F23= N ，沿x 轴正方向运动，在x=0到x=2m 过程中，该力作的功为：[ ] A 、8J B 、12J C 、16J D 、24J3．（热） 一定量的理想气体，在温度不变的条件下，当体积增大时，分子的平均碰撞频率Z 和平均自由程λ的变化情况是[ ]A 、 Z 减小而λ不变．B 、Z 减小而λ增大．C 、 Z 增大而λ减小．D 、Z 不变而λ增大．4.细棒可绕光滑轴转动，该轴垂直地通过棒的一个端点，今使棒从水平位置开始下摆，在棒转到竖直位置的过程中，下第 3 页 共 10 页述说法正确的是[ ]A 、角速度从小到大，角加速度从大到小；B 、角速度从小到大，角加速度从小到大；C 、角速度从大到小，角加速度从小到大；D 、角速度从大到小，角加速度从大到小。
2015年广东海洋大学数学考研真题
2015年广东海洋大学数学考研真题（请将答案写在答题纸上，写在试卷上不给分。
本科目满分150分）一、填空题（每小题4分，满分40分）1、23lim 1x x x →∞⎛⎫+= ⎪⎝⎭ .2、函数2256x y x x -=-+的间断点为 .3、曲线32()3f x x x =+的凹的区间 .4、函数(0)x y aa =>的n 阶导数()n y = .5、2562(sin 1)x x dx -+=⎰ .6、21cos 20lim t x x e dt x -→=⎰ .7、由曲线3y x =和2y x =所围成的平面图形的面积 . 8、设arctan y z x =, 则2z x y∂=∂∂ .9、设2ln()z x xy =, 则全微分dz = .10、设平面区域D ：222x y a +≤，则积分22x y D e dxdy --⎰⎰= .二、解答下列各题（每小题8分，满分80分） 1、求极限 201sinlim tan x x x x →.2、求不定积分3tan sec x xdx ⎰.3、求不定积分arccos xdx ⎰.4、计算定积分22ππ-⎰. 5、求函数y x =在区间[5,1]-上的最大值与最小值.6、设21lim 51x x mx n x →++=-，求常数,m n 的值.7、设sin 1cos x t t y t =-⎧⎨=-⎩确定了)(x y y =，求22dx y d .8、设2sin y x x =，求(6)(0)y .9、求由方程2sin 0xy y e x +-=确定的函数)(x y y =的微分dy .10、计算二重积分22y D x e dxdy -⎰⎰，其中D 是由直线0,1x y ==及y x =围成的区域.三、证明不等式：当01x <<时，2sin 12xx e x -+<+. (满分10分）四、在边长为a 的一块正方形铁皮的4个角上各截出一个小正方形，将4边上折焊成一个无盖方盒，问截去的小正方形边长为多大时，方盒的容积最大？ (满分10分）五、设函数2,1,(),1x x f x ax b x ⎧≤=⎨+>⎩为了使函数()f x 在1x =点处连续且可导，,a b 应取什么值？ (满分10分）。
广东海洋大学14-15第二学期高数期末考试试题A,B卷(含答案)汇编
广东海洋大学2014—2015学年第二学期《高等数学》课程试题课程号：19221101x2□√考试□√A 卷□√闭卷□考查□B 卷□开卷题号一二三四五六七八九十总分阅卷教师各题分数2118357685100实得分数一、填空题（共21分每小题3分）1．曲线⎩⎨⎧=+=012x y z 绕z 轴旋转一周生成的旋转曲面方程为122++=y x z ．2．直线35422:1z y x L =--=-+与直线⎪⎩⎪⎨⎧+=+-==tz t y tx L 72313:2的夹角为2π．3．设函数22232),,(z y x z y x f ++=，则=)1,1,1(grad f )6,4,2(．4．设级数∑∞=1n n u 收敛，则=∞→n n u lim 0．5．设周期函数在一个周期内的表达式为⎩⎨⎧≤<+≤<-=,0,10,0)(ππx x x x f 则它的傅里叶级数在π=x 处收敛于21π+．6．全微分方程0d d =+y x x y 的通解为Cxy =．7．写出微分方程xe y y y =-'+''2的特解的形式xaxe y =*．二、解答题（共18分每小题6分）1．求过点)1,2,1(-且垂直于直线⎩⎨⎧=+-+=-+-02032z y x z y x 的平面方程．班级：姓名：学号：试题共6页加白纸3张密封线GDOU-B-11-302解：设所求平面的法向量为n，则{}3,2,1111121=--=k j i n(4分)所求平面方程为32=++z y x (6分)2．将积分⎰⎰⎰Ωv z y x f d ),,(化为柱面坐标系下的三次积分，其中Ω是曲面)(222y x z +-=及22y x z +=所围成的区域．解：πθ20 ,10 ,2 :2≤≤≤≤-≤≤Ωr r z r (3分)⎰⎰⎰Ωv z y x f d ),,(⎰⎰⎰-=221020d ),sin ,cos (d d r rzz r r f r r θθθπ(6分)3．计算二重积分⎰⎰+-=Dy x y x eI d d )(22，其中闭区域.4:22≤+y x D 解⎰⎰-=2020d d 2rr eI r πθ⎰⎰--=-20220)(d d 212r e r πθ(4分)⎰-⋅-=202d 221r e π)1(4--=e π(6分)三、解答题（共35分每题7分）1．设vue z =，而22y x u +=，xy v =，求z d ．解：)2(232y y x x e y ue x e xv v z x u u z x z xy v v ++=⋅+⋅=∂∂⋅∂∂+∂∂⋅∂∂=∂∂(3分))2(223xy x y e x ue y e yv v z y u u z y z xy v v ++=⋅+⋅=∂∂⋅∂∂+∂∂⋅∂∂=∂∂(6分)yxy x y e x y y x x e z xy xy d )2(d )2(d 2332+++++=(7分)2．函数),(y x z z =由方程0=-xyz e z所确定，求yzx z ∂∂∂∂,．解：令xyz e z y x F z-=),,(，(2分)则,yz F x -=,xz F y -=,xy e F z z -=(5分)xye yzF F x z zz x -=-=∂∂，xye xzF F y z zz y -=-=∂∂．(7分)3．计算曲线积分⎰+-Ly x x y d d ，其中L 是在圆周22x x y -=上由)0,2(A 到点)0,0(O 的有向弧段．解：添加有向辅助线段OA ，有向辅助线段OA 与有向弧段OA 围成的闭区域记为D ，根据格林公式⎰⎰⎰⎰+--=+-OA DL yx x y y x y x x y d d d d 2d d (5分)ππ=-⋅=022(7分)4．设曲线积分⎰++Lx y x f x y x f e d )(d )]([与路径无关，其中)(x f 是连续可微函数且满足1)0(=f ，求)(x f ．解：由xQ y P ∂∂=∂∂得)()(x f x f e x'=+，即xex f x f =-')()((3分)所以)d ()(d d )1(C x e e e x f x x x+⋅=⎰⎰---⎰)(C x e x +=，(6分)代入初始条件，解得1=C ，所以)1()(+=x e x f x．(7分)5．判断级数∑∞=12)!2()!(n n n 的敛散性．解：因为)!2()!()!22(])!1[(limlim 221n n n n u u n nn n ++=∞→+∞→(3分))12)(22()1(lim 2+++=∞→n n n n 141<=(6分)故该级数收敛．(7分)四、（7分）计算曲面积分⎰⎰∑++y x z x z y z y x d d d d d d ，其中∑是上半球面221z y x --=的上侧．解：添加辅助曲面1,0:221≤+=∑y x z ，取下侧，则在由1∑和∑所围成的空间闭区域Ω上应用高斯公式得⎰⎰∑++y x z x z y z y x d d d d d d ⎰⎰∑+∑++=1d d d d d d yx z x z y z y x ⎰⎰∑++-1d d d d d d yx z x z y z y x (4分)d 3-=⎰⎰⎰Ωv (6分)34213π⋅⋅=π2=．(7分)五、（6分）在半径为R 的圆的内接三角形中，求其面积为最大的三角形．解：设三角形各边所对圆心角分别为z y x ,,，则π2=++z y x ，且面积为)sin sin (sin 212z y x R A ++=，令)2(sin sin sin πλ-+++++=z y x z y x F (3分)由⎪⎪⎩⎪⎪⎨⎧=++=+==+==+=πλλλ20cos 0cos 0cos z y x z F y F x F z y x (4分)得32π===z y x ．此时，其边长为R R 3232=⋅．由于实际问题存在最大值且驻点唯一，故当内接三角形为等边三角形时其面积最大．(6分)六、（8分）求级数∑∞=1n nnx 的收敛域，并求其和函数．解：1)1(lim lim1=+==∞→+∞→nn a a R n n n n ，故收敛半径为1=R ．(2分)当1-=x 时，根据莱布尼茨判别法，级数收敛；当1=x 时，级数为调和级数，发散．故原级数的收敛域为)1,1[-．(5分)设和为)(x S ，即∑∞==1)(n nnx x S ，求导得∑∞=-='11)(n n x x S x-=11，(6分)再积分得⎰'=x xx S x S 0d )()(x xxd 110⎰-=)1ln(x --=，)11(<≤-x (8分)七、（5分）设函数)(x f 在正实轴上连续，且等式⎰⎰⎰+=yx x ytt f x t t f y t t f 111d )(d )(d )(对任何0,0>>y x 成立．如果3)1(=f ，求)(x f ．解：等式两边对y 求偏导得)(d )()(1y f x t t f y x f x x+=⎰(2分)上式对任何0,0>>y x 仍成立．令1=y ，且因3)1(=f ，故有⎰+=xx t t f x xf 13d )()(．(3分)由于上式右边可导，所以左边也可导．两边求导，得3)()()(+=+'x f x f x f x 即)0(3)(>='x xx f ．故通解为C x x f +=ln 3)(．当1=x 时，3)1(=f ，故3=C ．因此所求的函数为)1(ln 3)(+=x x f ．(5分)广东海洋大学2014—2015学年第二学期《高等数学》课程试题课程号：19221101x2□√考试□A 卷□√闭卷□考查□√B 卷□开卷题号一二三四五六七八九十总分阅卷教师各题分数271577181214100实得分数一、填空题.（每小题3分，共27分）1.二元函数2241y x z --=的定义域是}4),({22<+y x y x 2.设向量)1,2,1(-=→a ，)2,1,1(=→b ，则→→⨯b a =(-5,-1,3)3.过点（1，1，1）且以)11,4,1(-=→n 为法线向量的平面方程为6114=+-+z y x 4.将yoz 坐标面上的抛物线z y 22=绕z 轴旋转所成的曲面方程是:zy x 222=+5.极限=++→→2222001sin)(lim yx y x y x 06.设函数)ln(xy z =，则yz∂∂=y 17.曲线32,1,t z t y t x =-==在点(1,0,1)处的切线方程是：31121-=-=-z y x 8.改变累次积分I=⎰⎰101),(ydx y x f dy的次序为I =⎰⎰10),(xdyy x f dx 9.微分方程xy y 2='的通解是2x ce二、单项选择题（每小题3分，共15分）班级：姓名：学号：试题共5页加白纸3张密封线GDOU-B-11-3021．设函数⎰=Φ3)()(x a dt t f x ，则=Φ')(x （D ）（A）)(x f （B）)(3x f （C）)(32x f x （D）)(332x f x 2.设函数y x z sin 2=，则yx z∂∂∂2等于（B ）(A)y x cos 2+(B)y x cos 2(C)x2(D)ycos 3．直线11121-+==-z y x 与平面1=+-z y x 的位置关系是（B ）（A）垂直（B）平行（C）夹角为4π（D）夹角为4π-4．设D 是第二象限内的一个有界区域，而且10<<y ，记⎰⎰=Dyxd I σ1，⎰⎰=Dxd y I σ22，⎰⎰=Dxd y I σ213，则321,,I I I 之间的大小顺序为（C ）（A）321I I I ≤≤（B）312I I I ≤≤（C）213I I I ≤≤（D）123I I I ≤≤5．微分方程0ln =-'y y y x 是（A ）（A）变量分离方程（B）齐次方程（C）一阶齐次线性微分方程（D）一阶非齐次线性微分方程三．计算由两条抛物线x y =2，2x y =所围成的图形的面积。
广东海洋大学食品微生物学2014,2015年考博真题
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博
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题
广东海洋大学
20名称：3401食品微生物学满分100
（所有答案写在答题纸上，写在试卷上不给分，答完后连同试卷一并交回。）
1.细菌的芽孢有何特点？举例说明有何实践重要性（15分）。
2.食品微生物指标有哪些？这些指标的意义？分别常用什么方法检测？（20分）
3.举例分析微生物的互生、共生、竞争、拮抗和寄生关系？（20分）
4.根据免疫学原理，设计一种快速灵敏的检测金黄色葡萄球菌或其肠毒素的方法，并说明原理（20分）
5.影响微生物生长的因素包括哪些?通过对这些因素的控制可以实现哪些食品加工与保藏?（25分）
广东海洋大学
2015年攻读博士学位研究生招生考试试题
考试科目（代码）名称：3401食品微生物学满分100分
（所有答案写在答题纸上，写在试卷上不给分，答完后连同试卷一并交回。）
1.叙述如何选用和设计微生物培养基。（25分）。
2.概述微生物的互生、共生、竞争、拮抗和寄生关系。试想它们分别在食品领域可以有何应用，举例分析？（25分）
3.鱼类腐败过程中微生物起到什么作用?从抑制微生物生长的角度概述控制鱼类腐败的措施和方法（25分）
2015年广东海洋大学考博真题3102渔业资源与渔场学
一、《渔业资源与渔场学》的学科概念及研究内容是什么？（15分）二、性腺成熟度包括哪些方法？各种方法的划分标准及计算式是什么？（15分）三、海洋环境的哪些因素与鱼类行动有密切关系？水温对鱼类行动会产生哪些影响？（20分）四、中国四大海区有哪些主要的渔场？南海有哪些主要种类的渔业资源？（20分）五、以北部湾为例，假设需要调查北部湾油田群建设工程对周边渔业资源产生的影响及其评价，应如何设计海上调查方案？（应包括调查方式、海上布点、调查内容、调查工具、样品处理、人员组织、经费预算、时间安排等）（30分）评分标准一、《渔业资源与渔场学》的学科概念及研究内容是什么？（15分）1、渔业资源和渔场学时研究鱼类资源和水产动物群体的生物学以及它们的行动状态与周围环境之间的相互关系，掌握渔业资源数量变动规律以及渔场形成原理的一门综合性基础应用科学。
2、该学科研究内容主要包括以下:渔业资源和渔场学的目的和任务是为了传授渔业资源生物学的有关基础知识和点差方法以及有关捕捞对象的洄游分布、渔场形成等，为掌握渔业资源数量变动，探索鱼群分布和确定中心渔场，为确保渔业资源的可持续利用提供科学依据。
主要内容包括：（1）掌握研究渔业资源生物学的基础理论和方法，如种群、年龄和生长、食性与丰满度、繁殖习性与繁殖力和鱼类群落结构机器生物多样性等，为渔业资源评估、群体数量变动、渔情预报（包括中心渔场的确定）提供最为基础的资料。
（2）掌握鱼类的群集与洄游研究方法和基本概念。
如鱼类集群的一半规律和原理、鱼类的洄游类型和研究方法。
（3）分析和掌握海洋环境与鱼类行动之间的关系。
例如了解世界各大洋流及其一般规律、各种海洋环境（生物和非生物）与鱼类行动的关系、厄尔尼诺对海洋渔业的影响以及全球环境的变化对渔业资源的影响。
（4）掌握渔场形成的基本理论和规律。
如渔场、渔期及其渔场类型渔区和渔场图的划分编制、渔场形成的一般原理、渔场的分布、评价与变动等，并对优良渔场形成的机泵原理进行阐述。
广东海洋大学高等数学往年试卷
广东海洋大学2006 ——2007学年第一学期《高等数学》课程试题课程号： 1920008□ 考试□ A 卷□ 闭卷□ 考查□ B 卷□ 开卷一． 计算（20分，各4分）.1.x x x x sin 2cos 1lim0-→. 2.⎰+x dx2cos 1.3.⎰-++1121sin 1dx xx . 4.x x x x )1232(lim ++∞→. 5.⎰262cos ππxdx .二.计算（20分，各5分）. 1.求)arcsin(tan x y =的导数。
2.求由方程0=-+e xy e y所确定的隐函数y 的二阶导数22dxyd 。
3.已知⎩⎨⎧==te y t e x tt cos sin ，求当3π=t 时dx dy的值。
4.设x y y x z 33-=，求xy zx z ∂∂∂∂∂2,.三.计算.（25分，各5分）.1. dx x x ⎰+9232.dx e x ⎰班级：计科1141 姓名： 阿稻学号：2014xx试题共2页加白纸4张密封线GDOU-B-11-3023.dttedt e xt xt x ⎰⎰→020222)(lim .4.求]1)1ln(1[lim 0xx x -+→. 5.dx x ⎰-202sin 1π.四.解答（14分，各7分）.1.问12+=x xy ()0≥x 在何处取得最小值？最小值为多少？ 2.证明x x xx<+<+)1ln(1.五.解答（21分，各7分）.1.求由2x y =与x y 2=围成图形的面积。
2.求由x x x y ),0(,sin π≤≤=轴围成的图形绕x 轴所产生的旋转体的体积。
3.计算σd y x D⎰⎰+)(22，其中D 是矩形闭区域：1,1≤≤y x .《高等数学》课程试题A 卷答案一. 计算 （20分 各4分）1.原式＝2sin sin 220lim =→x x x x 2.原式＝c x xdx +=⎰tan 21sec 212 3. 原式＝201arctan 211112π⎰-==+x dx x 4. 原式＝e x x x =++∞→)1221(lim 5. 原式＝83622cos 126-=+⎰πππdx x 二、计算 （20分 各5分） 1.x xy 22sec tan 11'-=2.两边对x 求导，得：0''=++xy y y e y yex yy +-=' 2)()'1()('''y y y e x y e y e x y y ++-+-= 32)(22y yy e x e y ye xy +-+= 3.tt tt t e t e t e t e dx dy tt t t sin cos sin cos cos sin sin cos +-=+-=2331313-=+-==πt dx dy 4.323y y x xz -=∂∂222233y x y x z x y z -=∂∂∂=∂∂∂三、计算 （20分 各5分）1.原式＝c x x dx x x x x ++-=+-+⎰)9ln(29219992223 2. 原式＝c e e x c e te dt te x xt t t +-=+-=⎰)(2)(223. 原式＝2222220lim=⎰→x xt xx xedte e4. 原式＝212111)1ln(lim lim20=+-=+-→→x x x x x x x 5. 原式＝222)cos (sin )sin (cos cos sin 244020-=-+-=-⎰⎰⎰ππππdx x x dx x x dx x x四、解答 （14分 各7分）1.解:0)x (1x 1'y 222=+-= 1x ±= 1x -=（舍）又 00x y 211x y ==== 故：函数在1x =取到最大值，最大值为21。
广东海洋大学第二学期高数试题与答案
GDOU-B-Il-302广东海洋大学2014—2015学年第二学期《高等数学》课程试丿课程 考试 A 卷 闭卷 号：□考查 □B 卷 □开卷填空(3X8=24分); 1.设 8 = {1, 2, -1}, b = { jv, 1, θ}, a 丄 Z> ,则 X = __ I [2.设a = { 2, 0, - 1}, b = { 0, 1, θ},贝∣J a X Z = ____线i 3.曲面z 2= A - ÷ y 2在点(1,1, √2)处的切平面方程为 ____________ I I:4.将mz 平面上的曲线A- -^- = I 绕X 轴旋转一周所得的旋转曲面的方 I I 程为 __________ I； 5.函数Z = In(3 ÷ A - + y 2)的驻点为 _________ II 6.设Z 为连接(-1, 0)到点(0,1)的直线段，则∖{y-x)ds = _____I -II 7.幕级数£匚的收敛半径为 _____________________ ； Λ = l 3 I⅛ 8.微分方程y" = &亠的通解为y = ________________ II 二.计算题(7X2=14分)姓名： 学号：试题共 5页 加白纸3张1.设Z = y In(JV2 + y2)> 求血.2.设函数Z = f(x, y)是由方程/ - ZyZ ÷ X = /所确定的具有连续偏导数的函数，求竺，⅛.∂x ∂x^三. 计算下列积分(7 X 4=28分)1.∫∫ (y - x~)dxdy ,其屮D是由V = O, y = x~及X = I .所I韦I成的闭区D域。
2.证明曲线积分J：： (2Xy - y~)dx + Cv2 - 2xy)√r在整个xoy平而内与路径无关，并计算积分值。
3.计算^(I- x)dydz + (2 - y')dzdx + (3 - z)dxdy中Σ 是球面rX2 + y2 + Z2 = 9 的外侧。
广东海洋大学数学物理方法2012--2014,2016,2017年考研真题
819《数学物理方法》 第 1 页 共 9 页 广东海洋大学2012年攻读硕士学位研究生入学考试
《数学物理方法》(819)试卷
（请将答案写在答题纸上，写在试卷上不给分。
本科目满分150分）
一、名词解释(30分，每小题6分)
1、定解问题
2、微分方程的古典解
3、位势方程
4、线性微分方程
5、Poisson 方程
二、填空题(20分，每空4分)
1、与热传导方程相似的物理问题有： 、 等。
2、Fourier 变换的积分表达式： 。
3、Dirichlet 边界条件表达式为： 。
4、微分方程特征函数为： 。
三、简答题(30分，每小题10分)
1、简述非齐次线性微分方程的定义，并指出下列方程的性质：
激波方程: 0t x u uu +=
KdV 方程: 60
t x xxx u uu u -+= 多空介质方程:
m
t u k u =∆ 2、简述二阶线性偏微分方程的分类方法，并指出下列方程的类型：43260+-++=xx xy yy x y u u u u u 。
3、简述分离变量法求解含有齐次边界条件的齐次线性偏微分方程的
步骤。
四、写出二维Laplace 方程的差分方程。
(10分)
五、设有一根拉紧的均匀柔软而有弹性的细弦，平衡时沿直线拉紧，
当它在铅直平面内作微小振动时，求弦上各点运动规律。
(15分)
六、用行波法求解下面的Cauchy 问题： (15分) 22222200230, ,3, 0==⎧∂∂∂+-=∈⎪∂∂∂∂⎨⎪==⎩x x x u u u x t R t t x x u t u。
广东海洋大学大学物理历年考题答案
广东海洋大学2010——2011 学年第 二 学期《大学物理III 》课程试卷课程号：√ 考试√ A 卷√ 闭卷□ 考查B 卷□ 开卷一、选择题（每小题３分，共３0分）1、有一质点在平面上运动，运动方程为j t i t r 2343+=，则该质点作（ ）A 曲线运动；B 匀速直线运动 ；C 匀变速直线运动 ；D 变加速直线运动。
2、对于一个质点系，系统的内力可以改变系统的（ ）A 总动量；B 总动能；C 总角动量；D 总质量 3、 0.5mol 的氧气，处于温度为T 的平衡态，则内能为（ ）RT DRT C RT BRT A45,5.0,25,234、麦克斯韦速率分布中最概然速率V p 的概念，下面表述正确的是（ ）A 是气体分子中大部分分子所具有的速率。
B 是气体分子速率的最大值。
C 是麦克斯韦速率分布函数的最大值。
D 速率大小与最概然速率相近的气体分子的相对数量最大。
5、两个点电荷相距一定的距离，如果在这两个点电荷连线的中垂线上的电场强度为0，那么这两个点电荷的带电情况是（ ）A 电量相同，电性相同；B 电量相同，电性不同；C 电量不同，电性相同；D 电量不同，电性不同。
6、稳恒磁场中,若闭合回路L 上满足⎰=⋅Ll d B 0,则一定有（ ）A 回路L 上每处的磁感强度均为零。
GDOU-B-11-302班级：姓名：学号：试题共 6页加白纸 2 张密封线B 回路L 上每处的磁感强度均与积分路径垂直。
C 这个磁场是保守场。
D 回路L 包围的电流代数和一定为零。
7、两个简谐运动方向相同，频率相同，振幅也相同且等于1，其相位差为60°，则这两个简谐运动合成的振幅为（ ）A 0.5；B 1 ；C 3；D 2。
8、一平面简谐波在弹性媒质中传播，在媒质中某质元从平衡位置运动到最大位移处的过程中，（ ）A 它的动能逐渐转化成势能。
B 它的能量逐渐增大。
C 它的势能逐渐转化成动能。
D 它的能量逐渐减小。
广东海洋大学地球物理流体力学2014,2015年考博真题
2014年攻读博士学位研究生招生考试试题考试科目（代码）名称：2701地球物理流体力学 满分100（所有答案写在答题纸上，写在试卷上不给分，答完后连同试卷一并交回。
）一、填空题(每题4分，共20分)1、研究流体运动，Lagrange 观点着眼于 ，Euler 观点着眼于 。
2、引入速度势的充要条件是 ，引入流函数的充要条件是 。
3、矢量形式地球物理动力学N -S 方程 。
4、连续方程为 ，其物理实质 是 。
5、U U ）（ 中的k 分量= 。
二、简答题 （每题6分，共30分）1、位势涡度守恒2、地转近似3、速度环流（数学表达式）和引起其变化的物理原因4、振动和波动的物理含义5、如果不计流体粘性作用，某正压流体而言，试说明当U >0或者U<0时，相对涡度的变化。
三、试用拉格朗日观点导出连续方程 dtd V =0（10分） 四、已知流场u=ay ，v=bx ，w =0，其中a 和b 为常数。
（10分）（1）试求流线方程式（2）该流动是否有旋？如有则求出其涡度（3）求出该流动的流函数五、设流体水平方向的速度与z 无关，z 为z 方向的涡度，H 为水深，f 为科氏参数，试推导浅水位涡守恒方程0)( Hf dt d z （10分） 六、对于不可压粘性的地球流体，写出z 方向的运动方程，并导出其无量纲方程（10分）七、如果不计流体粘性作用，某正压流体U (u , v , w )的初始场涡度平行于z 轴，涡度变化可表示为U U dtd ，试说明影响涡度变化的主要驱动机制（10分）2015年攻读博士学位研究生招生考试试题考试科目（代码）名称：2701地球物理流体力学满分100分（所有答案写在答题纸上，写在试卷上不给分，答完后连同试卷一并交回。
）一、简述题（15分）1、-平面(5分)2、摩擦边界层Ekman Pumping 的形成机制（5分）3、对于旋转流体，流体质点穿越等深线运动，产生何种波动，为什么？（5分）二、对于无粘浅水理论，试简述如下问题（25分）1、写出浅水方程及其物理性质，并讨论均质和浅水条件假定的意义和作用。
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广东海洋大学
2015年攻读博士学位研究生招生考试试题
考试科目（代码）名称：3701数学物理方法 满分100分 （所有答案写在答题纸上，写在试卷上不给分，答完后连同试卷一并交回。
）
一、 已知：矩形水槽截面的槽、槽宽及槽中的水在平衡时深度，
两端由刚性平面封闭，试推导水槽中的浅水重力波方程。
(20分)
二、 用行波法求解波动方程的解并解析其物理意义：（20分）
三、 一条半无限均匀细杆，热量沿x 轴一维传播，侧面绝热，
端点温度变化已知，杆的初始温度为0°C 。
用拉普拉斯积分变换法求x 点在时刻t 的温度分布(,)u x t 。
(20分)
222220
00 -,0sin , 0 t t t u u a x t t x u x u ==⎧∂∂-=∞<<∞>⎪∂∂⎨⎪==⎩
四、 用Fourier 变换求解波动方程的Chauchy 问题 (20分)
五、 在xoy 平面内区域D 有边界l ,域D 内u (x,y )满足：
试用数值差分法求解上述Laplace 方程。
(20分)
222220
00 -,0(), 0 - t t t u u a x t t x u x u x ϕ==⎧∂∂-=∞<<∞>⎪∂∂⎨⎪==∞<<∞⎩2222+=0 (,)l
u u x y u f x y ⎧∂∂⎪∂∂⎨⎪=⎩。