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首页 > 其他文档 > 复旦大学_数学分析_欧阳光中_陈传璋_朱学炎_金福临_答案.pdf

复旦大学_数学分析_欧阳光中_陈传璋_朱学炎_金福临_答案.pdf

复旦大学_数学分析_欧阳光中_陈传璋_朱学炎_金福临_答案.pdf
内容要点:
285parenleftBiggax?bx?z +bx?ax?z +ay?by?z +by?ay?z +az?bz?z +bz?az?zparenrightBiggk= a×rotb + b×rota + (b·?)a + (a·?)b(2) rot(a×b) =parenleftBiggbx ??x +by ??y +bz ??zparenrightBigga?parenleftBiggax ?28412. a166a149a254a = ra247a218a130r = acosti +asintj +btk(0 lessorequalslanttlessorequalslant 2pi)a27a152a227a164a138a27a245.a41a181a207a = xi +yj +zk,l : x = acost,y = asint,z = bt(0 lessorequalsla2838. a166a149a254a = ?yi +xj +ck(ca143a126a234)a27a130a54a254a181(1) a247a11a177x2 +y2 = 1,z = 0a182(2) a247a11a177(x?2)2 +y2 = 1,z = 0.a41a181(1) a207l : x2 +y2 = 1,z = 0a167a75l = costi + sintj + 0282(3) a207gradU = yzi +xzj +xyka75divgradU = ?(yz)?x + ?(xz)?y + ?(xy)?z = 0rotgradU =parenleftBigg?(xy)?y ??(xz)?zparenrightBiggi +parenleftBigg?(yz)?z ??(xy)?xparenrightBiggj +parenleftBigg?(xz)?x 281§3. a124a216a208a2181. a23H(t) = eta +e?tba167a217a165a,ba143a126a149a254a167ta143a235a234a167(1) a166 dHdt(2) a121a178 d2Hdt2 = Ha41a181a207H(t) = eta +e?tba167a,ba143a126a149a254a167a75(1) dHdt =280(1) a101a52a180la216a157a140(0,0)a58a167a140a242a219a58(0,0)a134a171a141Da27a62a46a94a152a94a173a130Ca235a26a229a53a167a117a180a69a235a207a171a141a67a164a10a252a235a207a171a141a113?P?y = ?Q?x a167a279(1) (x2 + 2xy?y2)dx+ (x2 ?2xy?y2)dy(2) (2xcosy?y2 sinx)dx+ (2ycosx?x2 siny)dy(3) az dx+ bz dy+ ?by?axz2 dz(4) (x2 ?2yz)dx+ (y2 ?2xz)dy+ (z2 ?2xy)dz(5) ex[ey(x?y+ 2) +y]dx+ex[ey(x?y) + 1]dya41a181(1278§2. a173a130a200a169a218a180a187a27a195a39a531. a23a51a44a52a221a47a171a141Da83?P?y = ?Q?x a167a193a121U(x,y) =integraldisplay xx0P(x,y)dx+integraldisplay yy0Q(x0

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