最新6多元微分与积分(复习)幻灯片.ppt

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1、6多元微分与积分(复习)内容小结1.微分定义:2.重要关系:函数可导函数可微偏导数连续函数连续方向导数存在内容小结3.隐函数存在定理4.隐函数(组)求导方法方法1.利用复合函数求导法则直接计算;方法2.代公式空间光滑曲面曲面在点法线方程1)隐式情况.的法向量切平面方程2.曲面的切平面与法线空间光滑曲面切平面方程法线方程2)显式情况.法向量多元函数微分法的应用1.在几何中的应用求曲线在切线及法平面(关键:抓住切向量)求曲面的切平面及法线(关键:抓住法向量)2.极值与最值问题极值的必要条件与充分条件求条件极值的方法(消元法,拉格朗日乘数法)求解最值问题(求区域内部的驻点和边界上可能的极

2、值点)1.2.3.4.5.6.7.8.9..几何应用问题10．11．13．12．14.15.12.13.14.15.16.17.18.19.20.21.22.23.积分1.2.3.4.5.6.7.8.9.10.复数1.2.3.4.17.17.17.17.17.17.17.17.17.关系副词引导的定语从句1.when指时间，在定语从句中作时间状语。IstillrememberthedaywhenIfirstcametothisschool.Thetimewhenwegottogetherfinallyarrived.October1,1949wasthedaywhenthePeopl

3、e’sRepublicofChinawasfounded.Doyouremembertheyearswhenhelivedinthecountrysidewithhisgrandparents.2.where指地点，在定语从句中作地点状语。ShanghaiisthecitywhereIwasborn.Ivisitedthefarmwherealotofcowswereraised.ThehousewhereIlivedtenyearsagohasbeenpulleddown.Isthistheplacewheretheyfoughttheenemy?3.why指原因，在定语从句中作原

4、因状语。Pleasetellmethereasonwhyyoumissedtheplane.Thereasonwhyhewaspunishedisunknowntous.Idon’tknowthereasonwhyhelooksunhappytoday.Kunmingisabeautifulplace______flowersareseenalltheyearround.Kunmingisabeautifulplace______iscalledtheCityofSpring.Kunmingisabeautifulplace______manywritersmentionedinth

5、eirbook.注意：关系副词引导的定语从句经常可以用“介词+关系代词”引导的定语从句来表示。when=on(in,at,during…)+which;where=in(at,on…)+which;why=forwhich.如：IwasinBeijingonthedaywhen(=onwhich)hearrived.Theofficewhere(=inwhich)heworksisonthethirdfloor.Thisisthechiefreasonwhy(=forwhich)wedidit.-73-定语从句关系词的判断方法①Thisisthemountainvillagewher

6、eIstayedlastyear.Thisisthemountainvillage(which)Ivisitedlastyear.②I’llneverforgetthedayswhenIworkedtogetherwithyou.I’llneverforgetthedays(which)Ispentwithyou.-74-Thereason__________youexplainedtotheteacherisgroundless.Thereason__________hedidn’tshowupwasthathewasstuckinthetrafficjam.2、关系代词和关系副词

7、的比较1、Doyoustillrememberthechickenfarm_____wevisitedthreemonthsago?A.whereB.whenC.thatD.what2、Thereweredirtymarksonhertrousers______shehadwipedherhands.A.whereB.whichC.whenD.thatShe'llneverforgetherstaythere________shefoundhersonwh