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Unit 1Paper TigersWesley YangAdditional Background Information(About Battle Hymn of the Tiger Mother)What follows is a comment on Battle Hymn of the Tiger Mother by Elizabeth Chang, an editor of The Washington Post's Sunday Magazine, which carried the article on January 8th, 2011.The cover of Battle Hymn of the Tiger Mother was catnip to this average parent's soul. Although the memoir seems to have been written to prove that Chinese parents are better at raising children than Western ones, the cover text claims that instead it portrays "a bitter clash of cultures, a fleeting taste of glory" and how the Tiger Mother “was humbled by a 13-year-old.” As a hopelessly Western mother married into a Chinese family living in an area that generates immigrant prodigies as reliably as clouds produce rain, I was eager to observe the comeuppance of a parent who thought she had all the answers.And, in many ways, "Tiger Mother" did not disappoint. At night, I would nudge my husband awake to read him some of its more revealing passages, such as when author Amy Chua threatened to burn her older daughter's stuffed animals if the child didn't improve her piano playing. "What Chinese parents understand," Chua writes, "is that nothing is fun until you're good at it." By day, I would tell my own two daughters about how Chua threw unimpressive birthday cards back at her young girls and ordered them to make better ones. For a mother whose half-Chinese children played outside while the kids of stricter immigrant neighbors could be heard laboring over the violin and piano, the book can be wickedly gratifying. Reading it is like secretly peering into the home of a controlling, obsessive yet compulsively honest mother—one who sometimes makes the rest of us look good, if less remarkable and with less impressive offspring. Does becoming super-accomplished make up for years of stress? That's something my daughters and I will never find out.Chua is a law professor and author of two acclaimed books on international affairs, though readers of "Tiger Mother" get only a glimpse of that part of her life, with airy, tossed off-lines such as "Meanwhile, I was still teaching my courses at Yale and finishing up my second book" while also "traveling continuously, giving lectures about democratization and ethnic conflict." Her third book abandons global concerns to focus intimately on Chua's attempt to raise her two daughters the way her immigrant parents raised her. There would be no play dates and no sleepovers: "I don't really have time for anything fun, because I'm Chinese," one of Chua's daughters told a friend. Instead, there would be a total commitment to academics and expertise at something, preferably an instrument. Though Chua's Jewish husband grew up with parents who encouraged him to imagine—and to express himself, he nonetheless agreed to let her take the lead in rearing the children and mostly serves as the Greek chorus to Chua's crazed actions.In Chinese parenting theory, hard work produces accomplishment, which produces confidence and yet more accomplishment. As Chua note s, this style of parenting is found among other immigrant cultures, too, and I'm sure many Washington-area readers have seen it, if they don't employ it themselves. Chua's older daughter, Sophia, a pianist, went along with, and blossomed, under this approach. The younger daughter, Lulu, whose instrument of Chua's choice was a violin, was a different story. The turning point came when, after years of practicing and performing, Lulu expressed her hatred of the violin, her mother and of being Chinese. Chua imagined a Western parent’s take on Lulu's rebellion: "Why torture yourself and your child? What's the point? (I)knew as a Chinese mother I could never give in to that way of thinking." But she nevertheless allowed Lulu to abandon the violin. Given that the worst Lulu ever did was cut her own hair and throw a glass, my reaction was that Chua got off easy in a society where some pressured children cut themselves, become anorexic, refuse to go to school or worse. No one but an obsessive Chinese mother would consider her healthy, engaging and accomplished daughter deficient because the girl prefers tennis to the violin—but that's exactly the point.And, oh, what Chua put herself and her daughters through before she got to her moment of reckoning. On weekends, they would spend hours getting to and from music lessons and then come home and practice for hours longer. At night, Chua would read up on violin technique and fret about the children in China who were practicing 10 hours a day. (Did this woman ever sleep?) She insisted that her daughters maintain top grades—Bs, she notes, inspire a "screaming, hair-tearing explosion" among Chinese parents and the application of countless practice tests. She once refused to let a child leave the piano bench to use the bathroom. She slapped one daughter who was practicing poorly. She threatened her children not just with stuffed-animal destruction, but with exposure to the elements. She made them practice on trips to dozens of destinations, including London, Rome, Bombay and the Greek island of Crete, where she kept Lulu going so long one day that the family missed seeing the palace at Knossos.Sometimes, you're not quite sure whether Chua is being serious or deadpan. For example, she says she tried to apply Chinese parenting to the family's two dogs before accepting that the only thing they were good at was expressing affection. "Although it is true that some dogs are on bomb squads or drug-sniffing teams," she concluded, "it is perfectly fine for most dogs not to have a profession, or even any special skills." On the one hand, she seems aware of her shortcomings: She is, she notes, "not good at enjoying life," and she acknowledges that the Chinese parenting approach is flawed because it doesn't tolerate the possibility of failure. On the other hand, she sniffs that "there are all kinds of psychological disorders in the West that don't exist in Asia." When not contemptuous, some of her wry observations about Western-style child-rearing are spot-on: "Private schools are constantly trying to make learning fun by having parents do all the work," and sleepovers are "a kind of punishment parents unknowingly inflict on their children through permissiveness."Readers will alternately gasp at and empathize with Chua's struggles and aspirations, all the while enjoying her writing, which, like her kid-rearing philosophy, is brisk, lively and no-holds-barred. This memoir raises intriguing, sometimes uncomfortable questions about love, pride, ambition, achievement and self-worth that will resonate among success-obsessed parents. Is it possible, for example, that Chinese parents have more confidence in their children's abilities, or that they aresimply willing to work harder at raising exceptional children than Westerners are? Unfortunately, the author leaves many questions unanswered as her book limps its way to a conclusion, with Chua acknowledging her uncertainty about how to finish it and the family still debating the pros and cons of her approach (anyone hoping for a total renunciation of the Chinese approach will be disappointed).Ending a parenting story when one child is only 15 seems premature; in fact, it might not be possible to really understand the impact of Chua's efforts until her daughters have offspring of their own. Perhaps a sequel, or a series ("Tiger Grandmother"!) is in the works. But while this battle might not have been convincingly concluded, it's engagingly and provocatively chronicled. Readers of all stripes will respond to "Tiger Mother."Structure of the TextPart I (Paras. 1-2)The author, an Asian living in the United States, introduces himself as a ‘banana’.Part II (Paras. 3-5)The author describes how he believes Asians are generally viewed in the United States and how he views Asian values himself. It is clear that his overall attitude toward his cultural roots is negative. Part III (Paras. 6-8)The author agrees that Asians (especially Chinese) are over-represented in American elite schools and that, percentage-wise, more Chinese earn median family incomes than any other ethnic group in the United States. However, he does not accept the idea that the Chinese are “taking over” top American schools. He particularly ridicules the idea that the United States has to worry about a more general Chinese “takeover”, as Amy Chua’s bo ok seems to suggest.Part IV (Paras. 9-14)In these paragraphs, the author tells the story of a Chinese American whose experience as a graduate of one of the most competitive high schools in the U.S. proves that while Asian overrepresentation in elite schools is a fact, the success of Asian students is not an indication of their higher intelligence but rather of their constant practice of test-taking. The fear that U.S. schools might become “too Asian” (too test-oriented) in response, narrowing students’ e ducational experience, has aroused general concern.Part V (Paras. 15-22)The author points out that the ethnic imbalance in elite schools is not only resented by white students and educators, but that even Asian students are beginning to raise serious doubts. They are tired of the crushing workload and believe there must be a better way. They envy their white fellow students who finally get to the top - strong, healthy, with a high level of academic achievement, and with time even for a girlfriend or boyfriend. They cannot help but still feel alienated in this society.Part VI (Paras. 23-28)In these Paragraphs, the author tells the story of another Chinese student who describes the subtle influence of his Chinese upbringing, which makes it difficult for him to be culturally assimilated.Part VII (Paras. 29-36)In these Paragraphs, the author discusses the problem of the “bamboo ceiling”—the fact that in spite of high academic achievement, virtually no Asians are found in the upper reaches of leadership. The author believes that this is because Asian upbringing fails to provide children with the requisite skills for leadership.Part VIII (Paras. 37-43)Between Para. 36 and Para. 37 in the original essay, there are many more case studies reflecting vividly the negative effects of Asian culture. But in order to limit the essay to a manageable length, we (the compilers) were unable to include them. Therefore, in this section, the essay comes to a somewhat abrupt conclusion.Interestingly enough, the author feels that the Battle Hymn of the Tiger Mother is well worth reading although he does not agree with Amy Chua, because, in his opinion, the book provides all the material needed to refute what ‘the Tiger Mother’ stands for. More importantly, the author thinks that Amy Chua should be praised for her courage to speak out and defy American mainstream views.Detailed Study of the Text1. Millions of Americans must feel estranged from their own faces. But every self-estrangedindividual is estranged in his own way. (Para. 1)Millions of Americans must feel alienated (separated) from the essence of themselves by their own faces.The author is referring here to ethnic minority people in the United States, especially Asians.Note that “face” here does not refer to skin color or facial features alone, but also to cultural differences. His point is that these attributes force him into the category of “immigrant”, though he doesn’t feel like one.2. You could say that I am a banana. But while I don't believe our roots necessarily defineus, I do believe there are racially inflected assumptions wired into our neural circuitry. (Para. 2)A banana is white inside and yellow outside. The term is often used ironically to refer to anAsian American who is like all other non-Asian Americans people except for the color of his skin.The author admits that people can call him a banana, but he does not like it, because he does not believe his Asian roots determine who he is. However, he has to admit that there are racially inflected assumptions wired into many Asian Americans’ neural circuitry.racially inflected assumptions: racially based prejudices, beliefs and ideaswired into our neural circuitry: deeply planted in our brains (in our minds)3. Here is what I sometimes suspect my face signifies to other Americans: An invisibleperson, barely distinguishable from a mass of faces that resemble it. A conspicuous person standing apart from the crowd and yet devoid of any individuality. An icon of so much that the culture pretends to honor but that it in fact patronizes and exploits. Not just people “who are good at math” and play the violin, but a mass of stifled, repressed, abused, conformist quasi-robots who simply do not matter, socially or culturally. (Para. 3) This is how I sometimes guess other Americans look at us. (This is what I sometimesthink my face means to other Americans.)An invisible person: a person much the same as others of the same group; a person who is hardly distinguishable; a person nobody will pay special attention todevoid of any individuality: without any individualityAsian culture is said to stress uniformity or conformity. The individual is encouraged to merge with the collective. Self-promotion or assertiveness is considered in bad taste whereas invisibility is regarded as a sign of modesty.icon：n. 偶像The successful Asian student has become a symbol to be worshipped.to patronize and exploit: to treat somebody in an offensively condescending manner and make use of him or herThe author says that American culture pretends to honor the ‘Tiger Child’ (the successful Asian) as an icon (a symbol of success and everything it represents), but actually it treats Asians in a condescending way and makes use of them.a mass of stifled, repressed, abused, conformist quasi-robots: a large number of peoplewho are not allowed to act or express themselves freely, treated in a harsh and harmful way, and made to behave similarly, like robots.do not matter socially or culturally: do not have much social or cultural importance.4. I've always been of two minds about this sequence of stereotypes. (Para. 4)of two minds: (BrE: in two minds) not decided or certain about something.this sequence of stereotypes: this series of stereotypes. On the one hand the author is angry that Asians should be viewed this way, and he thinks it racist, but on the other hand, he has to admit that these views do apply to many Asians.It is ironic to note that the author himself seems to be especially influenced by these racist prejudices. One may also wonder whether the stereotyped views some people have when they first encounter people of other races necessarily have devastating effects. For example, Chinese thought of Westerners as a mass of blue-eyed, yellow-haired, big-nosed, hairy chested aliens at one time. Fear of the unknown or unfamiliar is a common human reaction.5. Let me summarize my feelings toward Asian values: Damn filial piety. Damn gradegrubbing. Damn Ivy League mania. Damn deference to authority. Damn humility and hard work. Damn harmonious relations. Damn sacrificing for the future. Damn earnest, striving middle-class servility. (Para. 5)Now the author is talking about much more serious things. He is talking about his feelings toward Asian values rather than features or skin color, and his attitude is one of total rejection and condemnation. While we must realize that all cultures or civilizations have drawbacks, and we have every reason to listen to the bitter reactions of angry young Asians toward our shared culture, we should also remind ourselves that young people’s judgments may be hasty, imbalanced, and immature.Damn: Note that this word is generally considered extremely offensive and obscene in all its usages, and is therefore avoided, but here the author is so bitter that no other expression seems adequate. Indeed, he may have deliberately chosen this word to shock the Asian community, especially Asian parents.filial piety: love for, respect for, and obedience to one’s parentsgrade grubbing: striving for high academic scoresivy league mania: craze, obsession regarding entry to ivy league universitiesdeference to authority: respect for and submission to authorityhumility and hard work: modesty, humbleness; diligenceearnest striving middle-class servility: Middle-class people usually “hope to rise and fear to fall” (Bunyan) and therefore work slavishly and behave submissively.One may wonder whether what the author describes here is racially determined or mainly a reflection of social and economic conditions. Many of the values listed above are similar to those of the American Puritans when obedience, respect for the old, diligence, thrift, simple living, family loyalty, discipline, and sacrifice were considered essential virtues.6. I understand the reasons Asian parents have raised a generation of children thisway. …This is a stage in a triumphal narrative, and it is a narrative that is much shorter than many remember. (Para. 6)The author says that he understands why Asian parents have raised their children this way. It is natural for most Asian parents to try to improve their children’s lives through education.a stage in a triumphal narrative: A stage (the beginning stage) of a success story. Andmany Asians have achieved success in a much shorter time than people realize.7. Asian American success is typically taken to ratify the American Dream and to provethat minorities can make it in this country without handouts. (Para. 7)to be taken to: to be considered toto make it: to succeed8.Still, an undercurrent of racial panic always accompanies the consideration of Asians,and all the more so as China becomes the destination for our industrial base and the banker controlling our burgeoning debt. （Para. 7）But there always exists a feeling of racial panic, though it may not be obvious, whenever people think of Asians. This undercurrent is now becoming stronger as more American industrial companies move their manufacturing base to China, and China has become the banker controlling our growing national debt.9. But if the armies of Chinese factory workers who make our fast fashion and iPadsterrify us, and if the collective mass of high-achieving Asian American students arouse an anxiety about the laxity of American parenting, what of the Asian American who obeyed everything his parents told him? Does this person really scare anyone? (Para. 7)The author is pointing out the contradiction here: If…, then what about…? It is clear that he doubts if there is any reason for Americans to be afraid of the Asian American who obeys everything his parents tell him. Children brought up in this submissive culture cannot pose any threat.fast fashion: This is a contemporary term used to refer to products designed and brought to market quickly in order to capture ever-changing fashion trends.10.Earlier this year, the publication of Amy Chua's Battle Hymn of the Tiger Mother inciteda collective airing out of many varieties of race-based hysteria. But absent from themillions of words written in response to the book was any serious consideration ofwhether Asian Americans were in fact taking over this country. (Para. 8)to incite a collective airing out of many varieties of race-based hysteria: To provoke many people into stating openly various kinds of strong racist opinionsb ut absent from the millions of words…was any serious consideration…: But there wasno serious consideration in all these millions of words…11.I mean, I'm proud of my parents and my neighborhood and what I perceive to be myartistic potential or whatever, but sometimes I feel like I'm jumping the gun a generation or two too early. (Para. 9)The second sentence of this sentence means that I feel like I am changing into a new person a generation or two too early.This shows that the changes he has to make in response to a new cultural environment have come in conflict with his old cultural legacy, and he feels lost.12. I ride the 7 train to its last stop in Flushing, where the storefront signs are all written inChinese and the sidewalks are a slow-moving river of impassive faces. (Para. 10)the storefront signs: 店面招牌Note that Flushing (法拉盛) now has the largest Chinese community in New York city, larger than Chinatown.impassive faces: faces showing no emotionNote that etymologically, the word impassive is related to “passion” rather than “passive”.13. There are no set-asides for the underprivileged or, conversely, for alumni or otherprivileged groups. There is no formula to encourage “diversity” or any nebulous concept of “well-roundedness” or “character.” Here we have something like pure meritocracy. (Para. 12)set-asides: slots set aside for people in special categories 招生的保留名额for the underprivileged: 专为弱势群体（保留的名额）F or alumni or other privileged groups: 为校友及其他享有特权的团体（保留的名额）T here is no formula to encourage “diversity” or any nebulous concept of “well-roundedness” or “character.”：There are no special provisions to encourage diversity” (referring mainly to ethnic diversity, guaranteed by what was known as ‘affirmative action’) or any vague idea of “well-roundedness” (referring to set-asides for students with special athletic or other talents) or “character” (referring to set-asides for students of especially fine character, demonstrated, or example by community service.)Note that, according to the author, this school is different. It operates on the basis of something like pure meritocracy.meritocracy: a system in which advancement is determined only by ability and achievement.Here it refers particularly to a system of education in which admission to an educational institution, evaluation and promotion are all determined by ability and achievement (merit).14. This year, 569 Asian Americans scored high enough to earn a slot at Stuyvesant,a long with 179 whites, 13 Hispanics, and 12 blacks. Such dramatic overrepresentation,and what it may be read to imply about the intelligence of different groups of NewYorkers, has a way of making people uneasy. (Para. 13)to earn a slot: to get admitted into the school; to be allowed to enter the schoolslot: available position; opening; placedramatic over-representation: a disproportionately large percentage of those admitted15.But intrinsic intelligence, of course, is precisely what Asians don't believe in. (Para. 13)But Asians, of course, believe only in hard work. They don’t believe in natural intelligence.16.“Learning math is not about learning math,” an instructor at one called Ivy Prep wasquoted in The New York Times as saying. “It's about weightlifting. You are pumping the iron of math.” Mao puts it more specifically: “You learn quite simply to nail any standardized test you take.” (Para. 13)an instructor at one called Ivy Prep: a teacher at a school called Ivy Prep, meaning a school for preparing students to get into Ivy League universities.pumping the iron of math: lifting the iron of math, rather than an iron weight.Note that the author is playing on the slang expression “pumping iron”: to lift weights.to nail: to fix, secure, or make sure of, especially by quick action or concentrated effort.17. And so there is an additional concern accompanying the rise of the Tiger Children, onefocused more on the narrowness of the educational experience a non-Asian child might receive in the company of fanatically pre-professional Asian students. (Para. 14)an additional concern accompanying the rise of the Tiger Children: an additional worry related to the rise of high-achieving Asian American children.the narrowness of the educational experience: Non-Asian American parents are worried that their children’s education experience will be very narrow because they are surrounded by Asian students who are all obsessively pre-professional.pre-professional:Preparatory to the practice of a profession or a specialized field of study related to it.18. A couple of years ago, she revisited this issue in her senior thesis at Harvard, where sheinterviewed graduates of elite public schools and found that the white students regarded the Asian students with wariness. In 2005, The Wall Street Journal reported on “white flight” from a high school in Cupertino, California, that began soon after the children of Asian software engineers had made the place so brutally competitive that a B average could place you in the bottom third of the class. (Para. 14)to revisit the issue：to look at the issue again“white flight”: the fleeing (running away) of white studentsa B average could place you in the bottom third of the class: If your grade were no morethan B on average, then you would be quite likely to find yourself in the lowest third of the class.19.You could frame it as a simple issue of equality and press for race-blind quantitativeadmissions standards. In 2006, a decade after California passed a voter initiative outlawing any racial engineering at the public universities, Asians composed 46 percent of UC Berkeley's entering class; one could imagine a similar demographic reshuffling in the Ivy League, where Asian Americans currently make up about 17 percent of undergraduates. (Para. 16)to frame: to express in wordsto press for: to make a strong demand forrace-blind: treating different races equallyCompare: color-blindrace-blind quantitative admissions standards:没有种族歧视的招生名额原则racial engineering:designing a student body to reflect a pre-determined racial mix (the opposite of race-blind quantitative admissions standards)C ompare: social engineering; genetic engineeringto compose 46 percent: to make up/to represent 46 percentUC Berkeley's entering class：加州大学伯克利分校的新生班demographic reshuffling：changing the representation of component groups making up a larger group of people: in this case, changing the ethnic mix within the population of Ivy League undergraduates20.But the Ivies, as we all know, have their own private institutional interests a t stake intheir admissions choices, including some that are arguably defensible. Who can seriously claim that a Harvard University that was 72 percent Asian would deliver the same grooming for elite status its students had gone there to receive? (Para. 16)to have their… interests at stake: to have their… interests in danger/at risk/in jeopardy arguably defensible：It can be argued that some of those private interests are defensible.to deliver the same grooming: to give the same preparation for future elite employment and social position. grooming:梳理打扮21. He had always felt himself a part of a mob of “nameless, faceless Asian kids,” who were“like a part of the décor of the place.” (Para. 17)the décor of a place: the way the place is decorated22.“It's like, we're being pitted against each other while there are kids out there in theMidwest who can do way less work and be in a garage band or something—” (Para. 18) to pit us against each other: to force us to compete with each otherout there: used to say in a general way that someone or something existsway less: a lot less.Note that the word ‘way’ is an adverb here.or something: used to suggest another choice, etc., that is not specified.23.“The general gist of most high school movies is that the pretty cheerleader gets with thebig dumb jock, and the nerd is left to bide his time in loneliness. But at some point in the future,” he says, “the nerd is going to rule the world, and the dumb jock is going to work in a carwash”. (Para. 19)gist: the general or basic meaning of something said or written。
Chapter 6 Language and Cognitionl.语言与认知6.1. What is Cog nitio n 认知？а.Mental processes, information processing b.Mental process or faculty ofknowin g,i ncludi ng aware ness,percepti on, reas oning, and judgme nt.2. The formal approach:形式法structural patter ns, in cludi ng the study of morphological, syn tactic, and lexical structure.The psychological approach 心理法：Ianguage from the view of general systems ranging from percepti on, memory, atte nti on, and reas oning.The conceptual approach认知法：how Ianguage structures (processes& patterns) con ceptual content.6.2. Psycholi nguistics 心理语言学The study of the relati on ships betwee n lin guistic behavior and men tal activity.б.2.1 Language acquirement 语言习得① Holophrastic stage独词句阶段Twoword stage 双词句阶段Stage of three-word uttera nces 三词句阶段④ Flue ntgrammatical conv ersati on stage6.2.2 Lan guage comprehe nsior理解Mental lexicon (心智词库)：information about the properties of words, retrievable whe n un dersta nding Ian guage For example, we may use morphological rules to decomposea complex word like rewritable the first few times we encounter it and after several exposures we may store and access it as a unit or word. It means that freque ncy of exposure determ ines our ability to recall stored in sta nces Connectionism (连结主义)：readers use the same system of links between spelling un its and sound un its to gen erate the pronun ciatio ns of writte n words like tove and to access the pronun ciati ons of familiar words like stove, or words that are excepti ons to these patter ns, like love.Similarity and frequency play important roles in processing and comprehendingIan guage, with the no vel items being processed based on their similarity to the known onesWord recognition 单词识另廿:recognition of spoken words and printed ones.Cohort theory:集群模型Marsle n-Wilson & Welsh (1978)The first few pho nemes of a spoke n word activate a set of word can didates that are con siste nt with the in put. Eg. To an in structi on pick up the can dle ” liste ners sometimes gla nces first at a picture of a can dy.In teractive model:交互模型Higher process ing levels have a direct, -down” inftue nee on lower levels. Lexicalkno wledge can affect the percepti on of phon emes. eg.ln certa in cases, liste ners 'knowledge of words can lead to the inhibition of certain phonemes; in other cases, liste ners con ti nue to “ hear ” phon emes that have bee n removed from the speech sig nal and replaced by no ise. Race mode I竞争模型Pre-lexical route: computes phono logical in formati on from the acoustic sig nalLexical route: the phono logical in formatio n associated with a word becomes available whe n the word itself is accessed eg.l iste ners use phono tactic in formatio n such as the fact that initial /tl/ is illegal in English to help identify phonemes and word boun daries.Factors invo Ived in word recog niti on: ?Freque ncy effect: the ease with which a word is accesseddue to its more freque nt usage in the L.Recency effects: the ease with which a word is accessed due to its repeated occurre nee in the discourse or con text.Cotext: We recog nize a word more readily whe n the precedi ng words provide an appropriate con text for it.Lexical ambiguity 词法多义性eg.My friend drove me to the bank.Comprehe nsion of sen te nee句子的理解Serial models 串行模型:the sentence comprehension system continually and sequentially follows constraints of a Ianguage' grammar. Describe how the processor quickly constructs one or more representations of a sentence based on a restricted range of in formatio n that is guara nteed to be releva nt to its in terpretati on, primarily grammatical in formati on.Parallel models:并行模型emphasize that the comprehension system is sensitive to a vast range of in formati on, in clud ing grammatical, lexical, and con textual, as well as knowledge of the speaker/writer and of the world in general. Describe how theprocessor uses all releva nt in formati on to quickly evaluate the full range of possible in terpretati ons of a senten ce.Structural factors in comprehe nsio n 理解中的结构因素Comprehe nsion of writte nand spoken Ianguage can be difficult becauseit is not always easy to identify the constituents (phrases) of a sentence and the ways in which they relate to one another. Minimal attachment 最小配属:the“ structurally simp-etructuralsimplicity guides all initial analyses in sentence comprehension. Eg. The second wife will claim the in herita nee bel ongs to her.Garden path sentenee花园小径eg The horse raced past the barn fell. Fat people eat accumulates. Lexical factors in comprehe nsio n 词汇因素The human sentence processor is primarily guided by information about specific words that is stored in the lexic on. eg.The salesma n gla need at a/the customer with suspici on/ripped jea ns.Syntactic ambiguity 句法歧义Different possible ways in which words can be fit into phrases. Ambiguous category of some of the words in the senten ce. Eg. Joh n pain ted the car in the garage. Comprehension of text 语篇理解Resonance model:共振模型information in Iong-term memory is automaticallyactivated by the presenee of material that apparently bears a rough semantic relation to it.Discourse interpretation 语篇理解Schemata and drawing inferencesSchema图式a pre-existing knowledge structure in memory typically involving the no rmal expected patter ns of thin gs. eg.The customer en ters a restaura nt, looks for atable, decides where to sit, walks to the table …6.2.3. La nguage product ion 语言的生成(1) Access to words语言提取：步骤1.Conceptualization: what to express Word select ion: a competitive process 2.：select a word that corresp onds to the chose n concept. 3.:Morpho-phonological encoding: begins with the retrieval of all competitors.(2) Gen eratio n of sentence句子的生成1. Conceptual preparation®念准备:deciding what to say -a global plan is needed2. Word retrieval and applicati on of syn tactic kno wledge3. Processes of sentence gen erati on4. Functional planning: assigning grammatical functions Positional encoding: getting into positi ons foreach unit(3) Writte n Ian guage producti on:similar to those in the producti on of spoke n Ian guage. A major differe nt is that, once a syntactic lexicon unit and its morphological representation have been accessed, it is the orthographic rather tha n the phono logical form that must be retrieved and produced.6.3 Cognitive Linguistics 认知语言学Cognition is the way we think. Cognitive linguistics is the scientific study of therelatio n betwee n the way we com muni cate and the way we thi nk.6.3.1 Con strual and con strual operatio n识解及操作Construal 识解:the ability to conceive and portray the same situation in different ways(1) Attention / salience 注意力，突显:the operations grouped under salience have to do with our direct ion of atte ntio n towards someth ing that is salie nt to us. eg. We drove along the road.(2) Judgment / Comparison 判断，对比:the construal operations of it have to do with judging something by comparing it to something else. eg.There ' s a cat[figure] on the mat[gro und](3) . Perspective/ situatedness 视点，观察者位置:we view a scenein terms of our situatedness.It depends on two things : 1. Where we are situated in relation to the scene we ' re viewing. 2. How the scene is arranged in relation to our situatednessMy bike is in front of the car.6.3.2 Categorization 范畴化The process of classifying our experiences into different categories based on com mon alities and differe nces.Three levels: basic level superordi nate level subord in ate level.6.3.3 Image Schema意象图式Johnson, Mark.An image-schema is a “ skeletal mental representation of a recurrent pattern of embodied (especially spatial or kin esthetic) experie nce.1. A cen ter-periphery schema 中心-边缘图式The structure of an apple2. A containment schema 容器图示huma n bodies as containers3. A Cycle schema 循环图示Days Weeks4. A Force schema 力图示Physical: Wind, Gravity5. A link schema 连接图式6. A part-whole schema 部分-整体图式7. A path schema 路径图式8. A scale schema标量图式9. A verticality schema 垂直图式634 Metaphor 隐喻George Lakoff and Mark Joh nsonMetaphors are actually cognitive tools that help us structure our thoughts and experiences in the world around us. Metaphor is a conceptual mapping, not a linguistic one, from one domain to another, not from a word to another.Target domain 目标域-what is actually being talked about.Source doma in 源域-the doma in used as a basis for un dersta nding targetEg Time is money. The target domain,time,is conceptualized in terms of the source doma in of mon ey.1. Ontological metaphors实体隐喻means that human experienceswith physical objects provide the basis for ways of viewing events,activities, emotions, ideas, etc., as entities and substances. Eg. Inflation is lowering our standard of living2. Structural Metaphor 结构隐喻Provides rich highly structured, clearly deli neated source domai n to structure target doma in. eg.He attacked every weak point in my argume nt.3. Orientational Metaphor 方位隐喻Gives a concept a spatial orientation eg MORE IS UPaddi ng more of a substa nee, and percei ving the level of the substa nee rise.6.3.5 Metonymy 转喻is defined as a cognitive process in which the vehicle provides mental access to the target within the same domain. idealized cognitive models (ICMs) by LakoffOn the basis of the ontological realms, we may distinguish three categories:the world of “ concepttie world of “ fornth” world of “ things ” and “ events ”(1) Whole ICM and its part(s)整体与部分间的转喻：(i) Thing-and-Part ICM 事物及部分转喻eg. America for “ United StatesSca’IeICM 标量转喻eg, How old are you? for “what is your(agj e?bnstitution ICM.构成转喻eg.: wood for “ forest (旳)Eve nt ICM.事件转喻Eg.Bill smokedmarijuana. (v) Category-and-Member ICM.范畴及范畴成员转喻Eg .the pill for“ birthcontrol pill ”(vi)Cateeond-Property ICM.范畴及属性转喻Eg. blacks for“ black people ” (vii) Reduction I压缩转喻eg.crudefor “crude oil ”⑵Parts of an ICM部分与部分间的转喻(i) Action ICM.行为转喻eg.o author anew book (ii) Perception ICM.知觉转喻eg.sight for “thing seen (iii) Causation ICM.因果转喻eg.slow road for “slow traffic resulting from the poor state of the road (iv)Production ICM.生产转喻eg.I ' ve got a Ford for “car ” (v) Control ICM 控制转喻eg.The Mercedes has arrived. (vi) PossessionICM 领属转喻eg.He married money for “ pers on with mon ey" (vii) containment ICM 容器转喻(viii)Location ICMs 地点转喻(ix)Sign and Referenee ICMs符号和指代转喻6.3.6 Blending Theory 整合理论I.Cross-Space Map p ing跨空间映射 2.Ge nericSpace 类属空间3.Blend 整合4.Emergent Structure®创结构Chapter 7 Language, Culture, and Society7.1 Lan guage and culture语言和文化7.1.1 How does lang uage relate to cultureIn 20th century, "culture" emerged as a concept central to anthropology(the study of huma nity ), en compass ing all huma n phe nomena that are not purely results of huma n gen eticsLon don School 伦敦学派：Mali no wski 马林诺夫斯基:The meaning of a word greatly depe nds upon its occurre nee in a give n con textEth no graphy of com muni cati on 交际民族学：l.speech com mun ity 言语社团2. situatio n, eve nt and act 场景，事件，行为3.SPEAKING(situatio n,participa nts,e nds,act,seque nce,key,i nstrume ntalities, no rms,ge nres) Speech community言语社团:a group of people who form a community, and share the same Ian guage or a particular variety of Ian guageTheory of the con text of situatio n情景语境理论J. R. Firth (1890-1960):A. The releva nt features of the participa nts, pers ons, pers on alities.1. The verbal 言语action of the participants2.The non-verbal action of the participa ntsB. The releva nt objects.C. The effects of the verbal acti on.“ who speaks what to whom and whe n and to what end ”Halliday: Study Ian guage from a social semiotic or in teract ional perspective Functional interpretation of grammar as a resource for meaning potential Linguistic model in the study of literature7.1.2 Sapir-Whorf Hypothesis 萨丕尔-沃尔夫假设:Our language helps mould our way of thinking and, consequently, different Ianguages may probably express speakers ' unique ways of understanding the world.Linguistic determinism(语言决定论) Linguistic relativity (语言相对论)The stro ng versio n 强式说): The weak versi on (弱式说):7.1.3. Case studies个案研究Kaplan(1966): The structural organization of a text tends to be culturally specific. Nida(1998): Words are sometimes “ idiomgovettyed ” and “cultusaecific ”7.1.4 To which extent Do we need culture in our linguistic studyA study of linguistic issues in a cultural setting can greatly promote our understanding of motivatio n and directi on ality in lan guage cha nge.7.1.5 Culture in Language Teaching Classroon文化在语言学习中的重要作用:A. To get the students familiar with cultural differenee.B. To help the students tran sce nd their own culture and see things as the members of the target culture will.C. To emphasize the in separability of un dersta nding lan guage and un dersta nding culture through various classroom practices.7.2. Lan guage and Society7.2.1 How does language relate to society? Linguistics as a MONISTIC or AUTONOMOUS PURSUIT of an independent scienee —元性或自治性Linguistics as a DUALISTIC inquiry 二元性A situationally and socially variationist perspectiveA maxim in sociolinguistics: “ You are what 尔o即尔所言)”(WOMEN REGISTER女性语域LINGUISTIC SEXISM 语言性别歧视现象7.2.3 What should we know more about socioli nguistics 社会语言学的重要作用Sociolinguistics:社会语言学an interdisciplinary study of Ianguage use, attemptsto show the relati on ship betwee n Ian guage and society.7.2.4 What implicatio ns can we get from sociolin guistics ?社会语言学的重要启示:sociolinguistics' contributions: 1. Ithas contributed Jtg a change of emphasis in the content of Ian guage teachi ng. 2.…inno vati ons in materials and activities for the classroom. 3.…a fresh look at the nature of Ianguage development and use. 4.…a more fruitful research in this field.applied socioli nguistics 应用社会语言学In Ian guage classrooms In law courts In cli nic sett ings7.3 Cross-cultural Communi cati on 跨文化交际What should we know all about cross-cultural com muni cati on? I.Try to look at thi ngs from other persons point of view 2.Try to sense their feeling to a given issue3. Try to un dersta nd their way of knowing the world7.3.2 Case studies个案研究Whe n in Rome do as the Roma ns do Put yourself in other ' s shoes One culture ' s meat is anotherculture Honpotycand sincerity are key pointsto mutual un dersta nding.Chapter 8 Language in Use语言的使用What is pragmatics语用学? What' s the differenee between pragmatics and semantics 语义学？Pragmatics is the study of the use of Ian guage in com muni cati on, particularly the relati on ships betwee n senten ces and the con texts and situati ons in which they are used. Pragmatics includes the study of: (1) How the interpretation and use of utterances depe nds on kno wledge of the real world;(2)How speakers use and un dersta nd speech acts;(3) How the structure of senten ces is in flue need by the relati on ship betwee n the speaker and the hearer.Pragmatics is sometimes contrasted with semantics, which deals with meaning without refere nee to the users and com muni cative functions of senten ces.8.1 Speech act theory言语行为理论8.1.1 Performatives and con statives施为句和叙事句1. Performative: In speech act theory an uttera nee which performs an act, such as Watch out (= a warni ng).2. Con stative: An uttera nee which asserts somethi ng that is either true or force. E.g. Chicago is in the United States.3. Felicity eonditions of performatives 施为句的条件:(1) There must be a releva nt eonven ti onal procedure, and the releva nt participa nts and circumsta nces must be appropriate.(2) The procedure must be executed correctly and completely.(3) Very ofte n, the releva nt people must have the requisite thoughts, feeli ngs and in ten ti ons, and must follow it up with acti ons as specified.8.1.2 A theory of the illocutio nary act 会话含义理论1. What is a speech ac言语行为？A speech act is an uttera nee as a functional unit in com muni cati on. In speech act theory, uttera nces have two kinds of meaning.Propositional meaning (locutionary meaning)命题意义：This is the basic literal mea ning of the uttera nee which is conv eyed by the particular words and structures which the uttera nee contains. Illocutionary meaning (illocutionary force) 言外之意:This is the effect the utteranee or written text has on the reader or listener.A speech act which is performed in directly is sometimes known as an in direct speech act, such as the speech act of the requesti ng above. In direct speech acts are ofte n felt to be more polite ways of perform ing certa in kinds of speech act, such as requests and refusals.2. Locutionary act言内行为:A distinction is made by Austin in the theory of speech acts betwee n three differe nt types of acts invo Ived in or caused by the uttera nee of a senten ce. A locuti onary act is the say ing of someth ing which is meanin gful and can be un derstood.3. Illocutionary act 言外行为:An illocutionary act is using a sentence to perform a fun cti on.4. Perlocutionary act言后行为:A perlocutionary act is the results or effects that are produced by means of say ing someth ing.8.2 The theory of eon versati onal implicature 会话含义理论8.2.1 The cooperative prin ciple 合作原贝U1. Cooperative principle refers to the “ c-operation between speakers in using the maxims during the eonversation. There are four eonversational maxim会话准贝U :(1) The maxim of quantity 数量:a. Make your eon tributio n as in formative as required.b. Don' t make your eon tributi on more in formative tha n is required.(2) The maxim of quality 质量:Try to make your eontribution one that is true.a. Don' t say what you believe to be false.b. Don' t say that for which you lack adequate evide nee(3) The maxim of relati on 关系:Say things that are releva nt.(4) The maxim of manner方式:Be perspicuous.a. Avoid obscurity of expressi on.b. Avoid ambiguity.c. Be brief.d. Be orderly.2. Conversational implicature言外之意:The use of eonversational maxims to imply meaning during eonversation is called conversational implicature.8.2.2 Violation of the maxims 准则的违反1. Con versati onal implicature 言外之意In real com muni cati on, the in ten ti on of the speaker is ofte n not the literalmeaning of what he or she says. The real intention implied in the words is called conv ersatio nal implicature.r the speakers ' inten tio n through the words.8.2.3 Characteristics of implicature含义的特征：1. Calculability 可推导性2. Cancellability / defeasibility 可取消性3. Non-detachability 不可分离性4. Non-conventionality 非常规性8.3 Post-Gricean developme nts后格莱斯时期的发展8.3.1 Releva nee theory关联理论Every act of oste nsive com muni cati on com muni cates the presumpti on of its own optimal releva nee.8.3.2 The Q- and R-principles Q原则和R 原则The Q-pri nciple is in ten ded to inv oke the first maxim of Grice ' Quan tity, and the R-principle the relation maxim, but the new principles are more extensive than the Gricea n maxims.The definition of the Q-principle (hearer-based基于听话人)is:(1) Make your contribution sufficient 你的话要充分(cf. quantity);⑵ Say as much as you can (given Rt符合R 原则的前提下).The definition of the R-principle (speaker-based) is:(1) Make your con tributi on n ecessary (cf. Relati on, Quan tity-2, Mann er);(2) Say no more than you must (given Q)8.3.3 The Q-, I- and M-principles数量原则，信息量原则和方式原则Q-pri nciple:Speaker' maxim 准贝U: Do not provide a statement that is informationally weaker than your kno wledge of the world allows, uni ess provid ing a stron ger stateme nt would con trave ne the I-pri nciple.I-pri ncipleSpeaker' s maxim: the maxirhrainimization 最小化原贝USay as little as necessary, i.e. produce the minimal linguistic information sufficient to achieve your com muni cati onal en ds.Recipie nt ' s corollary: the en richme nt ruleAmplify the in formatio nal content of the speaker ' utiera nee, by fin di ng the most specific interpretation, up to what you judge to be the speaker -intended point. ' s m M-pri ncipleSpeaker' nsaxim: Do not use a prolix 冗长的，obscure模糊的or marked 显著的expressi on without reas on.Recipie nt ' s corollary: If the speaker used a prolixna r ked expressi on M, he did not mean the same as he would have, had he used the unmarked expression U - specifically he was trying to avoid the stereotypical associations and I-implicatures of U.Chapter 9 Language and Literature9.1 Theoretical background 概i术1. Style: Style refers to variation in a person ' speech or writing or a particular person ' s use of speech or writing at all times or to a way of speaking or writing at a particular period of time.2. Stylistics 文体学:According to H. G. Widdowson, stylistics is the study of literary discourse from a linguistic orientation. He treated literature as discourse, thus adopting a linguistic approach. This brings literature and linguistics closer.9.2 Some gen eral features of the literary lang uag文学语言的一些普遍特征9.2.1Foregro unding and grammatical form前景化和语法格式1. Foregrounding前景化:Foreground refers to the part of a scene nearest to the viewer, or figuratively the most noticeable position. Foregrounding means to put someth ing or some one in the most esse ntial part of the descripti on or n arrati on, other than in a backgro und positi on.2. In literary texts, the grammatical system of the Ianguage is often exploited,experime nted with, or made to “ deviate from other, more everyday, forms of Ian guage,and as a result creates in terest ing new patter ns in form and in meaning.9.2.2 Literal la nguage and figurative Ian guage字面语言和比喻语言1. Literal language: The first meaning for a word that a dictionary definition gives is usually called literal mea ning.2. Figurative Ianguage: A. k. a. trope, which refers to Ianguage used in a figurative way for a rhetorical purpose.We can use some figures of speech such as simile, metaphor, metonymy,syn ecdoche, etc.Simile 明喻：a way of comparing one thing with another, of explaining what one thing is like by showing how it is similar to another thing, and it explicitly signals itself in a text, with the words as or like. Metaphor 暗喻：like a simile, also makes a comparison between two unlike elements; but unlike a simile, this comparison is implied rather than stated.Metonymy 转喻：means a change of nameSynecdoche提喻：is usually classed as a type of metonymy. It refers to using then ame of part of an object to talk about the whole thing, and vice versa.9.2.3 The an alysis of literary Ian guage文学语言的分析9.3 The Ian guage in poetry诗歌语言9.3.1 Sou nd patterni ng 语音模式9.3.2 Differe nt forms of sound patterni ng 不同形式的语音模式1. Rhyme 押韵(end rhyme): The last word of a line has the same final sounds as the last word of ano ther line, sometimes immediately above or below, sometimes one or more lines away (cVC).2. Alliteration 头韵:The initial consonants are identical in alliteration (Cvc).3. Ass onance 准押韵:Ass onance describes syllables with a com mon vowel (cVc).4. Consonance辅押韵:Syllables ending with the same consonants are described as hav ing consonance (cvC).5. Reverse rhyme 反韵:Reverse rhyme describes syllables shari ng the vowel andin itial consonant (CVc).6. Pararhyme 压畐寸韵: Where two syllables have the same initial and final consonan ts, but differe nt vowels, they pararhyme (CvC).7. Repetitio n 反复：A complete match of the syllable (CVC).9.3.3 Stress and metrical patterni ng重音和韵律模式1. lamb 抑扬格:An iambic foot contains two syllables, an unstressed syllable followed by a stressed one.2. Trochee扬抑格:A trochaic foot contains two syllables as well, but in this case, the stressed syllable comes first, followed by an un stressed syllable.3. Anapest抑抑扬格:An anapestic foot consists of three syllables; two unstressed syllables are followed by a stressed one.4. Dactyl 扬抑抑格:A dactylic foot is similar to anapest, except reversed —a stressed syllable is followed by two un stressed on es.5. Spondee扬扬格:A spondaic foot consists of two stressed syllables; lines of poetry rarely con sist only of spon dees.6. Pyrrhic 抑抑格:A pyrrhic foot consists of two unstressed syllables.7. Metrical patterning 韵律模式(2) Dimeter (3)Trimeter (4)Tetrameter (5)Pentameter (6) Hexameter (7)Heptameter (8)Octameter9.3.4 Conven ti onal forms of meter and sound传统的韵律模式和语音模式1. Couplets对句:Couplets are two lines of verse, usually connected by a rhyme.2. Quatra ins 四行诗:Stan zasof four lin es, known as quatra ins, are very com mon in En glish poetry.3. Blank verse 无韵诗:Blank verse consists of lines in iambic pentameter which do not rhyme.9.3.5The poetic fun cti ons of sound and mete 语音和韵律在诗歌中的功能：1. For aesthetic pleasure2. To conform to a conven tio n / style / form3. To express or inno vate with a form4. To dem on strate tech ni cal skill, and for in tellectual pleasure5. For emphasis or con trast6. Ono matopoeia 拟声现象9.3.6 How to an alyze poetry?如何分析诗1. Read a poem more tha n on ce.2. Keep a dictionary and use it. Other reference books will also be invaluable. A good book on mythology and a Bible.3. Read so as to hear the sounds of the words in your mind. Poetry is writte n to be heard: its meanings are con veyed through sound as well as through print. One should read a poem as slowly as he can. Lip readi ng is a good habit.4. Always pay careful attention to what the poem is saying. One should make an effort to follow the thought continuously and to grasp the full implications and suggesti ons.5. As aids to the un dersta nding of a poem, we may ask some questi ons about.(1) Who is the speaker and what kind of person is he?(2) To whom is he speaking? What kind of person is he?⑶ What is the occasion?(4) What is the sett ing in time (time of day, seas on, cen tury)?(5) What is the setting in place (in doors or out, city or country, nation)?(6) What is the central purpose of the poem?9.4 The lang uage in fiction 小说中的语言941 Ficti onal prose and point of view 小说与视角1. First-person narrator (I-narrator叙述者：The person who tells the story may also be a character in the fictional world of the story, relat ing the story after the eve nt. I n this case, the critics call the n arrator a first-pers on n arrator or an l-n arrator because whe n the narrator refers to himself or herself in the story the first person pronoun “I i” used.2. Third-person narrator第三人称叙述者:If the narrator is not a character in the fictional world, he or she is usually called a third-person narrator, because reference to all the characters in the fictional world of the story will involve the use of the third-pers on pronouns, he, she, it or they.3. schema-orie nted Ian guag图式语言4. Deixis 指示功能:A term for a word or phrase which directly relates an utterance toa time, place, or a pers on.942 Speech and thought prese ntatio 言语和思维的表达1. Speech prese ntatior言语的表达：(1) Direct speech (DS)直接弓I语:A kind of speech presentation in which the character said in its fullest form.(2) In direct speech (IS)间接弓I语:A kind of speech prese ntati on in which the speaker ' s words are not reported as they were actually said.(3) Free in direct speech (FIS)自由间接引语:A further category which is an amalgam of direct and in direct speech features.(4) Narrator 'representation of speech acts (NRSA)叙述者对言语行为的表达：A mini malist kind of prese ntati on in which a part of passage can be see n as a summary of a Ion ger piece of discourse, and therefore eve n more back-gro un ded tha n in direct represe ntati on would be.(5) Narrator ' s representation of spe(NRS)叙述者对言语的表达：A possibility ofspeech presentation which is more minimalist than narrator ' s representation of speec acts, n amely a sentence which merely tells us the speech occurred, and which does not eve n specify the speech acts invo Ived.。
第一章：Basic Concepts of Words and Vocabulary注释：选择填空重点名词解释简答题（第0~5讲）1.1 What is a word【名词解释】词的概念a word is a minimal free form of a language that has a given sound and meaning and syntactic function 单词是一门语言中具有一定的声音、意义和语法功能并能够自由运用的最小语言单位【填空】词的特点1）a minimal free form of a language 一个语言的最小自由形式2）a sound unity 一个音的单位3）a unit of meaning 一个意义单位4）a form that can function alone in sentence 可以在句子中单独发挥作用的形式1）in visual terms 视觉角度一组有意义的字母打印或者写出来横排在一张纸上a meaningful group of letters printed or written horizontally across a piece of paper2）in terms of spoken language 口语角度a word is viewed as a sound or combination of sound which are made voluntarily withhuman vocal equipment 一个词被视为一个声音或声音的组合是由人类发声器官自动组合而成的3）semanticists 语义学家a word is a unit of meaning 一个词就是一个意义单位4）grammarians 语法学家a word be a free form that can function in sentence 一个单词是可以在句子中起到自由形式的作用【例子】书本第5页（重要）简答的时候加上例子好得分1.2 Sound and meaning【填空】声音与意义之间的关系1）there is no logical relationship between the sound which stands for a thing or an idea and the actual thing and idea itself 代表事物或思想的声音与实际事物和思想本身之间没有逻辑关系2）the symbolic connection between sound and meaning is almost always arbitrary声音和意义之间的联系几乎是任意性3）The relationship between the sound and the meaning of a word is convention单词的发音和意思之间的关系是约定俗称的4）woman, for example, become ‘femme’ in French and become ‘funu’ in Chinese1.3 Sound and form【简答】读音与拼写不一致的原因：1）more phonemes than letters in English 英语中音位数比字母数多The English alphabet was adopted form the Romans, which does not have a separate letter to represent each sound in the language so that some letters must do double duty or work together in combination 英语字母表是从罗马人那里继承来的，罗马人没有一个单独的字母来代表语言中的每个音，所以有些字母必须有双重功能或组合在一起2）the pronunciation has changed more rapidly than spelling over the years 发音比拼写变化得快3）some of the differences were created by the early scribes 有些差异是由早期的抄写员造成的1. Deliberately changed spelling of words either to make a line even or for easier recognition人们故意改变单词的拼写方式，或者是为了使单词排成一行，或者是为了更容易识别2. handwriting caused misunderstanding. To solve the problem in part, they changed theletter u to o when it came before m, n, or v. 笔迹造成误解。
Selected Solutions for Exercises inNumerical Methods with Matlab:Implementations and ApplicationsGerald W.RecktenwaldChapter6Finding the Roots of f(x)=0The following pages contain solutions to selected end-of-chapter Exercisesfrom the book Numerical Methods with Matlab:Implementations andApplications,by Gerald W.Recktenwald,c 2000,Prentice-Hall,Upper Saddle River,NJ.The solutions are c 2000Gerald W.Recktenwald.ThePDF version of the solutions may be downloaded or stored or printed onlyfor noncommercial,educational use.Repackaging and sale of these solutionsin any form,without the written consent of the author,is prohibited.The latest version of this PDFfile,along with other supplemental material for the book,can be found at /recktenwald.2Finding the Roots of f(x)=0 6–2The function f(x)=sin(x2)+x2−2x−0.09has four roots in the interval−1≤x≤3.Given the m-file fx.m,which containsfunction f=fx(x)f=sin(x.^2)+x.^2-2*x-0.09;the statement>>brackPlot(’fx’,-1,3)produces only two brackets.Is this result due to a bug in brackPlot or fx?What needs to be changed so that all four roots are found?Demonstrate that your solution works.Partial Solution:The statement>>Xb=brackPlot(’fx’,-1,3)Xb=-0.15790.05262.1579 2.3684returns two brackets.A close inspection of the plot of f(x)reveals that f(x)crosses the x-axis twice near x=1.3.These two roots are missed by brackPlot because there default search interval is too coarse.There is no bug in brackPlot.Implementing a solution using afiner search interval is left as an exercise.6–11Use the bisect function to evaluate the root of the Colebrook equation(see Exercise8) for /D=0.02and Re=105.Do not modify bisect.m.This requires that you write an appropriate function m-file to evaluate the Colebrook equation.Partial Solution:Using bisect requires writing an auxiliary function to evaluate the Cole-brook equation in the form F(f)=0,where f is the friction factor.The following form of F(f)is used in the colebrkz function listed below.F(f)=1√f+2log10/D3.7+2.51Re D√fMany other forms of F(f)will work.function ff=colebrkz(f)%COLEBRKZ Evaluates the Colebrook equation in the form F(f)=0%for use with root-finding routines.%%Input:f=the current guess at the friction factor%%Global Variables:%EPSDIA=ratio of relative roughness to pipe diameter%REYNOLDS=Reynolds number based on pipe diameter%%Output:ff=the"value"of the Colebrook function written y=F(f)%Global variables allow EPSDIA and REYNOLDS to be passed into%colebrkz while bypassing the bisect.m or fzero functionglobal EPSDIA REYNOLDSff=1.0/sqrt(f)+2.0*log10(EPSDIA/3.7+2.51/(REYNOLDS*sqrt(f)));Because the bisect function(unlike fzero)does not allow additional parameters to be passed through to the F(f)function,the values of /D and Re are passed to colebrkz via global variables.Running bisect with colebrkz is left to the reader.For Re=1×105and /D=0.02the solution is f=0.0490.Copyright c 2000,Gerald W.Recktenwald.Photocopying is permitted only for non-commercial educational purposes.Chapter6:Finding the Roots of f(x)=03 6–13Derive the g3(x)functions in Example6.4and Example6.5.(Hint:What is thefixed-pointformula for Newton’s method?)Partial Solution:Thefixed point iteration formulas designated as g3(x)in Example6.4 and Example6.5are obtained by applying Newton’s method.The general form of Newton’smethod for a scalar variable isx k+1=x k−f(x k) f (x k)Example6.4:The f(x)function and its derivative aref(x)=x−x1/3−2f (x)=1−13x−2/3Substituting these expressions into the formula for Newton’s method and simplifying givesx k+1=x k−x k−x1/3k−21−(1/3)x−2/3k=x k(1−(1/3)x−2/3k)−(x k−x1/3k−2)1−(1/3)x−2/3k=x k−(1/3)x1/3k−x k+x1/3k+21−(1/3)x−2/3k=(2/3)x1/3k+21−(1/3)x k=2x1/3k+63−x−2/3kRepeating this analysis for Example6.5is left as an exercise.Copyright c 2000,Gerald W.Recktenwald.Photocopying is permitted only for non-commercial educational purposes.4Finding the Roots of f(x)=0 6–17K.Wark and D.E.Richards(Thermodynamics,6th ed.,1999,McGraw-Hill,Boston,Example 14-2,pp.768–769)compute the equilibrium composition of a mixture of carbon monoxide and oxygen gas at one atmosphere.Determining thefinal composition requires solving3.06=(1−x)(3+x)1/2 x(1+x)1/2for x.Obtain afixed-point iteration formula forfinding the roots of this equation.Implement your formula in a Matlab function and use your function tofind x.If your formula does not converge,develop one that does.Partial Solution:Onefixed point iteration formula is obtained by isolating the factor of (3+x)in the numerator.3.06x(1+x)1/21−x =(3+x)1/2=⇒x=3.06x(1+x)1/21−x2−3=⇒g1(x)=3.06x(1+x)1/21−x2−3Anotherfixed point iteration formula is obtained by solving for the isolated x in the denomi-nator to getx=(1−x)(3+x)1/23.06(1+x)=⇒g2(x)=(1−x)(3+x)1/23.06(1+x)Performing10fixed point iterations with g1(x)givesit xnew1-7.6420163e-012-2.5857113e+003-1.0721050e+014-7.9154865e+015-7.1666488e+026-6.6855377e+037-6.2575617e+048-5.8590795e+059-5.4861826e+0610-5.1370394e+07Thus,g1(x)does not converge.The g2(x)function does converge to the true root of x= 0.340327....Matlab implementations of thefixed point iterations are left as an Exercise. Copyright c 2000,Gerald W.Recktenwald.Photocopying is permitted only for non-commercial educational purposes.Chapter6:Finding the Roots of f(x)=05 6–24Create a modified newton function(say,newtonb)that takes a bracket interval as input instead of a single initial guess.From the bracket limits take one bisection step to determine x0,the initial guess for Newton e the bracket limits to develop relative tolerances on x and f(x)as in the bisect function in Listing6.4.Solution:The newtonb function is listed below.The demoNewtonb function,also listed below, repeats the calculations in Example6.8with the original newton function and with the new newtonb function.Running demoNewtonb gives>>demoNewtonbOriginal newton function:Newton iterations for fx3n.mk f(x)dfdx x(k+1)1-4.422e-018.398e-01 3.526644293139032 4.507e-038.561e-01 3.521380147397333 3.771e-078.560e-01 3.521379706804574 2.665e-158.560e-01 3.5213797068045750.000e+008.560e-01 3.52137970680457newtonb function:Newton iterations for fx3n.mk f(x)dfdx x(k+1)1-4.422e-018.398e-01 3.526644293139032 4.507e-038.561e-01 3.521380147397333 3.771e-078.560e-01 3.521379706804574 2.665e-158.560e-01 3.5213797068045750.000e+008.560e-01 3.52137970680457The two implementations of Newton’s method give identical results because the input to newtonb is the bracket[2,4].This causes the initial bisection step to produce the same initial guess for the Newton iterations that is used in the call to newton.function demoNewtonb%demoNewtonb Use newton and newtonb to find the root of f(x)=x-x^(1/3)-2%%Synopsis:demoNewton%%Input:none%%Output print out of convergence history,and comparison of methodsfprintf(’\nOriginal newton function:\n’);r=newton(’fx3n’,3,5e-16,5e-16,1);fprintf(’\nnewtonb function:\n’);rb=newtonb(’fx3n’,[24],5e-16,5e-16,1);Copyright c 2000,Gerald W.Recktenwald.Photocopying is permitted only for non-commercial educational purposes.6Finding the Roots of f(x)=0 function r=newtonb(fun,x0,xtol,ftol,verbose)%newtonb Newton’s method to find a root of the scalar equation f(x)=0%Initial guess is a bracket interval%%Synopsis:r=newtonb(fun,x0)%r=newtonb(fun,x0,xtol)%r=newtonb(fun,x0,xtol,ftol)%r=newtonb(fun,x0,xtol,ftol,verbose)%%Input:fun=(string)name of mfile that returns f(x)and f’(x).%x0=2-element vector providing an initial bracket for the root%xtol=(optional)absolute tolerance on x.Default:xtol=5*eps%ftol=(optional)absolute tolerance on f(x).Default:ftol=5*eps%verbose=(optional)flag.Default:verbose=0,no printing.%%Output:r=the root of the functionif nargin<3,xtol=5*eps;endif nargin<4,ftol=5*eps;endif nargin<5,verbose=0;endxeps=max(xtol,5*eps);feps=max(ftol,5*eps);%Smallest tols are5*epsif verbosefprintf(’\nNewton iterations for%s.m\n’,fun);fprintf(’k f(x)dfdx x(k+1)\n’);endxref=abs(x0(2)-x0(1));%Use initial bracket in convergence testfa=feval(fun,x0(1));fb=feval(fun,x0(2));fref=max([abs(fa)abs(fb)]);%Use max f in convergence testx=x0(1)+0.5*(x0(2)-x0(1));%One bisection step for initial guessk=0;maxit=15;%Current and max iterationswhile k<=maxitk=k+1;[f,dfdx]=feval(fun,x);%Returns f(x(k-1))and f’(x(k-1))dx=f/dfdx;x=x-dx;if verbose,fprintf(’%3d%12.3e%12.3e%18.14f\n’,k,f,dfdx,x);endif(abs(f/fref)<feps)|(abs(dx/xref)<xeps),r=x;return;endendwarning(sprintf(’root not found within tolerance after%d iterations\n’,k));Copyright c 2000,Gerald W.Recktenwald.Photocopying is permitted only for non-commercial educational purposes.Chapter6:Finding the Roots of f(x)=07 6–27Implement the secant method using Algorithm6.5and Equation(6.13).Test your program by re-creating the results in Example6.10.What happens if10iterations are performed?Replace the formula in Equation(6.13)withx k+1=x k−f(x k)(x k−x k−1)f(x k k−1,whereεis a small number on the order ofεm.How and why does this change the results? Partial Solution:The demoSecant function listed below implements Algorithm(6.5)using Equation(6.13).The f(x)function,Equation6.3,is hard-coded into demoSecant.Note also that demoSecant performs ten iterations without checking for convergence.function demoSecant(a,b);%demoSecant Secant method for finding the root of f(x)=x-x^(1/3)-2=0%Implement Algorithm6.5,using Equation(6.13)%%Synopsis:demoSecant(a,b)%%Input:a,b=initial guesses for the iterations%%Output:print out of iterations;no return values.%copy initial guesses to local variablesxk=b;%x(k)xkm1=a;%x(k-1)fk=fx3(b);%f(x(k))fkm1=fx3(a);%f(x(k-1))fprintf(’\nSecant method:Algorithm6.5,Equation(6.13)\n’);fprintf(’n x(k-1)x(k)f(x(k))\n’);fprintf(’%3d%12.8f%12.8f%12.5e\n’,0,xkm1,xk,fk);for n=1:10x=xk-fk*(xk-xkm1)/(fk-fkm1);%secant formula for updating the rootf=fx3(x);fprintf(’%3d%12.8f%12.8f%12.5e\n’,n,xk,x,f);xkm1=xk;xk=x;%set-up for next iterationfkm1=fk;fk=f;endCopyright c 2000,Gerald W.Recktenwald.Photocopying is permitted only for non-commercial educational purposes.8Finding the Roots of f(x)=0 Running demoSecant with an initial bracket of[3,4](the same bracket used in Example6.10) gives>>demoSecant(3,4)Secant method:Algorithm6.5,Equation(6.13)n x(k-1)x(k)f(x(k))0 3.00000000 4.00000000 4.12599e-011 4.00000000 3.51734262-3.45547e-032 3.51734262 3.52135125-2.43598e-053 3.52135125 3.52137971 1.56730e-094 3.52137971 3.52137971-8.88178e-165 3.52137971 3.52137971-2.22045e-166 3.52137971 3.521379710.00000e+007 3.52137971 3.521379710.00000e+00Warning:Divide by zero.>In/werk/MATLAB_Book/SolutionManual/roots/mfiles/demoSecant.m at line228 3.52137971NaN NaN9NaN NaN NaN10NaN NaN NaNThe secant method has fully converged in6iterations.Continuing the calculations beyond convergence gives afloating point exception because f(x k)−f(x k−1)=0in the denominator of Equation(6.13).In general,it is possible to have f(x k)−f(x k−1)=0before the secant iterations reach convergence.Thus,thefloating point exception exposed by demoSecant should be guarded against in any implementation of the secant method.Implementing thefix suggested in the problem statement is left as an exercise for the reader.Copyright c 2000,Gerald W.Recktenwald.Photocopying is permitted only for non-commercial educational purposes.Chapter6:Finding the Roots of f(x)=09 6–33Write an m-file function to compute h,the depth to which a sphere of radius r,and specific gravity s,floats.(See Example6.12on page281.)The inputs are r and s,and the output ish.Only compute h when s<0.5.The s≥0.5case is dealt with in the following Exercise.If s≥0.5is input,have your function print an error message and stop.(The built-in error function will be useful.)Your function needs to include logic to select the correct root from the list of values returned by the built-in roots function.Partial Solution:The floata function listed below performs the desired computations.We briefly discuss three of the key statements in floata The coefficients of the polynomial are stored in the p vector.Thenc=getreal(roots(p));finds the real roots of the polynomial.The getreal subfunction returns only the real elements of a ing getreal is a defensive programming strategy.The sample calculation in Example6.12obtained only real roots of the polynomial,so getreal would not be necessary in that case.Thek=find(c>0&c<r);statement extracts the indices in the c vector satisfying the criteria0≤c k≤r.Then h=c(k);copies those roots satisfying the criteria to the h vector.No assumption is made that only one root meets the criteria.If more than one root is found a warning message is issued before leaving floata.Testing of floata is left to the reader.Copyright c 2000,Gerald W.Recktenwald.Photocopying is permitted only for non-commercial educational purposes.10Finding the Roots of f(x)=0 function h=floata(r,s)%float Find water depth on a floating,solid sphere with specific gravity<0.5%%Synopsis:h=floata(r,s)%%Input:r=radius of the sphere%s=specific gravity of the sphere(0<s<1)%%Output:h=depth of the sphereif s>=0.5error(’s<0.5required in this version’)elsep=[1-3*r04*s*r^3];%h^3-3*r*h+4*s*r^3=0c=getreal(roots(p));k=find(c>0&c<r);%indices of elements in c such that0<c(k)<rh=c(k);%value of elements in c satisfying above criterionendif length(h)>1,warning(’More than one root found’);end%==============================function cr=getreal(c)%getreal Copy all real elements of input vector to output vector%%Synopsis:cr=getreal(c)%%Input:c=vector of numerical values%%Output cr=vector of only the real elements of c%cr=[]if c has only imaginary elementsn=0;for k=1:length(c)if isreal(c(k))n=n+1;cr(n)=c(k);endendif n==0,cr=[];warning(’No real elements in the input vector’);endCopyright c 2000,Gerald W.Recktenwald.Photocopying is permitted only for non-commercial educational purposes.。
现代大学英语精读6文章概述如何使我们不为穷人的存在而内疚A brief summary of the essayIn the essay, the author brings up 5 historical solutions in presenting both historical solutions and current designs at first. He then concentrates on 5 current designs for getting the poor off our conscience. In presenting both historical solutions and current designs he expresses his critical attitudes implicitly. At the end of the essay, he warns the policy makers and people who are wealthy that "civil discontent and its consequences do not come from contented people.”and that poverty is the permanent ailment of society.Five solutions:1. The next life theory 2. Utilitarianism 3. Poor people’s fault 4. Survival of the fit test 5. Vague denial Five designs:1. Incompetent government 2. Harmful to the poor 3. Adverse effect on incentive 4. Adverse effect on freedom 5. Simple psychological denialThe main idea of the essay:Based on the analysis of historical solutions and current designs, the author ironically criticizes the attitude of getting the poor off our conscience, on which the scholars and politicians have been elaborating for centuries.1、Why the author chooses such a title as this essay?Look at the following photos. Millions and millions of people are struggling for their survival, thousands and thousands of people die of hunger, cold and illness. While ‘Millennium Development Goals are to meet the needs of the world’s poorest”, do you think the author really tries t o call people to get the poor off their conscience?“Plutarch was led to say”implies that it was the actual existence of the rich and poor or the logic of his analysis that made him come to such a conclusion: …If the Rome republic suffered from the same problems 2,000 years ago, it proves the author’s point that poverty is a perpetual (permanent) problem.2.five historical solutionspara. 3 The first solution (next-life theory)Does the author really think that this is an admirable solution?No, he doesn’t.He is being ironical here. He calls it “an admirable solution”because now the rich “get the poor off their conscience”.Para. 4:The second solution (utilitarianism)utilitarianism is a general philosophical idea like idealism. which means the greatest happiness of the greatest number. Utilitarianism is the moral doctrine that we should always act to produce the greatest possible balance of good over had for everyone affected by our action.Consequently, the greatest happiness of all constitutes the standard that determines whether an action is right or wrong. If they promote the greatest human welfare actions are right, if they do not actions are wrong.Para. 5: the third solution (poor people’s fault)Para. 7: the forth solution (Social Darwinism -- survival of the fittest)…the rich were not responsible for either its creation or its amelioration:The rich were not to blame for the existence of poverty so they should not be asked to undertake the task of solving the problem.Para. 9: the fifth solution (more vague denial of poverty)It declined in popularity, and references to it acquired a condemnatory tone:People began to reject Social Darwinism because it seemed to glorify brutal force and oppose treasured values of sympathy, love and friendship. Therefore, when it was mentioned, it was usually the target of criticism.3.Para. (10-11):a transition（1）Why does the author call it a revolution?Because it broke away from the traditional conception that the federal government was not responsible for social welfare. The Social Security Act of 1935 laid foundation for the current social welfare system of the United States. Readers can easily sense that the author is for the revolution.（2）What did people feel when a number of social welfare measures were put into practice? Were they right in thinking so? (para.10)People felt that the policy of ignoring the poor and refusing assistance had been abandoned. Since the government was making efforts to relieve the misery of the poor, they did not need to pay attention to any more.They were not completely right. The government did take many measures, but the desire to get the poor off our conscience still lingered on, waiting for chances to come back.4.five current designsPara.12: the first designdesign: planWhat is the argument of the first design?The argument is: Most of the assistance to the poor has to be undertaken by the government, but the government is in essence incompetent and ineffective and will make a mess of thejob. Therefore, the government should not be asked to aid the poor.What is the essence of the first design?The essence of the first design is to take away the responsibility to aid the poor from the government and to put an end to the social welfare policies since the New Deal.Para.13: analysis of the first designIn paragraph 12 and 13 , the author, on three occasions, mentions the pentagon or national defense. Why does he make these references?The author wants to point out the ironical fact that those people who attack the government or the bureaucracy will not include the military establishment. They want the government to do less or nothing in social welfare but more on “national defense”. The author is highly critical of such a view. He opposes huge military expenditures.What is the basic view of the author?On the whole, the author is positive about public service and government employees. He thinks that the American government has recruited many talented and dedicated people. His criticism is directed at the military establishment. Para. 14-15: the second designThe second design is: Any form of public help to the poor will hurt the poor themselves. Such help will destroy poor people’s motivation, make them lazy and break up their marriages. This is another typical argument put forward today by the conservatives in the U.S. in the discussion of social welfare reform.Does the author agree to the argument?No, the author thinks the accusations are groundless. Hefurther points out that those who support the design have no way to prove that the damage of the aid to the poor is greater than the damage to them caused by a loss of public assistance.Para.16: the third designThe third design: When you give public assistance to the poor, you take money away (through taxes) from the rich and give it ( in the form of public assistance) to the poor. The result is the rich become less willing to work hard and create wealth and the poor are encouraged to remain idle.The author’s view:The author uses two rhetorical questions to counter the argument. He implies that it is not the case that most poor people would prefer welfare to paying job. As for corporate executives, they are working very hard, showing no sign of lack of incentive. To say they are being lazy because they are not paid enough is an insult to the business executives. (the author is using a clever retort here.)Para.17-18: the forth design:The forth design argues that transferring money from the rich to the poor through the government has bad effect on freedom. By freedom, the designers mean spending as much money as one sees fit and giving the government as little as possible.This is possibly the most transparent of all the designs: No mention is ordinarily made of the relation of income to the freedom of the poor:The author is being ironical when he uses the word “transparent”. He means it is the most obvious that when these people talk about freedom they only have in mind the freedom of the rich.Para. 19: the fifth design: psychological denialThis is a psychic tendency that in various manifestations is common to us all.We all have the tendency to close our eyes to unpleasant things or refuse to think about them. This tendency may take different forms.5.conclusionIn the last part, the author subtly points out that public assistance to the poor is in the interest of conservatives. The ending seems not that dramatic but it is in line with the mild irony of the whole piece.肯尼迪总统就职演说The speech claims that all Americans should take on the responsibility of defending freedom and they should oppose Autocratic, poverty, disease and war that are enemies of mankind and in order to accomplish this task, to ensure common prosperity of human life, we compose of large global alliance.General analysis of a political speech1. He must try every possible means to arouse the feelings of audience. What he says represents the interests of the whole people. successful appeal to the emotion of the audience2. specific policyThe speech must have high-sounding words and empty promises3. The speech must be concise and short4. clever-choice of words to convey different meanings/tones.5. the use of biblical style to make it formal/ rigid.6. the use of a lot of rhetorical devices to make his address as powerful/ impressive as possible.1。
Basic Concepts of the Theory of SetsIn discussing any branch of mathematics, be it analysis, algebra, or geometry, it is helpful to use the notation and terminology of set theory. This subject, which was developed by Boole and Cantor in the latter part of the 19th century, has had a profound influence on the development of mathematics in the 20th century. It has unified many seemingly disconnected ideas and has helped to reduce many mathematical concepts to their logical foundations in an elegant and systematic way.A thorough treatment of theory of sets would require a lengthy discussion which we regard as outside the scope of this book. Fortunately, the basic notions are few in number, and it is possible to develop a working knowledge of the methods and ideas of set theory through an informal discussion . Actually, we shall discuss not so much a new theory as an agreement about the precise terminology that we wish to apply to more or less familiar ideas.In mathematics, the word “set” is used to represent a collection of objects viewed as a single entityThe collections called to mind by such nouns as “flock”, “tribe”, …crowd”, “team‟, are all examples of sets, The individual objects in the collection are called elements or members of the set, and they are said to belong to or to be contained in the set. The set in turn ,is said to contain or be composed of its elements.We shall be interested primarily in sets of mathematical objects: sets of numbers, sets of curves, sets of geometric figures, and so on. In many applications it is convenient to deal with sets in which nothing special is assumed about the nature of the individual objects in the collection. These are called abstract sets. Abstract set theory has been developed to deal with such collections of arbitrary objects, and from this generality the theory derives its power.NOTATIONS. Sets usually are denoted by capital letters: A,B,C,….X,Y,Z ; elements are designated by lower-case letters: a, b, c,….x, y, z. We use the special notationx∈S.To mean that “x is an element of S “or” x belongs to S”. If x does not belong to S, we write x∈S. When convenient ,we shall designate sets by displaying the elements in braces; for example，the set of positive even integers less than 10 is denoted by the symbol{2,4,6,8}whereas the set of all positive even integers is displayed as {2,4,6,…},the dots taking the place of “and so on”.The first basic concept that relates one set to another is equality of sets:DEFINITION OF SET EQUALITY Two sets A and B are said to be equal (or identical) if they consist of exactly the same elements, in which case we write A=B. If one of the sets contains an element not in the other, we say the sets are unequal and we write A≠B.SUBSETS. From a given set S we may form new sets, called subsets of S. For example, the set consisting of those positive integers less than 10 which are divisibleby 4(the set {4, 8}) is a subset of the set of all even integers less than 10.In general, we have the following definition.DEFINITION OF A SUBSET.A set A is said to be a subset of a set B, and we write A⊂B.Whenever every element of A also belongs to B. We also say that A is contained in B or B contains A. The relation is referred to as set inclusion.The statement A⊂B does not rule out the possibility that B A. In fact, we may have both A⊂B and B⊂A, but this happens only if A and B have the same elements. In other words, A=B if and only if A⊂B and B⊂A .This theorem is an immediate consequence of the foregoing definitions of equality and inclusion. If A⊂B but A≠B, then we say that A is a proper subset of B: we indicate this by writing A⊂B.In all our applications of set theory, we have a fixed set S given in advance, and we are concerned only with subsets of this given set. The underlying set S may vary from one application to another; it will be referred to as the universal set of each particular discourse.The notation {x∣x∈S. and x satisfies P} will designate the set of all elements x in S which satisfy the property P. When the universal set to which we are referring id understood, we omit the reference to S and we simply write{x∣x satisfies P}.This is read “the set of all x such that x satisfies p.” Sets designated in this way are said to be described by a defining property For example, the set of all positive real numbers could be designated as {X∣X>0};the universal set S in this case is understood to be the set of all real numbers. Of course, the letter x is a dummy and may be replaced by any other convenient symbol. Thus we may write {x∣x>0}={y∣y>0}={t∣t>0} and so on .It is possible for a set to contain no elements whatever. This set is called the empty set or the void set, and will be denoted by the symbol φ. We will consider φto be a subset of every set. Some people find it helpful to think of a set as analogous to a container (such as a bag or a box) containing certain objects, its elements. The empty set is then analogous to an empty container.To avoid logical difficulties, we must distinguish between the element x and the set {x} whose only element is x , (A box with a hat in it is conceptually distinct from the hat itself.)In particular, the empty set φis not the same as the set {φ}.In fact, the empty set φcontains no elements whereas the set {φ} has one element φ(A box which contains an empty box is not empty).Sets consisting of exactly one element are sometimes called one-element sets.UNIONS, INTERSECTIONS, COMPLEMENTS. From two given sets A and B, we can form a new set called the union of A and B. This new set is denoted by the symbol A∪B(read: “A union B”). And is defined as the set of those elements which are in A, in B, or in both. That is to say, A∪B is the set of all elements which belong to at least one of the sets A,B.Similarly, the intersection of A and B, denoted by A∩B(read: “A intersection B”) is defined as the set of those elements common to both A and B. Two sets A and B are said to be disjoint if A∩B=φ.If A and B are sets, the difference A-B (also called the complement of B relative to A)is defined to be the set of all elements of A which are not in B. Thus, by definition, A-B={X|X∈A and X B}. The operations of union and intersection have many formal similarities with (as well as differences from) ordinary addition and multiplications of union and intersection, it follows that A∪B=B∪A andA∩B=B∩A. That is to say, union and intersection are commutative operations. The definitions are also phrased in such a way that the operations are associative:(A∪B)∪C=A∪(B∪C)and(A∩B)∩C=A=∩(B∩C).The operations of union and intersection can be extended to finite or infinite collections of sets.VocabularySet 集合proper subset 真子集Set theory 集合论universal set 泛集Branch 分支empty set 空集Analysis 分析void set 空集Geometry 几何学union 并，并集Notation 记号，记法intersection交，交集Terminology 术语，名词表complement余余集Logic 逻辑relative to 相对于Logical 逻辑的finite有限的Systematic 系统的disjoint不相交Informal 非正式的infinite无限的Formal正式的cardinal number基数，纯数Entity 实在物ordinal number序数Element 元素generality一般性，通性Abstract set 抽象集subset子集Designate 指定，divisible可除的Notion 概念set inclusion 集的包含Braces 大括号immediate consequence 直接结果Identical 恒同的，恒等的Notes1. In discussing any branch of mathematics, be it analysis, algebra, or geometry, it is helpful to use the notation and terminology of set theory.意思是：在讨论数学的任何分支时，无论是分析，代数或几何，利用集合论的记号和术语是有帮助的。
Review (Chapter 1-5)9Basic Concepts of Control System9Definitions, terms, block diagram, ……9System modeling and representation9Dynamics of system----modeling9Various models: differential equation; transfer function; statespace model; signal flow graphs……;Relationship betweenvarious models9Linearization of nonlinear system9Control system characteristics9Solution of linear differential equations: time response9Solution of the state Equation9Routh’s stability criterion and steady-state error9…………2007-11-222Outline of Chapter 69Introduction9Basic Concepts of Root Locus Method 9Geometrical Properties (Construction Rules)9Generalized Root Locus9Performance characteristics9………2007-11-223ROOT LOCUS1. IntroductionFor a system designer: two things are very important.1) The stability-----determined by the roots obtained from thecharacteristic equation 1+G(s)H(s)=0 (Solving theequation or applying Routh’s criterion to this equation). 2) The degree of stability-----i.e.,the amount of overshoot, thesettling time of the controlled variable(Specifications). The graphical methods in this text bookthe root-locus method------in this chapterthe frequency response approach-----in thenext chapter2007-11-225ROOT LOCUS1. IntroductionThe Root Locus Method:–The Root Locus Concept–What is root locus? Why use it?–Root Locus Sketching–How to plot root locus?–Performance characteristics–Where and how to use it?2007-11-226ROOT LOCUS1. IntroductionDefinition:The root locus is a plot of the roots of the characteristic equation of the closed-loop system as a function of one system parameter varies, such as the gain of the open-loop transfer function.It is a method that determines how the poles move around the s-plane as we change one control parameter.This plot was introduced by Evans in 1948 and has been developed and used extensively in control engineering.2007-11-227ROOT LOCUS1. IntroductionThe difference between the root locus method and the Routh-Hurwitz method:The Root Locus Method -----tells us the position of the poles in the s-plane for each value of a control parameter. The Routh-Hurwitz Method----could only tell us for which values of the control parameter the poles would be to the left of a given vertical(垂直）axis in the s-plane.2007-11-2282007-11-229For a control system underlying :The poles of C(s)/R(s)(transient-response modes) are related to the Zeros (z i )and the Poles (p j )of the open-loop transfer function G(s)H(s) and also the gain----static loop sensitivity.G(s)H(s)-R(s)C(s))()()()(s D s N s R s C =)())(()())(()()(2121n m p s p s p s z s z s z s K s H s G −−−−−−= )()(1)()()(s H s G s G s R s C +=0)())(()())(()()(12121=−−−+−−−=+m n z s z s z s K p s p s p s s H s G ROOT LOCUS1. IntroductionROOT LOCUS1. IntroductionThe advantage of the root locus method:•The roots of the characteristic equation of the system can be obtained directly.•The characteristic of the system can be completely and accurately yielded•Design a system with relative ease. Such as using MATLAB2007-11-22102007-11-2212Basic Concepts of Root Locus MethodROOT LOCUSPlotting roots of a characteristic equation)2()(+=s s Ks G The open-loop transfer function:222222)2()()(nn ns s K s s KK s s K s R s C ωζωω++=++=++=The closed-loop transfer function:Ks −±−=112,1The roots of the characteristic equation are:Example 6-1:G(s)-R(s)C(s)2007-11-2213Basic Concepts of Root Locus Method11122,1−±−=−±−=K j j s n n ζωζωAnalysis: , it is a function of Kwhen K=0----the roots are s 1=0 and s 2= -2 (which also are the poles of the open loop transfer function)K=1----the roots s 1= s 2= -10<K<1----the roots s 1,2are real and lie on the negative real axis of the s-plans between –2 and –1 and 0 to –1, respectively K>1----the roots are complex and are given byK s −±−=112,1∵ROOT LOCUSPlotting roots of a characteristic equationGain of the open-loop transfer function)2()(+=s s Ks G2007-11-2214ROOT LOCUSPlotting roots of a characteristic equationK=0----s 1=0 and s 2= -2 (which also are the poles of the open loop transfer function)0<K<1----the roots s 1,2are real and lie on the negative real axis of the s-plansbetween –2 and –1 and 0 to –1, respectivelyK=1----the roots s 1= s 2= -1K>1----the roots are complex and are given by 11122,1−±−=−±−=K j j s nn ξωξωReIm[s]-20-1Open-loop poles(K=0)Sketch above roots now.)2()(+=s s Ks G K=1K ↑Note: each point in thelocus is closed-loop root, so the locus is called root locus .K ↑2007-11-2215Let’s look the location of closed-loop roots in detail.The roots of the characteristic equation are determined for a number of values of K : such as-1.0-j7.0-1.0+j7.050.0-1.0-j1.414-1.0+j1.4143-1.0-j1.0-1.0+j1.02-1.0-j0-1.0+j01.0-1.5-j0-0.5+j00.75-1.707-j0-0.293+j00.5-2.0-j0-0+j00s 2s 1K ROOT LOCUSPlotting roots of a characteristic equation)2()(+=s s Ks G 1,211s j K =−±−2007-11-2216ROOT LOCUSPlotting roots of a characteristic equation-20j2.0j1.0j ωσ-1-j1.0-j2.0[s]K=0K=00.50.5The values of K at point on thelocus are underlined0.750.751.02.02.03.03.0K ↓∞∞↑KLie all possible roots of the characteristic equation for all the values of K from zero to infinity (K>=0)K ↑↓ÅÆthe roots ↑↓ÅÆthe time response ↑↓The root-locus plotContain two branches (K as a parameter))2()(+=s s Ks G2007-11-2217Plotting roots of a characteristic equation2)2()(s s K s G +=The open-loop transfer function:KK K s 821222,1−±−=The roots of the characteristic equation are:G(s)-R(s)C(s)Example 6-2:222222)2()2()()(nn n n s s s s K s s K s R s C ωζωωζω+++=+++=The closed-loop transfer function:When K>0, system stable.2007-11-2218222,182121KK j Kj s nn−±−=−±−=ζωζωPlotting roots of a characteristic equationAnalysis: , it is a function of K when K=0----the roots are s 1=s 2=0 (which also are thepoles of the open loop transfer function)K=8----the roots s 1= s 2= -4K>8----the roots are real and lie on the negative real axis of the s-plans,and s 1→-∞, s 2 →-2respectively 0<K<8----the roots s 1,2are complex-conjugate poles and lie on the left half of the s-plansKK K s 821222,1−±−=2)2()(ss K s G +=2007-11-2219ReIm[s]ROOT LOCUSPlotting roots of a characteristic equationK ↑-2 2 Open-loop Poles (K=0)Note: each point in the locus is closed-loop root .Sketch above roots now. K=0----the roots are s 1=s 2=0 (which also are open-loop poles)K=8----the roots s 1= s 2= -4K>8----the roots are real and lie on the negative real axis of the s-plans,ands 1→-∞, s 2 →-2respectively0<K<8----the roots s 1,2are complex-conjugate poles and lie on the LHPKK K s 821222,1−±−=0-4Open-loop Zero (K=0)2)2()(s s K s G open +=2007-11-2220ROOT LOCUSPlotting roots of a characteristic equation:Review Exs.There are 2 branches locus (2 closed-loop roots ).ReIm[s]K ↑-20-4-∞ReIm[s]K ↑-20-1-∞∞Start:open-loop Poles (K=0)End:open-loop Zero (K=0) or infinity point2007-11-2221Plotting roots of a characteristic equation)(1)(T s s s G +=If K=1 in Ex. 6-1, time constant T adjustable, the open-loop transfer function:111)(1)()(2++=++=Ts s T s s s R s C The closed-loop transfer function:G(s)-R(s)C(s)Example 6-3:The characteristic equation is:12=++Ts s 0112=++s Ts 1)(2+=s Tss G eqo 421222,1−±−=T T s2007-11-2222Plotting roots of a characteristic equationReIm [s]T=2-1T ↑-∞j -j T=0T=0The characteristic equation is:012=++Ts s 0112=++s Ts 1)(2+=s Tss G eqo 421222,1−±−=T T s Open Poles are: +j, -jOpen Zero is: 0Sketching the roots locus: 2 branchesSo, not only K can be adjusted.T=0----the roots are s 1=s 2=±j; Zero:0T=2----the roots s 1= s 2= -10<T<2----the roots s 1,2are complex-conjugate poles and lie on the LHP T>2----the roots are real and s 1→-∞, s 2→0respectively2007-11-2223σj ωThe complex-conjugate poles:dn nj j ωσζωζω+=−±−21The root with a damping ratio ζlies on a linemaking the angle η=cos -1ζwith the negative real axis.Plotting roots of a characteristic equations 1s 2dn j j ωζω=−21-ζωn =σωnη=cos -1ζ2007-11-2224The analysis of the root locus with increase of K: K ↑1) A decrease in the damping ratio ζ. This increases the overshoot of the time response. ζ↓→Mp ↑, t s ↑2)An increase in the undamped natural frequency ωn . The value of ωn is the distance from the origin to the complex root. ωn ↑3)An increase in the damped natural frequency ωd . The value ωd is the imaginary component of the complex root and is equal to the frequency of the transient response. ωd ↑4)No effect on the rate of decay σ: that is , it remains constant for all values of gain equal to or greater than K α.5)For K>= K α, σ= -ζωn is constant, the system can never become unstableROOT LOCUSPlotting roots of a characteristic equation :Ex.6-1-aσj ω j ωd ββ ηγ ηδ K =0 K =0j ωd γj ωd δK αK βK γK δηβηδ2007-11-2225ROOT LOCUSQualitative analysis of the root locusConclusion:The branches of the root locus have been “pulled to the left”,or farther from the imaginary axis. For values of static loop sensitivity greater than Ka, the roots are farther to the left than for the original system.Therefore, the transients will decay faster, yielding a more stable system .(1) A zero is added to the simple second-order system :)()(a s s K s G +=)()()(a s s b s K s G ++=-a K=0K=0K α∞←KK=∞σj ω-b-aσj ωK=0K=0K α∞↑K K ↓∞2007-11-2226Conclusion:The branches of the root locus have been “pulled to the right”,or closer to the imaginary axis. For values of static loop sensitivity greater than Ka, the roots are closer to the imaginary axis than for the original system.Therefore, the transients will result in a less stable system.ROOT LOCUSQualitative analysis of the root locus(2) A pole is added to the simple second-order system :)()(a s s Ks G +=))(()(c s a s s Ks G ++=-aσj ωK=0K=0K α∞↑K K ↓∞σj ωK=0K=0K α∞←KK=∞-cK=∞K=0ROOT LOCUSQualitative analysis of the root locusGeneral conclusion:the addition of a zero to a system has the general effect of pulling the root locus to the left, tending to make it a more stable and faster-responding system (shortersettling time Ts)The addition of a pole to a system has the effect ofpulling the root locus to the right, tending to make it a less stable and slower-responding systemFor more complex transfer functions root-locus see Fig. 7.5, P206.2007-11-2227ROOT LOCUSProcedure outline of plotting root locusStep 1:Derive the open-loop transfer function G(s)H(s) of the systemStep 2:Factor the numerator and denominator of G(s)H(s)Step 3:Plot the zeros and poles of G(s)H(s) in the s-planeStep 4:Use the geometrical shortcuts summarized in Sec.7.8 to determine the locus that describes the roots of closed-loop characteristicequationStep 5:Calibrate the locus in terms of K(or other parameter we care about).If K is predetermined, the location of the exact roots of 1+G(s)H(s)are known. If the location of the roots is specified, K can be determined Step 6:Once roots have been found, c(t) can be gotten.Step 7:Does the response meet the desired specification?Adjustable? Compensation?2007-11-22282007-11-2229ROOT LOCUSOpen-loop transfer functionThe open-loop transfer function is of the form:∏∏−+==−−=++++=mn m j jmwh hu m w p s sz s K b s b s s a s a s K s H s G 1111)()()()()()()()( Where:a i andb j -----real or complex, may lie in the left-half plane (LHP)or right-half plane (RHP)K -------defined as the static loop sensitivity , positive/negative z h -------the zeros of G(s)H(s), z 1=-a 1,z 2=-a 2,…, z w =-a wp j -------the poles of G(s)H(s), p 1=…=p m =0, p m+1=-b 1,…,p m+u =-b u2007-11-2230ROOT LOCUSPoles of Closed-loop transfer function(1) The relationship between the poles and zeros of closed-loop transfer function and the open-loop transfer function:G(s)H(s)-R(s)C(s)The closed-loop transfer function:)()(1)()()()(s H s G s G s R s Y s +==φ2007-11-2231Where:K 1-------the gain of the forward paths, K 1r -----the root locus gain of the forward pathK 2-------the gain of the feedback paths, K 2r -----the root locus gain of the feedback pathROOT LOCUSPoles of Closed-loop transfer functionThe forward transfer function G(s) and the feedback transfer function H(s):∏∏∏∏====−−=++=q i i mfj j r q i i m fj j ps szs K sTssK s G 1111111111)()()1()1()(τ∏∏∏∏====−−=++=hi il j jrh i il j jps zs K s Ts K s H 1212212122)()()1()1()(τ2007-11-2232ROOT LOCUSPoles of Closed-loop transfer functionThe open-loop transfer function G(s)H(s):∏∏∏∏∏∏∏∏====−==−==−−−−=−−=++=h i i q i imlj j f j jrm n i im wj jrm n i im wj jps p s szs z s K p s sz s K s T ss Ks H s G 121112111111)()()()()()()1()1()()(τWhere:K=K 1*K 2------the open-loop gain of the systemK r =K 1r *K 2r ------the root locus gain of the open-loop system w=f+l ------the zero number of open-loop system n=m+q+h ------the pole number of open-loop system2007-11-2233ROOT LOCUSPoles of Closed-loop transfer function∏∏∏∏=−===−+−−−=+=Φwj irmn i imhj jfi ir z s K p s s ps z s K s H s G s G s 1112111)()()()()()(1)()(The closed-loop transfer function:1) The root locus gain of closed-loop system is equal to the root locus gainof the forward path of the open-loop system. 2) The closed-loop zeros are composed of the zeros of forward path andthe poles of feedback 3) The closed-loop poles are relative of open-loop zeros-poles and the rootlocus gain Kr.2007-11-2234(2)The characteristic equation of the system Δ(s):)()(1)(=+=Δs H s G s The root locus of closed-loop transfer function Φ(s):the corresponding values of s that satisfies the above Equation for any value of K from zero to infinityπβ)21()()(h j j eFes H s G +−==ROOT LOCUSPoles of Closed-loop transfer function1)()()()()()(11−=−−−−=u m w p s p s s z s z s K s H s G Then:2007-11-2235For K>0For K<0π)21()()(h j es H s G +=Poles of Closed-loop transfer function…,2,1,0180)21()()(±±=°+=∠h h s H s G Angle condition:1)()(=s H s G Magnitude condition:1)()(=s H s G …,2,1,0360)()(±±=°=∠h h s H s G Angle condition:Magnitude condition:2007-11-2236Poles of Closed-loop transfer functionExample 6-4:In the case of the following single loop system we have (with K a variable parameter, K>0)G(s)⊕_ryK1)(0)(1)(−=⇔=+=Δs KG s KG s The characteristic equation Δ(s):{}ππ2)(,1)(l s KG s KG +=∠=Poles of Closed-loop transfer function: ConclusionThe only possible locations for the poles in the s-plane are the ones that verify the angle condition above. K is then obtained from the magnitude condition.From s(angle)→K(magnitude)All that needs to be done then is to identify the locations in the s-plane that are valid locations for the poles for a given value of the parameter K.From given K→s location2007-11-22372007-11-2238Application of the magnitude and angle conditionsOnce the open-loop transfer function G(s)H(s) has been determined and put into the proper form, the poles and zeros of this function can be plotted in the s-plane. For example:))()(()()2)(/1()/1()()(3212122221p s p s p s s z s K s s T s s T s K s H s G n n −−−−=++++=ωζωFor the quadratic factor s 2+2ζωs+ ωn 2with the damping ratio ζ<1:dn n j j p ωσζωζω±=−±−=23,21Notes:1)The complex poles or zeros always occur in conjugate pairs.2)σis the damping constant, ωd is the damping natural frequencyof oscillation2007-11-2239σj ωz 1]2p 0p 3=σ-j ωdp 2=σ+j ωdp 1Application of the magnitude and angle conditionss-p 1s-z 1s-p 3s-p 2s Notes:1) a multiple pole or zeros is indicated on the pole-zero diagramby ×]q or ⊙]q ,q is the multiplicity of the pole or zero.2) all angles are considered positive, measured in the counter-clockwise(CCW) sense))()(()()()(32121p s p s p s s z s K s H s G −−−−=Pole-zero diagram:There are 4 Poles and 2 Zeros s2007-11-2240Application of the magnitude and angle conditionsPole-zero diagram:s-p 1s-z 1s-p 3s-p 2s z 1]2p 0p 3=σ-j ωdp 2=σ+j ωdσj ωFor example:s = -4+j4, p 1= -1, then°=−∠=+−=−+−=−8.126)(54)3(4312211p s p s orj p s s2007-11-2241Application of the magnitude and angle conditionsThe roots of the characteristic equation 1+G(s)H(s)=0 must satisfy the two condition:ysensitivit loop z s z s z s p s p s p s s K wmn m =−−−−−−=− 2121⎩⎨⎧<>+=−=∠∑∑0360180)12()()()()(K for h K for h terms r denominato of angles terms numerator of angles s H s G 12121=−−−−−−−mn mw p s p s p s s z s z s z s K Magnitude condition:⎩⎨⎧<°>°+=−∠−−−∠−∠−−∠++−∠=∠−03600180)12()()()()()()(11K for h K for h p s p s s m z s z s s H s G m n w Angle condition:2007-11-2242Application of the magnitude and angle conditionsExample 6-5:)2.01)(5.01)(1()25.01()()(0s s s s K s H s G ++++=5.2)5)(2)(1()4()()(K K s s s s K s H s G r =++++=Step1.The poles and zeros are plotted Step2.Φ’s are denominator angles and ψ’s are numerator angles, the l ’s are the lengths of the directed segmentsstemming from the denominator factors and the (l )’s are the lengths of the directed segments stemming from the numerator factorsσj ω-1-2-4-5Search pointΦ3Φ1Φ2ψ1l 3(l )1l 2l 12007-11-2243Application of the magnitude and angle conditions⎩⎨⎧<°>°+=−−−=∠03600180)12()()(3211K for h K for h s H s G φφφψStep3.Arbitrarily choose a search point. If the following angles condition is satisfy, this search point is a point on the locus.Once the complete locus has been determined. The locus can becalibrated in terms of the root-locus gain for any root s 1as following:1321)(l l l l K =4)(52111131211+=+=+=+=s l s l s l s l 1)the appropriate sign must be given to the magnitude of K, compatible withthe particular angle condition that is utilized to obtain the root locus.2)Since complex roots must occur in conjugate pairs, the locus issymmetrical about the real axis.Notes:2007-11-2244Application of the magnitude and angle conditionsσj ω-1-2-4-5K a K bK a K a K bK bK=0K=∞K=∞K=0K=0K=∞K>0σj ω-1-2-4-5K=0K=-∞K=-∞K=0K=0K=-∞K=-2.5K<0For K<0, the three branches of the root locus lie in the left half plane for K>-2.5Notes:The root locus for this system:)5)(2)(1()4()()(++++=s s s s K s H s G2007-11-2245Application of the magnitude and angle conditions)5)(2)(1()4()()(++++=s s s s K s H s G The root locus plotted by MATLABK>0。
