数学分析数学分析PPT (10).pdf

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9、2()2(222xyzxzyyzx?yazxaxayzazaxyaxyzxyzII?IIII?IIII?II2,2,2?kjia)2()2()2(222xyzxzyyzx?(,)222(0,0,0)(,)(2)(2)(2)x y zU x y zxyz dxyxz dyzxy dzC?F2222220001(2)()23xyzx dxy dyzxy dzxyzxyzC?FFF?11.?)0(2222?xyxyxyxyxjia?0?x()$%&?II?()$%&?II2222222222yxyxxyxxyxyyxyxy)(?a(,)22(1,0)()()(,)(,)x yxy dxxy dyV

10、x yU x yCxy?F2222101arctanln()2xydxxyydyCxyCxxyx?FF?12.?kjiaxyzyxzxzyxyzzyx)2()2()2(?5?kjiazyxaaa?xazxyyzazazyxxyazxyzII?IIII?II)(2,)(222?yayxzzxaxyII?II)(22?a(,)UU x y z?(2)(2)(2)dUxyz yzdxxyz zxdyxyz xydz?)()(2222zxdyxdzzdxyydzzdyxyzdx?)(22xydzxdyydxz?)()()()(222zyxxyzdxyzdzxydyzxd?(,)(,)()V x y z

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13、?green?FFF()$%&II?II?IIDCdxdyyuxudsnu22220?),(000yxM0),(),(20022002?II?IIyyxuxyxu?u x y(,)?0?3?),(03MOD?2222yuxuII?II0?FFF()$%&II?II?IIDCdxdyyuxudsnu22220?u15.?uu x y?(,)?vv x y?(,)?22vuF?p.2?F?0:()Fp.0?)(21xxpxxppvvuupFFvvuupFxF?II?7?12()pyyppyyuuvvFpFpFuuyF?I?Ivv?)()()2()(2222422xxxxxxpxxppvvuuvup

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17、uyyQy?320)(ruruzzRz?ruurxxruxPxx?II5203)(3?ruuryyruyQyy?II5203)(3?9ruurzzruzRzz?II5203)(3?0?II?II?IIzRyQxP?),(000zyx0?3?0SJ?0S?0SP?Gauss?0SJ02()1cos(,)11()44SuPQRudSdxrrnxyz?P?JIIII&)?$IIII%(FFFFFr n0dydz?21cos(,)14uudSrrn?PI&)?$I%(FFr n021cos(,)14Suudrrn?I&)?$I%(FFr nS?3?r?cos()1?00?IIFFdSnuS?21cos(,)14uudSrrn?PI&)?$I%(FFr nFF?0),(412SdSzyxu?3?0?3?FFP()$%&II?dSnurruzyxu1),cos(41),(2000nr?10