{"id":5177,"date":"2014-03-21T06:00:16","date_gmt":"2014-03-20T21:00:16","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=5177"},"modified":"2014-09-10T16:40:10","modified_gmt":"2014-09-10T07:40:10","slug":"post-5177","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5177","title":{"rendered":"\u30d9\u30af\u30c8\u30eb\u95a2\u6570\u306e\u6975\u9650\uff0c\u9023\u7d9a\u3068\u5c0e\u95a2\u6570"},"content":{"rendered":"

\u3000\u30d9\u30af\u30c8\u30eb\u95a2\u6570\u306e\u6975\u9650\uff0c\u9023\u7d9a\u53ca\u3073\u5c0e\u95a2\u6570\u306f\uff0c\u30b9\u30ab\u30e9\u30fc\u95a2\u6570\u306e\u305d\u308c\u3068\u3088\u304f\u4f3c\u305f\u898f\u5247\u306b\u5f93\u3044\u307e\u3059\uff0e\u4ee5\u4e0b\u306e\u8a18\u8ff0\u306f\u5b58\u5728\u3059\u308b\u985e\u4f3c\u3092\u793a\u3057\u3066\u3044\u307e\u3059\uff0e<\/p>\n

    \n
  1. \u30d9\u30af\u30c8\u30eb\u95a2\u6570 \\bold{A}(u) \u306f u_0 \u306b\u304a\u3044\u3066 \u9023\u7d9a<\/em> \u3067\u3042\u308b\u3068\u8a00\u308f\u308c\u308b\uff0e\u4eee\u306b\u4efb\u610f\u306e\u6b63\u306e\u6570 \\varepsilon \u304c\u3042\u3063\u3066\u3053\u3053\u3067 \\left|u - u_0\\right| < \\delta[\/latex] \u3092\u6e80\u305f\u3059 [latex]\\left|\\bold{A}(u) - \\bold{A}(u_0)\\right| < \\varepsilon[\/latex] \u304c\u5b58\u5728\u3059\u308b\u3088\u3046\u306a\u3042\u308b\u6b63\u306e\u6570 [latex]\\delta[\/latex] \u3092\u898b\u3064\u3051\u3089\u308c\u308b\u306a\u3089\uff0e\u3053\u306e\u3053\u3068\u306f\u6b21\u306e\u8a18\u8ff0\u3068\u7b49\u4fa1\u3067\u3042\u308b\uff0e[latex]\\lim\\limits_{u \\rightarrow u_0}\\bold{A}(u) = \\bold{A}(u_0)[\/latex]<\/li> <li><img src='https:\/\/s0.wp.com\/latex.php?latex&bg=T&fg=000000&s=0' alt='' title='' class='latex' \/>\\bold{A}(u) \u306e\u5fae\u5206\u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u308b\uff0e
    \n\\displaystyle \\frac{d\\bold{A}}{du} = \\lim\\limits_{\\Delta{u} \\rightarrow 0}\\frac{\\bold{A}(u + \\Delta {u}) - \\bold{A}(u)}{\\Delta{u}}\\cdots (7)
    \n\\bold{A}(u) = A_1(u)\\bold{i} + A_2(u)\\bold{j} + A_3(u)\\bold{k} \u306e\u3088\u3046\u306a\u5834\u5408\uff0c
    \n\\displaystyle \\frac{d\\bold{A}}{du} = \\frac{dA_1}{du}\\bold{i} + \\frac{dA_2}{du}\\bold{j} + \\frac{dA_3}{du}\\bold{k}
    \n\u3000d^2\\bold{A}\/du^2 \u7b49\u306e\u3088\u3046\u306a\u9ad8\u968e\u306e\u5c0e\u95a2\u6570\u3082\u540c\u69d8\u306b\u5b9a\u7fa9\u3055\u308c\u308b\uff0e<\/li>\n
  2. \u4eee\u306b \\bold{A}(x, y, z) = A_1(x, y, z)\\bold{i} + A_2(x, y, z)\\bold{j} + A_3(x, y, z)\\bold{k} \u306a\u3089\u3070
    \n\\displaystyle d\\bold{A} = \\frac{\\partial\\bold{A}}{\\partial x}dx + \\frac{\\partial\\bold{A}}{\\partial y}dy + \\frac{\\partial\\bold{A}}{\\partial z}dz\\cdots(8)
    \n\u306f \\bold{A} \u306e \u5fae\u5206<\/em> \u3067\u3042\u308b\uff0e<\/li>\n
  3. \u7a4d\u306e\u5c0e\u95a2\u6570\u306f\u30b9\u30ab\u30e9\u30fc\u95a2\u6570\u306e\u305d\u308c\u306e\u898f\u5247\u306b\u5f93\u3046\uff0e\u3057\u304b\u3057\u306a\u304c\u3089\uff0c\u30af\u30ed\u30b9\u7a4d\u306e\u5f93\u3046\u9806\u5e8f\u306f\u91cd\u8981\u304b\u3082\u3057\u308c\u306a\u3044\uff0e\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u6319\u3052\u308b\uff0e
    \n\\displaystyle (a)\\ \\frac{d}{du}(\\phi\\bold{A}) = \\phi\\frac{d\\bold{A}}{du} + \\frac{d\\phi}{du}\\bold{A}
    \n\\displaystyle (b)\\ \\frac{\\partial}{\\partial y}(\\bold{A} \\cdot \\bold{B}) = \\bold{A} \\cdot \\frac{\\partial \\bold{B}}{\\partial y} + \\frac{\\partial\\bold{A}}{\\partial y} \\cdot \\bold{B}
    \n\\displaystyle (c)\\ \\frac{\\partial}{\\partial z}(\\bold{A} \\times \\bold{B}) = \\bold{A} \\times \\frac{\\partial\\bold{B}}{\\partial z} + \\frac{\\partial\\bold{A}}{\\partial z} \\times \\bold{B}<\/li>\n<\/ol>\n