高等数学-微积分第1章(英文讲稿).doc

《高等数学-微积分第1章(英文讲稿).doc》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、高等数学-Calculus微积分（双语讲稿）Chapter1FunctionsandModelsCalculus(FifthEdition)高等数学-Calculus微积分（双语讲稿）Chapter1FunctionsandModels1.1Fourwaystorepresentafunction1.1.1☆Definition(1-1)function:AfunctionfisarulethatassignstoeachelementxinasetAexactlyoneelement,calledf(x),inasetB.seeFig.2andFig.3Conceptions:

2、domain;range(Seefig.6p13);independentvariable;dependentvariable.Fourpossiblewaystorepresentafunction:1)Verbally语言描述(byadescriptioninwords);2)Numerically数据表述(byatableofvalues);3)Visually视觉图形描述(byagraph);4)Algebraically代数描述(byanexplicitformula).1.1.2AquestionaboutaCurverepresentafunctionandcan’

3、trepresentafunctionTheway(Theverticallinetest):Acurveinthexy-planeisthegraphofafunctionofxifandonlyifnoverticallineintersectsthecurvemorethanonce.SeeFig.17p171.1.3☆Piecewisedefinedfunctions(分段定义的函数)Example7(P18)1－xifx≤1f(x)＝﹛x2ifx＞1Evaluatef(0)，f(1)，f(2)andsketchthegraph.Solution：1.1.4Aboutab

4、solutevalue(分段定义的函数)⑴∣x∣≥0；⑵∣x∣≤0Example8(P19)Sketchthegraphoftheabsolutevaluefunctionf(x)＝∣x∣.Solution：1.1.5☆☆Symmetry，(对称)EvenfunctionsandOddfunctions(偶函数和奇函数)⑴SymmetrySeeFig.23andFig.24⑵①Evenfunctions:Ifafunctionfsatisfiesf(－x)＝f(x)foreverynumberxinitsdomain，thenfiscallanevenfunction.Examp

5、lef(x)＝x2isevenfunctionbecause:f(－x)＝(－x)2＝x2＝f(x)②Oddfunctions:Ifafunctionfsatisfiesf(－x)＝－f(x)foreverynumberxinitsdomain，thenfiscallanoddfunction.Examplef(x)＝x3isevenfunctionbecause:f(－x)＝(－x)3＝－x3＝－f(x)③Neitherevennoroddfunctions:1.1.6☆☆Increasinganddecreasingfunction(增函数和减函数)⑴Definition(1

6、-2)increasinganddecreasingfunction:①AfunctionfiscalledincreasingonanintervalIiff(x1)＜f(x2)wheneverx1＜x2inI.①AfunctionfiscalleddecreasingonanintervalIiff(x1)＞f(x2)wheneverx1＜x2inI.SeeFig.26.andFig.27.p218高等数学-Calculus微积分（双语讲稿）Chapter1FunctionsandModels1.2Mathematicalmodels:acatalogofessentialf

7、unctionsp251.2.1Amathematicalmodelp25Amathematicalmodelisamathematicaldescriptionofareal-worldphenomenonsuchasthesizeofapopulation,thedemandforaproduct,thespeedofafallingobject,theconcentrationofaproductinachemicalreaction,thelifeexpectancyof