数学专业英语 微分学论文翻译.doc

《数学专业英语 微分学论文翻译.doc》由会员上传分享，免费在线阅读，更多相关内容在应用文档-天天文库。

1、信息0801姬彩云200801010129DifferentialCalculus微分学HistoricalIntroduction历史介绍/D/x*p2R6r$]$NewtonandLeibniz,quiteindependentlyofoneanother,werelargelyresponsiblefordevelopingtheideasofintegralcalculustothepointwherehithertoinsurmountableproblemscouldbesolvedbymoreorlessroutinemethods.Thesuccessfulacc

2、omplishmentsofthesemenwereprimarilyduetothefactthattheywereabletofusetogethertheintegralcalculuswiththesecondmainbranchofcalculus,differentialcalculus.+V0E$f!k%w6l-{(Thecentralideaofdifferentialcalculusisthenotionofderivative.Liketheintegral,thederivativeoriginatedfromaproblemingeometry—thepr

3、oblemoffindingthetangentlineatapointofacurve.Unliletheintegral,however,thederivativeevolvedverylateinthehistoryofmathematics.Theconceptwasnotformulateduntilearlyinthe17thcenturywhentheFrenchmathematicianPierredeFermat,attemptedtodeterminethemaximaandminimaofcertainspecialfunctions.Fermat’side

4、a,basicallyverysimple,canbeunderstoodifwerefertoacurveandassumethatateachofitspointsthiscurvehasadefinitedirectionthatcanbedescribedbyatangentline.Fermatnoticedthatatcertainpointswherethecurvehasamaximumorminimum,thetangentlinemustbehorizontal.Thustheproblemoflocatingsuchextremevaluesisseento

5、dependonthesolutionofanotherproblem,thatoflocatingthehorizontaltangents.Thisraisesthemoregeneralquestionofdeterminingthedirectionofthetangentlineatanarbitrarypointofthecurve.ItwastheattempttosolvethisgeneralproblemthatledFermattodiscoversomeoftherudimentaryideasunderlyingthenotionofderivative

6、.Atfirstsightthereseemstobenoconnectionwhateverbetweentheproblemoffindingtheareaofaregionlyingunderacurveandtheproblemoffindingthetangentlineatapointofacurve.Thefirstpersontorealizethatthesetwoseeminglyremoteideasare,infact,ratherintimatelyrelatedappearstohavebeenNewton’steacher,IsaacBarrow(1

7、630-1677).However,NewtonandLeibnizwerethefirsttounderstandtherealimportanceofthisrelationandtheyexploitedittothefullest,thusinauguratinganunprecedentederainthedevelopmentofmathematics.Althoughthederivativewasoriginallyformulatedtostudytheprob