數(shù)學(xué)專業(yè)英語(yǔ)(吳炯圻-第2版)2-1

第二章

精讀課文——入門必修數(shù)學(xué)學(xué)院Keypoints:

usefultermsanddefinitionsofMathematics,equationDifficultpoints:

SomemathematicaltermsRequirements:

1.掌握所講課文的生詞和詞組

2.理解并掌握課外作業(yè)里面的漢譯英

3.理解所講段落的翻譯技巧與方法NewWords&Expressions:algebra代數(shù)學(xué) geometrical幾何的algebraic代數(shù)的identity恒等式arithmetic算術(shù),算術(shù)的measure測(cè)量，測(cè)度axiom公理 numerical數(shù)值的,數(shù)字的conception概念，觀點(diǎn)operation運(yùn)算constant常數(shù) postulate公設(shè)logicaldeduction邏輯推理proposition命題 division除，除法 subtraction減，減法formula公式 term項(xiàng)，術(shù)語(yǔ)trigonometry三角學(xué)variable變化的，變量2.1數(shù)學(xué)、方程與比例Mathematics,EquationandRatioMathematicscomesfromman’ssocialpractice,forexample,industrialandagriculturalproduction,commercialactivities,militaryoperationsandscientificandtechnologicalresearches.1－AWhatismathematics數(shù)學(xué)來(lái)源于人類的社會(huì)實(shí)踐，比如工農(nóng)業(yè)生產(chǎn)，商業(yè)活動(dòng)，軍事行動(dòng)和科學(xué)技術(shù)研究。Andinturn,mathematicsservesthepracticeandplaysagreatroleinallfields.Nomodernscientificandtechnologicalbranchescouldberegularlydevelopedwithouttheapplicationofmathematics.反過(guò)來(lái)，數(shù)學(xué)服務(wù)于實(shí)踐，并在各個(gè)領(lǐng)域中起著非常重要的作用。沒(méi)有應(yīng)用數(shù)學(xué)，任何一個(gè)現(xiàn)在的科技的分支都不能正常發(fā)展。Fromtheearlyneedofmancametheconceptsofnumbersandforms.Then,geometrydevelopedoutofproblemsofmeasuringland,andtrigonometrycamefromproblemsofsurveying.Todealwithsomemorecomplexpracticalproblems,manestablishedandthensolvedequationwithunknownnumbers,thusalgebraoccurred.

很早的時(shí)候，人類的需要產(chǎn)生了數(shù)和形的概念。接著，測(cè)量土地問(wèn)題形成了幾何學(xué)，測(cè)量問(wèn)題產(chǎn)生了三角學(xué)。為了處理更復(fù)雜的實(shí)際問(wèn)題，人類建立和解決了帶未知數(shù)的方程，從而產(chǎn)生了代數(shù)學(xué)。Before17thcentury,manconfinedhimselftotheelementarymathematics,i.e.,geometry,trigonometryandalgebra,inwhichonlytheconstantsareconsidered.17世紀(jì)前，人類局限于只考慮常數(shù)的初等數(shù)學(xué)，即幾何學(xué)，三角學(xué)和代數(shù)學(xué)。Therapiddevelopmentofindustryin17thcenturypromotedtheprogressofeconomicsandtechnologyandrequireddealingwithvariablequantities.Theleapfromconstantstovariablequantitiesbroughtabouttwonewbranchesofmathematics----analyticgeometryandcalculus,whichbelongtothehighermathematics.17世紀(jì)工業(yè)的快速發(fā)展推動(dòng)了經(jīng)濟(jì)技術(shù)的進(jìn)步，從而遇到需要處理變量的問(wèn)題。從常量到變量的跳躍產(chǎn)生了兩個(gè)新的數(shù)學(xué)分支-----解析幾何和微積分，他們都屬于高等數(shù)學(xué)。Nowtherearemanybranchesinhighermathematics,amongwhicharemathematicalanalysis,higheralgebra,differentialequations,functiontheoryandsoon.現(xiàn)在高等數(shù)學(xué)里面有很多分支，其中有數(shù)學(xué)分析，高等代數(shù)，微分方程，函數(shù)論等。Mathematiciansstudyconceptionsandpropositions,Axioms,postulates,definitionsandtheoremsareallpropositions.Notationsareaspecialandpowerfultoolofmathematicsandareusedtoexpressconceptionsandpropositionsveryoften.數(shù)學(xué)家研究的是概念和命題，公理，公設(shè)，定義和定理都是命題。符號(hào)是數(shù)學(xué)中一個(gè)特殊而有用的工具，常用于表達(dá)概念和命題。Formulas,figuresandchartsarefullofdifferentsymbols.SomeofthebestknownsymbolsofmathematicsaretheArabicnumerals1,2,3,4,5,6,7,8,9,0andthesignsofaddition“+”,subtraction“-”,multiplication“×”,division“÷”andequality“=”.公式，圖形和圖表都是不同的符號(hào)……..Theconclusionsinmathematicsareobtainedmainlybylogicaldeductionsandcomputation.Foralongperiodofthehistoryofmathematics,thecentricplaceofmathematicsmethodswasoccupiedbythelogicaldeductions.數(shù)學(xué)結(jié)論主要由邏輯推理和計(jì)算得到。在數(shù)學(xué)發(fā)展歷史的很長(zhǎng)時(shí)間內(nèi)，邏輯推理一直占據(jù)著數(shù)學(xué)方法的中心地位。Now,sinceelectroniccomputersaredevelopedpromptlyandusedwidely,theroleofcomputationbecomesmoreandmoreimportant.Inourtimes,computationisnotonlyusedtodealwithalotofinformationanddata,butalsotocarryoutsomeworkthatmerelycouldbedoneearlierbylogicaldeductions,forexample,theproofofmostofgeometricaltheorems.現(xiàn)在，由于電子計(jì)算機(jī)的迅速發(fā)展和廣泛使用，計(jì)算機(jī)的地位越來(lái)越重要?，F(xiàn)在計(jì)算機(jī)不僅用于處理大量的信息和數(shù)據(jù)，還可以完成一些之前只能由邏輯推理來(lái)做的工作，例如，證明大多數(shù)的幾何定理。回顧：1.如果沒(méi)有運(yùn)用數(shù)學(xué)，任何一個(gè)科學(xué)技術(shù)分支都不可能正常的發(fā)展。2.符號(hào)在數(shù)學(xué)中起著非常重要的作用，它常用于表示概念和命題。1－AWhatismathematicsAnequationisastatementoftheequalitybetweentwoequalnumbersornumbersymbols.1－BEquation等式是關(guān)于兩個(gè)數(shù)或者數(shù)的符號(hào)相等的一種描述。Equationareoftwokinds----identitiesandequationsofcondition.Anarithmeticoranalgebraicidentityisanequation.Insuchanequationeitherthetwomembersarealike,orbecomealikeontheperformanceoftheindicatedoperation.等式有兩種－恒等式和條件等式。算術(shù)或者代數(shù)恒等式都是等式。這種等式的兩端要么一樣，要么經(jīng)過(guò)執(zhí)行指定的運(yùn)算后變成一樣。Anidentityinvolvinglettersistrueforanysetofnumericalvaluesofthelettersinit.含有字母的恒等式對(duì)其中字母的任一組數(shù)值都成立。Anequationwhichistrueonlyforcertainvaluesofaletterinit,orforcertainsetsofrelatedvaluesoftwoormoreofitsletters,isanequationofcondition,orsimplyanequation.Thus3x-5=7istrueforx=4only;and2x-y=10istrueforx=6andy=2andformanyotherpairsofvaluesforxandy.一個(gè)等式若僅僅對(duì)其中一個(gè)字母的某些值成立，或?qū)ζ渲袃蓚€(gè)或者多個(gè)字母的若干組相關(guān)的值成立，則它是一個(gè)條件等式，簡(jiǎn)稱方程。因此3x-5=7僅當(dāng)x=4時(shí)成立，而2x-y=0，當(dāng)x=6,y=2時(shí)成立，且對(duì)x,y的其他許多對(duì)值也成立。Arootofanequationisanynumberornumbersymbolwhichsatisfiestheequation.Toobtaintherootorrootsofanequationiscalledsolvinganequation.方程的根是滿足方程的任意數(shù)或者數(shù)的符號(hào)。求方程根的過(guò)程被稱為解方程。Therearevariouskindsofequations.Theyarelinearequation,quadraticequation,etc.方程有很多種，例如：線性方程，二次方程等。Tosolveanequationmeanstofindthevalueoftheunknownterm.Todothis,wemust,ofcourse,changethetermsaboutuntiltheunknowntermstandsaloneononesideoftheequation,thusmakingitequaltosomethingontheotherside.Wethenobtainthevalueoftheunknownandtheanswertothequestion.解方程意味著求未知項(xiàng)的值，