资源描述：
《数学专业英语_微分学论文翻译》由会员上传分享，免费在线阅读，更多相关内容在学术论文-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,werelargelyresponsiblefordevelopingtheideasofintegralcalculustothepointwherehithertoinsurmountableproblemscouldbesolvedbymoreo
2、rlessroutinemethods.Thesuccessfulaccomplishmentsofthesemenwereprimarilyduetothefactthattheywereabletofusetogethertheintegralcalculuswiththesecondmainbranchofcalculus,differentialcalculus.+V0E$f!k%w6l-{(Thecentralideaofdifferentialcalculusisthenotionofderiva
3、tive.Liketheintegral,thederivativeoriginatedfromaproblemingeometry—theproblemoffindingthetangentlineatapointofacurve.Unliletheintegral,however,thederivativeevolvedverylateinthehistoryofmathematics.Theconceptwasnotformulateduntilearlyinthe17thcenturywhentheF
4、renchmathematicianPierredeFermat,attemptedtodeterminethemaximaandminimaofcertainspecialfunctions.Fermat’sidea,basicallyverysimple,canbeunderstoodifwerefertoacurveandassumethatateachofitspointsthiscurvehasadefinitedirectionthatcanbedescribedbyatangentline.Fe
5、rmatnoticedthatatcertainpointswherethecurvehasamaximumorminimum,thetangentlinemustbehorizontal.Thustheproblemoflocatingsuchextremevaluesisseentodependonthesolutionofanotherproblem,thatoflocatingthehorizontaltangents.Thisraisesthemoregeneralquestionofdetermi
6、ningthedirectionofthetangentlineatanarbitrarypointofthecurve.ItwastheattempttosolvethisgeneralproblemthatledFermattodiscoversomeoftherudimentaryideasunderlyingthenotionofderivative.Atfirstsightthereseemstobenoconnectionwhateverbetweentheproblemoffindingthea
7、reaofaregionlyingunderacurveandtheproblemoffindingthetangentlineatapointofacurve.Thefirstpersontorealizethatthesetwoseeminglyremoteideasare,infact,ratherintimatelyrelatedappearstohavebeenNewton’steacher,IsaacBarrow(1630-1677).However,NewtonandLeibnizwerethe
8、firsttounderstandtherealimportanceofthisrelationandtheyexploitedittothefullest,thusinauguratinganunprecedentederainthedevelopmentofmathematics.Althoughthederivativewasoriginallyformulatedtostudytheprob
