摘要Laplace方程是最典型，最简单但应用广泛的椭圆型偏微分方程。
用边界元法解边值问题，由不同的边界归化方法可以得到不同的边界积分方程，数值求解边界积分方程也有好几种方法。
本文考虑用Green公式和基本解推导得出直接边界积分方程来求解二维Laplace方程的Dirichlet问题，该直接边界积分方程是第一类Fredholm积分方程。
对二维问题，一般的带对数积分核第一类Fredholm积分方程并不总是唯一可解的，特别是对外边值问题，解在无穷远处的形态有很大的影响。
人们在用直接边界元方法进行计算时，并不刻意去考虑积分方程的可解性，但可解性的问题是不能回避的，这涉及到原问题的解与边界积分方程的解的等价性问题。
事实上，对内边值问题，第一类Fredholm直接边界积分方程的可解性条件是自然得到满足的，本文对此做了验证。
对外边值问题，考虑到二维Dirichlet 问题的解应当在无穷远处有界，故解的边界积分表达式要做修正，对积分方程的解要有约束，这样去解边界积分方程得出的解才等同于原问题的解。
一般来说，直接边界积分方程可以很方便的用配点法求解，还未见有实际用Galerkin边界元来解的报道。
本文采用Galerkin边界元方法求解直接边界积分方程，是为了验证这两种方法的效率和精度，且Galerkin法易于进行收敛性分析。
Galerkin 边界元方法是把积分方程转化为等价的边界变分方程，经用边界元离散后，通过求解线性代数方程组和计算解的离散的积分表达式求得原问题的数值解，该方法需要在边界上计算重积分。
本文推出了第一重积分的解析计算公式，对外层积分则采用高斯数值积分。
对外边值问题，第一类Fredholm积分方程的解要附加在边界上积分为零的条件，本文采用Lagrange乘子放松这个约束，求解扩展的变分方程时，可同时得出解在无穷远的值。
本文采用常单元和线性元这两种离散方式，分别用Fortran90编写了计算程序，对误差与边界元的数量的关系做了数值实验。
综合教程3 text A 课后答案Unit 1V ocabularyI. 1. 1) insurance 2) On balance 3) aside from 4) cut back5) resist 6) hawl 7) supplemented 8) sprayed9) wicked 10) illustrated 11) budget 12) digest13) boundary 14). get by 15) at that point2. 1) cut back/down 2) pick up 3) get by 4) get through5) face up to 6) turn in 7) turning out 8) think up3. 1) pursued his mathematical studies and taught himself astronomy.2) often generate imsleading thoughts.3) is patronized by international celebrities drawn to its French food and service.4) be suspected of doing everything for money.5) before he gets through life.4. 1) their indoor/ a profit / to invest in2) device / the improvement / scale3) their household / stacked / temptation / never dined outII. Confusable words1.1) house 2) Home 3) family 4) household2.1) doubt 2) suspected 3) doubted 4) supected 5) suspectIII. Word formation1. rise 2 final 3 regular 4 cash 5 hows / whys6 upped7 yellowed8 bottled9 lower 10 searchStructure1) when it comes to changing your life2) when it comes to such matters as keeping the room tidy.3) when it comes to emotional intelligence4) when it comes to managing minor matters.2. 1) Not everyone agrees on what is right and what is wrong2) but, unfortunately, money isn‘t everything3) not all American like them4) Not all p eople share the same interestsComprehensive ExercisesI. Cloze(A) 1. gets by 2 temptation 3 get through 4 picked up 5 improvements6 aside from7 suspect8 supplement9 profit 10 primarily11 spraying 12 stacking(B) 1 While 2 escape 3 begin 4 Because/As5 quit6 start7 on8 but /also9 be 10 close 11 have 12 cutting13 cook/prepare 14 cities 15 however 16 familyII. TranslationA decade ago, Nancy did what so many Americans dream about. She quit an executive position and opened/set up a household equipment store in her neighborhood. People like Nancy made the decision primarily because of their desire to improve the quality of their lives.But , to run a small business is by no means an easy job. Without her steady income, Nancy had to cut back on her daily expenses. Sometimes she did not even have the money to pay the premiums for the various kinds of insurance she needed. Once she could not even pick up the phone bill and had to ask her parents to loan her some money.Fortunately. Through her own hard work, she has now got through the most difficult time. She is determined to continue pursuing her vision of a better life.Unit 2V ocabularyI. 1. 1) decades 2) historic 3) imposed 4) racial5) slender 6) closing in on 7) settlement 8) site on9) mission 10) authorized 11) terminal 12) make the best of13) exploits 14) religious 15) on the side2. 1)Children‘s toy guns now look so real that they can often pass for the real thing.2)The rest of them used to be really nasty to me, but Susie always stood up forme.3)The local government has laid down strict rules and regulations to be followedby all soccer fans in the upcomng 2002 FIFA World Cup in South Korea.4)Tim was quite unhappy to take on all the household chores when his wife wentout to work.5)Sterling promised to be in th e school library by eight o‘clock but it looks likehe‘s let us down again.6) My professor suggested that I draw on the data accumulated over the yearswhen I work on my project.7) I‘m afraid something unexpected has come up; I won‘t be able to see you offtonight. V ery sorry indeed.8) The Oscar winner said this top acting award would give hope for the future toactors who may have given up hope.3. 1) are fully confident that the Americans will not be able to justify theirmeasures to protect the struggling American steel industry.2) in the eyes of Joe Klein, staff writer of the New Y orker and author of TheNatural, the most talented politician of his generation and the mostcompelling.3) people are really intent on destroying themselves with drugs.4) could forge a completely different approach to life.5) is our conviction that cloning of human beings is bound to cause manyethical and social problems in the long run.4. 1) As for , do not compel, capture of , have forged,2) would starve, At huge risk, the mission, transport,3) who abolished, liberated, In the eyes of , expoitsII. Words with multiple meanings1. I‘ll tell you about my research project in a minute, but first let‘s hear aboutyour French trip.2. Most McDonald‘s lo ok almost the same on the outside, but actually there areabout 16 different basic designs.3. Loaning money from the banks is but one of the methods we can use to getthrough a financial crisis.4. This second-hand car has been nothing but trouble; it‘s always breakingdown.5. In your resume you‘ve mentioned everything but one vital point.6. Our technicians have discovered a simple but effective solution to theproblem.7. I am sorry, but I think you shouldn‘t have delayed your homework.8. The bankruptcy of the company was not caused by evil, but by simpleignorance.III. Usage1 lonely2 friendly3 weekly4 lovely5 cowardly6 kindly/saintly7 lively8 motherlyStructure1. 1)A letter posted today will probably reach him the day after tomorrow2) Thus encouraged , we made a still bolder plan for the next year.3) Our government has banned imports of cosmetics containing animal productsfrom 18 countires, mostly in Europe, for fear that they could cause mad cow disease.4) Hav ing graduated from St. Mary‘s College, Joyce applied to the University ofCalifornia at Los Angeles.2. 1) we come to appreciate the value of life2) people will come to like genetically modified crops someday3) we have come to realize the necessity of hiring a computer –security expert4) came to understand that the Chinese preferred ―teaching by holding the hand‖Comprehensive Exercises.I. Cloze(A) 1. Underground 2. forged 3. stand up 4. transport 5. compelled6. convictions7. lieberating8. mission9. abolish 10. intent on11 risk(B) 1 who 2. the 3. along 4. in 5 that 6. through7. not 8. as 9. referred 10. escape 11. where 12. If13 in 14. even 15. until 16 instead 17. asII. TranslationHenson‘s painful life as a slave strengthened his determination to struggle for freedom. Shortly after he achieved freedom he became a member of an organizaion that assisted fugitive slaves. He secrectly retruned to the United States from Canada several times to help others to travel the Underground Railroad to freedom. Once some slave catchers closed in on the escaping sliaves and Henson when they were on the run. He disguised them and successfully avoided capture. In addition , later he buit a small settlement in Dresden, Canada for escaped slaves, setting up a chapel and a school where they could learn useful ways of making a living. He held to he conviction that slavery would be abolished , all the slaves would be liberated, and the day was bound to come when racial discrimination no longer existed.Unit 3V ocabularyI. 1. 1) tranquil 2) analyze 3) by a small margin 4) civilize 5 rural6) close up 7) era 8) paste 9) without so much 10) sideways11)barricaded 12)hook up to 13) error 14) chart 15) Bathed 2.1) The shock of an accident or a physical injury may sometimes bring aboutimmediate inability to think clearly—even when the injury is not to the head.2) In his autobiography,Mr. Hanson looked back on his second career, taken upat the age of sixty, as the happiest time of his life when his creativity was exercised to the full.3) The heavy rain cut off electricity to large parts of the South and caused thepolluted rivers to flood, wheich later contaminated the entire region.4)If the TV has to fit into a limited speace, it‘s a good idea to choose a model thathas a front-facing speaker, asuch as Ferguson or Hitachi.5)Both sides are trying to wear the other down by obstinately sticking to hteirown positions in the negotiations.6)The secret of a successful school lies in effective co-operation betweenprofessional leadership , the government and the local authority.7) Many suburban residents in the United States put up an invisible electronicfence around their premises to prevent their pets from running away.8) The initials VA T stand for V alue Added Tax, which is a type of tax paid by theperson who buys the goods or services.3. 1) which is likely to make people vulnerable to asthmas has been found byresearchers ast the Department of Clinical Medicine in Oxford.2) with mirrored doors had to be bulit in so as to make their small bedroom looklarger3) feature the space shuttle Challenger blowing up in January 1986 –killing allseven crew.4)can be held at bay by increasing your intake of fruit and vegetables , which areboth low in calories and rich in Vitamin C.5)are a major barrier to the country‘s economic growth due to the fact thatimported oil has absorbed 40% of its foreign exchanged.4. 1) looked back on, tranqil, urban life2) was puzzled, stand for, electronic rather3) advertisements, featuring, his premisesII. Collocation1) away 2)inside/in 3)forward/through 4)back 5) off6) home 7) back down 8) in, outIII. Usage1. 1. Internet is not such an unusual word as it used to be2.Most men do not look unattrative in them.3.Wealthy as she is, she is not unconcerned by her sudden unemploymet4.This claim is not unrealistic in view of a sharp decrease in the city‘s violentcrimes.5.His poor health is not unrelated to his unhealthy way of life.Structure1.1)It never occurred to me to ask him what was intended by that remark. I thoughthe was just joking.2) It occurred to me that the names of their children—Rose, Lily andDaisy—were the names of flowers.3)When he heard her say so, it occurred to him that for convenience he also couldcontact the local travle agency and ask them to take care of everything.4) Has it never occurred to you that the problems in the Middle East arecomplicated and difficult to solve?2 1) If they don‘t agree to work extra hours for no extra say, chances are that theywill be dismissed2)Research is being carried out on the disease and progress is being made atpresent. Chances are that there will be a cure within the next ten years.3) If you are eating lots of fatty food, chances are that you‘ll put on severalpounds in a matter of weeks4) He left his office an hour ago but hasn‘t got home yet. Chances are that he‘s gotstruck in a traffic jam.I. Cloze.(A) 1.Statistics 2. rural 3. era 4) stood for 5)on the latch6.vulnerable7. barriers8.at bay9. electronic 10 reflection11. puzzle 12. civilized(B) 1.worse/scarier 2.tougher/harder 3. Y es/True 4 barricading 5. from6 not7 every 8.However 9. say 10back/at bay 11. chances 12. Therefore 13.when 14.leave 15. Don‘t 16. head/brains II. TranslationA burglary is reported every 15 seconds in the United States .Statistics show burglars entered more than 2 million homes last year . Actually it is almost impossible to keep a determined burglar out. All you can do is discourage him for a few minutes, thus exposing him to police patrols or those wandering around. Common sense tells us that lighting is a barrier to criminal activity. A light should be fixed in the doorway and switched on at night. Believe it or not, some people, particularly children who happen to be the last to come in, leave their doors on the latch at night. Doors of hollow core, even when locked, are vulnerable to break-ins. Thus doors o solid core or steel are much preferred as they make it difficult for the burglar to pry open. If you decide to buy an alarm device, be sure to ask for its signs and put them up on both windows and doors. Finally , a word of warning—whenyou travel, make sure that you have a trusted neighbor collect and keep all the deliveries of newspapers and mail until you return. This is because a collection of newspapers and mail on the front doorstep or in your mailbox is an advertisement that no one is home.Unit 4V ocabularyI. 1. 1) rocket 2) garbage 3) knock off 4) complicated5) locality 6) cursed 7) came around 8) deputy9) heave 10) caught sight of 11) arrangement 12) blinked13) isolated 14). disabled 15) regardless of2. 1)One of the aims of modern natural science is to work up universal principles orlaws from pieces of data.2)Uncle Fred unfortunately had a car accident on his way home that Saturdayafternoon and passed away in a local hospital three days later..3)It is reported that a man tends to go for a woman whose character or appearancehas something in common with his mother‘s.4)Grandma has not a high fever; do you think we should send for the doctor?5)The old woman was awarded ￡230,981 in damages in the High Court injuriessuffered when she was knocked down by a motorcycle.6) One of the my university classmates called on me this morning. It was the firsttime we had met after we graduated ten years ago.7) Cathy turned down the well-paid job because it involved too many businesstrips.8) Julia and her husband finally came up with a unique plan to celebrate theirwedding anniversary.3. 1)…put the government at your service, giving you what you‘ve paid for2) …are keeping the patient under close observation on account of her criticalcondition.3)…this complicated technical problem is even beyond the wits of the skilledtechnicians.4)…are alike in the details of their black and white lines though they all seem tohave the same appearance.5)…bugged by her persistent complaining about her routine life, soaring prices,the polluted surroundings, and the like.4. 1)column / wits / complicated / knock down / their appearance / mode of2) isolating himself from / supreme / On account of / alike3) is really bugged / makes like/ is going over / is left alone/ adoptedII. Usage1) high 2) easy 3) deep 4) real 5) steady 6) funnyIII. Word formationWTO World Trade Organization 世界贸易组织GDP gross domestic product 国内生产总值ATM automated teller machine 自动出纳机V AT value-added tax 增值税CAD computer-aided design 计算机辅助设计IT information technology 信息技术IDD international direct dial 国内直拨电话MTV music television 音乐电视radar radio detecting and ranging 雷达IOC International Olympic Committee 国际奥委会VIP very important person 大人物Laser light amplification by stimulated emission of radiation 激光CPU central processing unit 中央处理器IPO Initial Public Offerings 首次公开募股、发行原始股Structure1) Bernard was believed to have been killed in a car-bomb attack a year and a halfago.2) As a freshman, Jane is so curious about university life that she wants to beinvolved in all kinds of campus activities.3)What worries us most is that little seems to have been done to remedy the tradedeficit.4)He got to the railway station only to be told that the train had already left.2. 1)His opponent having gained a lead of almost 60,000votes, the candidatepublicly admitted that he had lost his election bid.2) All the guests having left his house, the host kicked off his shoes andstrectched out on the couch.3) His voice (being ) almost drowned by the big noise from the audience, thespeaker had to stop his lecture.4) The roads being wet and slippery after the heavy rain, I drove very carefully. Comprehensive ExercisesI. Cloze(A) 1. deputy 2 complicated 3 on account of 4 caught sight of 5 go over6 appearance7 nationality8 isolated9 locality 10 organization11 garbage 12 leave alone(B) 1 with 2 drowned/buried/lost 3 at 4 away5 from6 sign7 However8 later9 found/figured 10 alients 11 conducted 12 None13 at 14 times 15 but 16 likeII. TranslationExtraterrestrials have been a topic of interest to experts and laymen/nonprofessionals alike. Researchers of various nationalities and organizations are adopting different modes of investigation in search of them. Some keep close observation on starts with extremely high levels of rare, radioactive elements. They believe such elements have resulted from extraterrestrial technology that is still beyond human wit to understand. Some try to isolate radio signals from the ―noise‖ of the universe. And some claim that they have caught sight of extraterrestrials and can even describe their appearance in detail. Researchers work up the complicated data they collect into a series of reports and books. Although no definite answer has yet been found, the explorer s‘hope shows no sign of fading out on account of their frustrations and they hold to the belief that their hard efforts will prove worthwhile.Unit 5V ocabularyI. 1. 1)sprinkled 2)in turn 3) reversed 4) repay5)at sea 6)on your behalf 7)statement 8) specific9)got to 10)in secret 11)unloaded 12)accord 13)weep14)quote. 15) under way2. 1)came across 2)make out 3)hope for 4) over5) put away 6)brings back 7)got to 8)go about3. 1) …diminish, people are working to increase the use of solar energy2) …appreciate what they already have3) are exposed to more information than were children of the past, it does notfollow that they automatically become more sophisticated.4) …has been immersed in British history and culture.5) …in a flash on June 1, 2000 when he lost both legs in a serious trafficaccdient.4. 1)my sincere/considerate of/ with gratitude/2) assembled/amid the/impressed on/ in quest of3) was marvelous/had undergone /swift/and the restII. Collocation1.fond of2.sick of3. thoughtful of4. confident of5. conscious of6.critical of7. guilty of8. uncertain ofIII. Usage1.To know what people really think, pay regard to what they do, rather thanwhat they say.2.It is cooperation, rather than conflict, that will enable you to achieve yoursuccess3.Ann made students think for themselves rather than telling them what to think4.I think I ‗ll stay at home this evening rather than go/going home5.Most people are content to let perfect days happen at random rather thanplan/planing for themStructure1) it was taken for granted2) Most young people take tap water for granted3) took it for granted that they were married4) then the second is taken for granted2. 1) The 1980s saw the start of the development of some special economic zones inChina.2)The past decade has seen the release of many films, some of them good, somethem bad, and a few of them very brilliant.3) The last 100 years have seen the material wealth of humankind explodebeyond all previous imagining.4)We have been at your service for five years. The future will see us developingnew ideas and plans to suit more of your needs.Comprehensive ExercisesI. Cloze(A) 1. at sea 2 Turning over 3 reverse 4 got to 5 repay6 gratitude7 appreciated8 assembled9 immersed 10 unloading 11 swift(B) 1 all 2 reason 3 better 4 for5 year6 together7 because8 by9 brings 10 that 11 for 12 the13 harvest 14 from 15 if 16 reward 17 itself 18 foodII. TranslationAmid the atmosphere of Thanksgiving , rather than joining his friends in celebration of the holiday. George was immersed in the diary left to him by his father, who died at sea after he completed twosuccessive trips around the world. The diary brought back every moment George has spent with his father and many of the specific things his father did on his behalf. George‘s father used to impress on him the need to undergo all kinds of hardship in quest of excellence. He also taught him that nothing in the world could be taken for granted. Even today, George still remembers how his father would quote Aesop‘s famous saying ―Gratitude is the sign of a noble soul‖ and tell him to acord the greatest importance to it.Unit 6V ocabularyI. 1. 1)flutter/fluttering 2)acute 3)cling to 4) streaming5)fancy 6)mock 7)fierce 8)masterpiece9)nonsense 10)bare 11)subtracted 12) victim13) Sin 14)look the part. 15)for the rest2. 1)The Minister reluctantly gave in/gave up and resigned.2)He was trying to figure out why the camera wasn‘t working.3)The guide dog sized up the traffic and decided to lead its measter across the road.4)Small –pox wiped out some Native Indian tribes.5)The typhoon destroyed everything on its way, knocking down houses and pullingup tress.6)The waterproof coating will wear away very quickly or after many yearsdepending on use and care.7)After a few minutes, my blood pressure became normal and I was allowed to situp again.8)Our main aim in producing the magazine is to give readers inspiratio n and ideasfor their homes and it‘s heart-warming to hear of/about the success we‘ve had. 3. 1)…usually stand out in childhoos memories.2) …a joint bechelor‘s degree program in environmental studeis together withDuke University.3)…still stalks the country4)…scarcely any surface water in the desert5)…for change in the electrion law is so persistent that both houses havepromised to consider it.4. 1)dreary / mingled with / Here and there / not to excess / a merry2) called to us / in a whisper / in tune with3) was …wet through / backward / won‘t hear of / turn loose yourII. Words with multiple meanings1.He went to Paris on business last month.2.The train to Brussels goes at 2:25 p.m3.As soon as they arrived at the meadow, the shepherd let the sheep go.4.We went exploring together in the mountain./ We will go exploring together in themountains.5.Let‘s go and have a drink in the bar.6.The store is going to close up soon.7.South Koreans went crazy when their soccer players beat the Spanish team in thequarter-finals.8.When Mother came out of the house, she found her children gone.III. Usage1. a little white wooden house2.long, curly red hair3. a large old round table4. a cheap Indian restaurant5. a huge cool chocolate ice-cream6.rapid technological advance7. a handsome young Chinese AmericanStructure1) …The kitchen smells of rubber.2) …It smells of rose.3) … It tastes of fish.4)…It tastes of gasoline.2. 1)I killed the spider by hitting it.2) The little girl supported herself by selling matches.3)Y ou can unlock the door by turning the key to the right.4)She tried to get help by screaming.Comprehensive ExercisesI. Cloze(A) 1.victiim 2 in tune 3Scarcely 4 in a whisper 5 cling to6 merry7 sat up8 nonsense9 fancy 10 fierce11 sin 12 masterpiece(B) 1 As 2 whose 3 that 4 or5 jail6 Her7 so8 buy9 not 10 figured 11 collect 12 when13 into 14 deliver 15 including 16 feel 17 take 18 Bring19 in 20 smallII. TranslationHere and there we see young artists who stand out from other people. They may be in worn outjeans all the year round, or walk barefoot/inbare feet even in winter, or drink to excess, or cling to the fancy of creating a masterpiece without actually doing any creative work. In fact, many of them act like this just to look the part, or to be―in tune with‖ other artist. They have forgotten that only through persistent effort canone achieve success.Unit 7V ocabularyI. 1. 1)pledge 2)betray 3)transit 4)went off5)off balance 6)laundry 7)retail 8)disorder9)limitations 10)section 11)tilted 12)transferred13)delivery 14)lean 15)linger2. 1)messing around 2)hang on 3)was laid up with 4) are gaining on 5)kicked up 6)cool down 7) drop off 8)was reaching out3. 1) …sometimes didn‘t register with(with her)2) …strained his back during a practice session. That explains why he was absent from today‘s game.3)…was transferred from Rather‘s account to my account.4) …are lean for taxi drivers because there are few tourists5) …the most profitable business in Amercia.4. 1)was gaining / was laid up in / In time/ scar on2) a cripple/crippled / surgery / limitations / in literature3) on (straight) commission / on the phone / territory / a strain on/ never registerswithII. Usage3.I never did go over these books, although I probably should have.4.I know this is a personal question. Y ou don‘t have to anser me if you don‘twant to.5.I think this topic should have attracted far more attention from philosophersthan it has.6.―I think you‘re right.‖—―I‘m sure I7.―He thought that the condition was hereditary in his case.‖—―Well, it mightbe.8.―Sugar?‖—―‖No. Maybe next time.‖9.The house is only a buuilding. It is a place to live, nothing more.10.DIANE: Y ou didn‘t ! Tell me you didn‘t !FA THER: Oh, yes. Anything for my children.III. Word Family1.1)bored 2)boredom 3)bored 4) boringly 5) boring2. 1) encouraged 2) encouraging 3) encouraging 4) encouragement3. 1) frozen 2)freeze 3)freezing 4)freezer 5)freezeStructure1. 1)She had to finish reading all the mail that arrived that morning before leaving/she left her office.2) It took Jane years of hard practice before she learned to write English well.3) Because they learned it the hard way, they will not trust anyone before heproves himself trustworthy.4) Before you criticize him, I think you should let hime explain why he acted inthe way he did.2. 1) Whenever I felt like talking2)don‘t feel like writing3) Those who felt like hearing the story again4) I feel like going for /taking a walkComprehensive ExercisesI. Cloze(A) 1 off feet 2 signature 3 commission 4 on the phone 5 laid up6 surgery7 representative8 territory9 disorder 10 linger 11 applying for 12 dignity(B) 1 in 2 on 3 read 4 But 5 for 6 and 7 on8 worry 9 Now 10 because 11 then 12 the 13 or 14 bother/have 15 doing 16 in 17 looking 18 Why 19 money 20 reaaly 21 noII. TranslationTom was born a cripple, with one of his lower limbs useless. Early in his childhood, he learned that unless he so exerted himself as to rise above his limitations, he could not earn a living, and unless he succeeded in making a living on his own, he could not win/gain the respect of others. That was the price he had to pay for his dignity as a human being.Tom applied for numerous jobs, only to be turned down, before he finally got one as a delivery boy for a Pizza Hut. He then worked as a slaes representative for a sports wear company in a territory no one lese would want. Today he owns a fairly profitable retail shop in his hometown, and hires several people to work for him on straight commission.Unit 8V ocabularyI. 1. 1)residence 2)gave birth to 3)fuse/merge 4) primitive5)genes 6)compromise 7)mixture 8)union9)beforehand 10)started out 11)comment 12)catalog13) theoretical 14)all the world 15)opposed2. 1)calls for 2)woke up 3)took up 4)runs out of5)sums up 6)broke down 7)lashed out at 8)has grown into 3. 1)…is dotted with colorful houses2) …inherited a weak economy from the Conservative government3) …lashed out at the racial discrimination that has plagued the American Blacksfor more than two hundred years.4) …are immune to the disease5) … will not tolerate such offensive behavior4. 1)am not opposed to / in principle / terrifying / an identical twin/ atomic。
