数学与应用数学专业英语期末考试试题

1一、英文表示：1.13.25thirteen-point-two-five2.anblogthelogarithmofntothebasebequalsa3.5/8fiveeighths4.3152axthefifthrootofasquaredplusxtotheminusonethird5.0x5232axtotheminustwothirdsplusthefifthrootofasquaredequalszero6.))((a2233babababacubedplusbcubedequalsaplusbintoasquaredminusabplusbsquared二、英语名词定义1.EquationAnequationisastatementoftheequalitybetweentwoequalnumbersymbols.2.FunctionThemoderndefinitionofafunctionyofxissimplyamappingfromaspaceXtoanotherspaceY.AmappingdefinedwheneverypointxofXhasadefiniteimagey,apointofY.3.Thelimitofasequencef(n)(forexampleLnf)(limn):Asequencef(n)issaidtohavealimitLif,foreverypositivenumber,thereisanotherpositivenumberN(whichmaydependon)suchthatLnf)(foralln=NInthiscase,wesaythesequencef(n)convergestoLandwewriteLnf)(limn,orLnf)(asn.Asequencewhichdoesnotconvergeiscalleddivergent.4.Thederivativeoffunctionf(x)Thederivative)x(‘fisdefinedbytheequationhxfhxffh)()(lim)x(0‘providedthelimitexists.Thenumber)x(‘fisalsocalledtherateofchangeoffatx.5.StatisticalpopulationAstatisticalpopulationisthesetofmeasurements(orrecordofsomequalitativetrait)correspondingtotheentirecollectionofunitsaboutwhichinformationissought.三几何图形的名称1.圆Circle2.椭圆ellipse3.长方形rectangle4.正方形square5.平行四边形parallelogram6.三角形triangle7.立方体cube8.圆锥cone9.曲线curve10.双曲线hyperbola四．英译汉1.Thisdeviceforrepresentingrealnumbersgeometricallyisaveryworthwhileaidthathelpsustodiscoverandunderstandbettercertainpropertiesofrealnumbers.However,thereadersshouldrealizethatallpropertiesofrealnumbersthataretobeacceptedastheoremsmustbededuciblefromtheaxiomswithoutanyreferencetogeometry.Thisdoesnotmeanthatoneshouldnotmakeuseofgeometryinstudyingpropertiesofrealnumbers.Onthecontrary,thegeometryoftensuggeststhemethodofproofofparticulartheorem,andsometimesageometricargumentismoreilluminatingthanapurelyanalyticproof(onedependingentirelyontheaxiomsfortherealnumbers).Inthisbook,geometricargumentsareusedtolargetohelpmotivateorclarifyaparticulardiscuss.译文：几何化地表示实数的方法是一种非常有益的辅助手段，它可以帮助我们发现和更好的了解实数的某些性质。然而，读者应该意识到，那些将要被采用作为定理的所有有关实数的性质时不应该使用几何学。相反地，几何学经常启发特殊定理的证明方法，而且，有时候，几何学方面的论点比纯分析（它完全依赖与实数的公理）的证明更直观。在本书中，几何学的论点会大范围地使用，以帮助人们推动或阐明一些特殊的讨论。22.Equationsareofverygreatuse.Wecanuseequationsinmanymathematicalproblems.Wemaynoticethatalmosteveryproblemgivesusoneormorestatementthatsomethingisequaltosomething;thisgivesusequations,withwhichwemayworkifweneedto.Tosolveanequationmeanstofindthevalueoftheunknownterm.Todothis,wemustchangethetermsaboutuntiltheunknowntermstandaloneononesideoftheunknownandtheanswertothequestion.Tosolvetheequation,therefore,meanstomoveandchangethetermsaboutwithoutmakingtheequationuntrue,untilonlytheunknownquantityisleftononeside,onmatterwhichside.译文：方程的用处很大。我们能将方程用于许多数学问题。我们或许注意到几乎每一个问题都给了我们以一种或多种表示某物和某物相等的说明；这就是给出了方程，如果我们需要的话，我们就可以进行运算、解方程就是找出未知数的值。要做到这点我们必须一项直到使未知项单独处于方程的一边为止，这样一来，就是使得它等于方程另一边的那些项。然后，我们就得到未知数的值也就是问题的答案。因此解方程意味着进行移项，而不是方程失真，直到方程的一边（无论那一边）只留下一个未知数时为止。3.Thestudyofdifferentialequationisonepartofmathematicsthat,perhapsmorethananyother,hasbeendirectlyinspiredbymechanics,astronomy,andmathematicalphysics.Itshistorybeganinthe17thcenturywhenNewton,Leibniz,andtheBernoullissolvedsomesimpledifferentialequationsarisingfromproblemsingeometryandmechanics.Theseearlydiscoveries,beginningabout1690,graduallyledtothedevelopmentofalotof“specialtricks”forsolvingcertainspecialkingsofdifferentialequations,Althoughthesespecialtricksareapplicableinrelativelyfewcases,theydoenableustosolvemanydifferentialequationsthatariseinmechanicsandgeometry.译文：微分方程的研究是数学的一个部分，它可能比其他部分，更多地直接受到了理学，天文学和数学物理的推动。它的历史开始于17世纪，当时，牛顿，莱布尼茨和伯努利家族解决了一些来源于几何学和力学的简单的微分方程。这些早期发现，大约开始于1690年，逐渐导致了解决一些特定类型的微分方程的大量的“特殊窍门”的发展。尽管这些特殊窍门只适用于相当少的情形，它们确实能使我们解决许多起源与力学和几何学的微分方程。4.Alargevarietyofscientificproblemsariseinwhichonetriestodeterminesomethingfromitsrateofchange.Forexample,wecouldtrytocomputethepositionofamovingparticlefromaknowledgeofitsvelocityoracceleration.Oraradioactivesubstancemaybedisintegratingataknownrateandwemayberequiredtodeterminetheamountofmaterialpresetafteragivetime.Inexamplelikethese,wearetryingtodetermineanunknownfunctionfromprescribedinformationexpressedintheformofanequationinvolvingareleastoneofthederivativesoftheunknownfunction.Theseequationsarecalleddifferentialequations,andtheirstudyformsoneofthemostchallengingbranchesofmathematics.译文：大量的科学问题人们根据事物的变化率去确定改事物（的量）。例如，我们可能试图根据速度或加速度的知识计算一个移动微粒的位置；又如，某种放射性物质可能正在以已知的速度进行衰变，需要我们确定在给定的时间后遗留物质的总量。在类似的例子中，我们力求通过以方程的形式表述的指定来确定未知函数，而这种方程至少包含了未知函数的一个导数。这些方程被称为微分方程，而且它们的研究形成了数学上最具有挑战性的分支之一。5.Indiscussinganybranchofmathematics,beitanalysis,algebra,orgeometry,itishelpfultousethenotationandterminologyofsettheory.Thissubject,whichwasdevelopedbyBooleandCantorinthelatterpartofthe19thcentury,hashadaprofoundinfluenceonthedevelopmentofmathematicsintheinthe20thcentury.Ithasunifiedmanyseeminglydisconnectedideasandhashelpedtoreducemanymathematicalconceptstotheirlogicalfoundationsinanelegantandsystematicway.Inmathematics,theword“set”isusedtorepresentacollectionofobjectsviewedasasingleentity.Theindividualobjec