[研究生入學(xué)考試]清華大學(xué)微積分課件全x-全文預(yù)覽
【正文】 ? yx ff?????])0,0()0,0([l i m0yfxff yx ??????????????22 )()(1220s i n])()[(lim yxyx????01s i nl i m0??? ???2222221c os1s i n2),(yxyxxyxxyxf x??????不連續(xù)！不存在！所以 ),(,),(lim00yxfyxf xxyx????2021/11/10 31 全微分的幾何意義 ),( 000 yxM0P1RRN1N0Q1P1SS1Q),( 00 dyydxxM ??zoxy),( yxfz ??????),(0yxfzyy NP0曲線?????),(0yxfzxx RP0曲線2R122111 SRRPSP ??dyyzRQRPM 01121 ????dxxzNQSRM 01012 ???? dyyzdxxzSPMM 0011 ??????的豎坐標(biāo)增量切平面在點 0M2021/11/10 32 )(高階偏導(dǎo)數(shù)定義：.),(,),(,),(),(的偏導(dǎo)函數(shù)稱為的二元函數(shù)上在則各偏導(dǎo)數(shù)仍然是定義中處處有偏導(dǎo)數(shù)在區(qū)域若二元函數(shù)yxfDyyxfxyxfDyxfz?????.),(,),(),(的二階偏導(dǎo)數(shù)則稱它們是存在的偏導(dǎo)數(shù)也和如果偏導(dǎo)函數(shù)yxfyyxfxyxf????三、高階偏導(dǎo)數(shù) 2021/11/10 33 ),()( 22yxfx fxfx xx????????),()( 22yxfyfyfy yy????????),()(2yxfxyfxfy yx?????????),()(2yxfyxfyfx xy?????????的二階偏導(dǎo)數(shù)關(guān)于 xf的二階偏導(dǎo)數(shù)關(guān)于 yf的二階混合偏導(dǎo)數(shù)后對先對 yxf的二階混合偏導(dǎo)數(shù)后對先對 xyf2021/11/10 34 的二階偏導(dǎo)數(shù)求例 )2c o s (]1[ yxxyz ???][解 )2s i n ( yxyxz ?????由 )2s i n (2 yxxyz ?????)2c o s (22yxxz ????? )2c o s (422yxyz ?????得到)]2s i n ([2yxyyxyz ???????? )2c o s (21 yx ???)]2s i n (2[2yxxxyxz ???????? )2c o s (21 yx ???xyzyxz??????? 22可見2021/11/10 35 ??????????)0,0(),(0)0,0(),(),(]2[ 2222yxyxyxyxxyyxf設(shè)例yxfxyf?????? )0,0()0,0( 22 和求][解xyfy??? ),0(,0 計算對于)( 2222yxyxxyx ????22222222222)()(2)(2yxyxxyxxxyyxyxy????????222244)(]
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