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    (完整word版)高等数学公式大全(完整版).pdf

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    (完整word版)高等数学公式大全(完整版).pdf

    高等数学公式导数公式:基本积分表:三角函数的有理式积分:222212211cos12sinududxxtguuuxuux,axxaaactgxxxtgxxxxctgxxtgxaxxln1)(logln)(csc)(cscsec)(seccsc)(sec)(22222211)(11)(11)(arccos11)(arcsinxarcctgxxarctgxxxxxCaxxaxdxCshxchxdxCchxshxdxCaadxaCxctgxdxxCxdxtgxxCctgxxdxxdxCtgxxdxxdxxx)ln(lncsccscsecseccscsinseccos22222222CaxxadxCxaxaaxadxCaxaxaaxdxCaxarctgaxadxCctgxxxdxCtgxxxdxCxctgxdxCxtgxdxarcsinln21ln211csclncscseclnsecsinlncosln22222222CaxaxaxdxxaCaxxaaxxdxaxCaxxaaxxdxaxInnxdxxdxInnnnarcsin22ln22)ln(221cossin222222222222222222222020一些初等函数:两个重要极限:三角函数公式:诱导公式:函数角 A sin cos tg ctg-sin cos-tg-ctg 90-cos sin ctg tg 90+cos-sin -ctg -tg 180-sin-cos -tg-ctg 180+-sin -cos tg ctg 270-cos -sin ctg tg 270+-cos sin-ctg -tg 360-sin cos-tg-ctg 360+sin cos tg ctg 和差角公式:和差化积公式:2sin2sin2coscos2cos2cos2coscos2sin2cos2sinsin2cos2sin2sinsinctgctgctgctgctgtgtgtgtgtg1)(1)(sinsincoscos)cos(sincoscossin)sin(xxarthxxxarchxxxarshxeeeechxshxthxeechxeeshxxxxxxxxx11ln21)1ln(1ln(:2:2:22)双曲正切双曲余弦双曲正弦.590457182818284.2)11(lim1sinlim0exxxxxx文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2倍角公式:半角公式:cos1sinsincos1cos1cos12cos1sinsincos1cos1cos122cos12cos2cos12sinctgtg正弦定理:RCcBbAa2sinsinsin余弦定理:Cabbaccos2222反三角函数性质:arcctgxarctgxxx2arccos2arcsin高阶导数公式莱布尼兹(Leibniz)公式:)()()()2()1()(0)()()(!)1()1(!2)1()(nkknnnnnkkknknnuvvukknnnvunnvnuvuvuCuv中值定理与导数应用:拉格朗日中值定理。时,柯西中值定理就是当柯西中值定理:拉格朗日中值定理:xxFfaFbFafbfabfafbf)(F)()()()()()()()()(曲率:23333133cos3cos43cossin4sin33sintgtgtgtg222222122212sincossin211cos22coscossin22sintgtgtgctgctgctg文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2.1;0.)1(limMsMM:.,13202aKaKyydsdsKMMsKtgydxydss的圆:半径为直线:点的曲率:弧长。:化量;点,切线斜率的倾角变点到从平均曲率:其中弧微分公式:定积分的近似计算:bannnbannbanyyyyyyyynabxfyyyynabxfyyynabxf)(4)(2)(3)()(21)()()(1312420110110抛物线法:梯形法:矩形法:定积分应用相关公式:babadttfabdxxfabykrmmkFApFsFW)(1)(1,2221均方根:函数的平均值:为引力系数引力:水压力:功:空间解析几何和向量代数:文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2。代表平行六面体的体积为锐角时,向量的混合积:例:线速度:两向量之间的夹角:是一个数量轴的夹角。与是向量在轴上的投影:点的距离:空间,cos)(.sin,cos,cosPrPr)(Pr,cosPr)()()(2222222212121221221221cbacccbbbaaacbacbarwvbacbbbaaakjibacbbbaaababababababababaajajaajuABABABjzzyyxxMMdzyxzyxzyxzyxzyxzyxzyxzzyyxxzzyyxxuu(马鞍面)双叶双曲面:单叶双曲面:、双曲面:同号)(、抛物面:、椭球面:二次曲面:参数方程:其中空间直线的方程:面的距离:平面外任意一点到该平、截距世方程:、一般方程:,其中、点法式:平面的方程:113,22211;,1302),(,0)()()(1222222222222222222220000002220000000000czbyaxczbyaxqpzqypxczbyaxptzzntyymtxxpnmstpzznyymxxCBADCzByAxdczbyaxDCzByAxzyxMCBAnzzCyyBxxA多元函数微分法及应用文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2zyzxyxyxyxyxFFyzFFxzzyxFdxdyFFyFFxdxydFFdxdyyxFdyyvdxxvdvdyyudxxuduyxvvyxuuxvvzxuuzxzyxvyxufztvvztuuzdtdztvtufzyyxfxyxfdzzdzzudyyudxxududyyzdxxzdz,隐函数,隐函数隐函数的求导公式:时,当:多元复合函数的求导法全微分的近似计算:全微分:0),()()(0),(),(),(),(),()(),(),(),(22),(),(1),(),(1),(),(1),(),(1),(),(0),(0),(yuGFJyvvyGFJyuxuGFJxvvxGFJxuGGFFvGuGvFuFvuGFJvuyxGvuyxFvuvu隐函数方程组:微分法在几何上的应用:),(),(),(30)(,()(,()(,(2),(),(),(1),(0),(,0),(0),(0)()()()()()(),()()()(000000000000000000000000000000000000000000000000000zyxFzzzyxFyyzyxFxxzzzyxFyyzyxFxxzyxFzyxFzyxFzyxFnzyxMzyxFGGFFGGFFGGFFTzyxGzyxFzztyytxxtMtzztyytxxzyxMtztytxzyxzyxzyxyxyxxzxzzyzy、过此点的法线方程:、过此点的切平面方程、过此点的法向量:,则:上一点曲面则切向量若空间曲线方程为:处的法平面方程:在点处的切线方程:在点空间曲线方向导数与梯度:文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2上的投影。在是单位向量。方向上的,为,其中:它与方向导数的关系是的梯度:在一点函数的转角。轴到方向为其中的方向导数为:沿任一方向在一点函数lyxflfljieeyxflfjyfixfyxfyxpyxfzlxyfxflflyxpyxfz),(gradsincos),(grad),(grad),(),(sincos),(),(多元函数的极值及其求法:不确定时值时,无极为极小值为极大值时,则:,令:设,00),(,0),(,00),(,),(,),(0),(),(22000020000000000BACBACyxAyxABACCyxfByxfAyxfyxfyxfyyxyxxyx重积分及其应用:DzDyDxzyxDyDxDDyDxDDDayxxdyxfaFayxydyxfFayxxdyxfFFFFFaaMzxoydyxxIydyxyIxdyxdyxyMMydyxdyxxMMxdxdyyzxzAyxfzrdrdrrfdxdyyxf23222232222322222D22)(),()(),()(),(,)0(),0,0(),(,),(),(),(,),(),(1),()sin,cos(),(,其中:的引力:轴上质点平面)对平面薄片(位于轴对于轴对于平面薄片的转动惯量:平面薄片的重心:的面积曲面柱面坐标和球面坐标:文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 ZZ7B4A2X9Q2文档编码:CS8G8Y6Z6W6 HR9P9K2Z3H6 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