{"id":4353,"date":"2013-12-15T06:00:15","date_gmt":"2013-12-14T21:00:15","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=4353"},"modified":"2014-09-10T16:51:02","modified_gmt":"2014-09-10T07:51:02","slug":"post-4353","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4353","title":{"rendered":"\u4e00\u69d8\u53ce\u675f"},"content":{"rendered":"

\u3000\u524d\u56de\u306e\u8a18\u4e8b\u3067\u8ff0\u3079\u305f\u8003\u3048\u306f un<\/sub> \u304c x \u306e\u95a2\u6570\u306e\u5834\u5408\uff0cun<\/sub>(x) \u3068\u8a18\u8ff0\u3059\u308b\u304c\uff0c\u306b\u62e1\u5f35\u3067\u304d\u307e\u3059\uff0e\u305d\u306e\u3088\u3046\u306a\u5834\u5408\uff0c\u6570\u5217\u307e\u305f\u306f\u7d1a\u6570\u304c\u53ce\u675f\u3059\u308b\u304b\u767a\u6563\u3059\u308b\u304b\u306f x \u306e\u7279\u5b9a\u306e\u5024\u306b\u4f9d\u5b58\u3057\u307e\u3059\uff0e\u6570\u5217\u3084\u7d1a\u6570\u304c\u53ce\u675f\u3059\u308b x \u306e\u5024\u306e\u96c6\u5408\u306f\u53ce\u675f\u9818\u57df\u3068\u547c\u3070\u308c\uff0c\\cal R \u3068\u8868\u8a18\u3057\u307e\u3059\uff0e<\/p>\n

\u3000\u7d1a\u6570 u1<\/sub>(x) + u2<\/sub>(x) + … \u306f\u9818\u57df \\cal R \u5185\u306e S(x) \u306e\u5408\u8a08\u306b\u53ce\u675f\u3057\u307e\u3059\uff0c\u3082\u3057 ε > 0 \u304c\u3042\u3063\u3066ε \u3068 x \u306e\u4e21\u8005\u306b\u4f9d\u5b58\u3059\u308b\u3042\u308b\u6570 N \u304c\u3042\u308a\uff0c|S(x) – Sn<\/sub>(x)| < ε \u3092\u6e80\u305f\u3057\uff0c\u5e38\u306b n > N \u3067\u3042\u3063\u3066 Sn<\/sub>(x) = u1<\/sub>(x) + … + un<\/sub>(x) \u306e\u5834\u5408\u306b\u306f\uff0e\u3082\u3057 ε \u306e\u307f\u306b\u4f9d\u5b58\u3057\uff0cx \u306b\u306f\u4f9d\u5b58\u3057\u306a\u3044 N \u3092\u898b\u3064\u3051\u3089\u308c\u308b\u306a\u3089\uff0c\u305d\u306e\u7d1a\u6570\u306f \\cal R \u5185\u306e S(x) \u306b\u4e00\u69d8\u53ce\u675f\u3057\u307e\u3059\uff0e\u4e00\u69d8\u53ce\u675f\u7d1a\u6570\u306b\u306f\u6b21\u306e\u5b9a\u7406\u306b\u793a\u3059\u3088\u3046\u306b\u591a\u304f\u306e\u5229\u70b9\u304c\u3042\u308a\u307e\u3059\uff0e<\/p>\n

    \n
  1. \u4eee\u306b un<\/sub>(x), n = 1, 2, 3, … \u304c a ≤ x ≤ b \u306e\u7bc4\u56f2\u3067\u9023\u7d9a\u3067\u3042\u308a\uff0c\u304b\u3064 ∑ un<\/sub>(x) \u304c a ≤ x ≤ b \u306e\u7bc4\u56f2\u3067 S(x) \u306b\u4e00\u69d8\u53ce\u675f\u3059\u308b\u306a\u3089 S(x) \u306f a ≤ x ≤ b \u306e\u7bc4\u56f2\u3067\u9023\u7d9a\u3067\u3042\u308b\uff0e<\/li>\n
  2. \u4eee\u306b ∑u<\/sub>(x) \u304c S(x) \u306b a ≤ x ≤ b \u306e\u7bc4\u56f2\u3067\u4e00\u69d8\u53ce\u675f\u3057\uff0c\u304b\u3064 un<\/sub>(x), n = 1, 2, 3, … \u304c a ≤ x ≤ b \u306e\u7bc4\u56f2\u3067\u7a4d\u5206\u53ef\u80fd\u3067\u3042\u308b\u5834\u5408\u306f\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3064\uff0e
    \n\\displaystyle \\int^{b}_{a}S(x)dx = \\int^{b}_{a}(u_1(x) + u_2(x) + \\cdots)dx = \\int^{b}_{a}u_1(x)dx + \\int^{b}_{a}u_2(x)dx + \\cdots<\/li>\n
  3. \u4eee\u306b un<\/sub>(x), n = 1, 2, 3, … \u304c\u9023\u7d9a\u3067\u304b\u3064 a ≤ x ≤ b \u306e\u7bc4\u56f2\u3067\u9023\u7d9a\u3057\u3066\u5fae\u5206\u53ef\u80fd\u3067\u3042\u308a\uff0c\u3055\u3089\u306b ∑un<\/sub>(x) \u304c S(x) \u306b\u53ce\u675f\u3057\uff0c∑u’n<\/sub>(x) \u304c a ≤ x ≤ b \u306e\u7bc4\u56f2\u3067\u4e00\u69d8\u53ce\u675f\u3059\u308b\u306a\u3089\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3064\uff0e
    \n\\displaystyle S'(x) = \\frac{d}{dx}(u_1(x) + u_2(x) + \\cdots) = u'_1(x) + u'_2(x) + \\cdots<\/li>\n
  4. \u6b63\u306e\u5b9a\u6570 Mn<\/sub> \u304c\u5b58\u5728\u3057 n = 1, 2, 3, … \u3067 \\cal R \u9818\u57df\u5185\u306e Mn<\/sub> \u306b\u304a\u3044\u3066 |un<\/sub>| ≤ Mn<\/sub> \u3067\u3042\u308a\uff0c\u304b\u3064 ∑Mn<\/sub> \u304c\u53ce\u675f\u3059\u308b\u5834\u5408\uff0c\u6545\u306b ∑un<\/sub>(x) \u306f \\cal R \u306b\u4e00\u69d8\u53ce\u675f\u3059\u308b\uff0e<\/li>\n<\/ol>\n

    \u3000\u4e00\u69d8\u53ce\u675f\u306e\u91cd\u8981\u306a\u5224\u5b9a\u6cd5\u304c\u3042\u308a\uff0c\u3057\u3070\u3057\u3070 Weierstrass M test \u3068\u547c\u3070\u308c\u307e\u3059\u304c\uff0c\u4e0a\u8a18\u306b\u793a\u3057\u305f\u3068\u304a\u308a\u3067\u3059\uff0e<\/p>\n