{"id":5700,"date":"2014-08-11T06:00:05","date_gmt":"2014-08-10T21:00:05","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=5700"},"modified":"2017-05-04T15:32:12","modified_gmt":"2017-05-04T06:32:12","slug":"post-5700","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5700","title":{"rendered":"\u7dda\u7a4d\u5206"},"content":{"rendered":"

\"Fig. — Fig. 6-2<\/figcaption><\/figure>\n
\u3000C<\/em> \u3092 xy<\/em> \u5e73\u9762\u306b\u304a\u3044\u3066 2 \u70b9 $A (a_1, b_1)$ \u304a\u3088\u3073 $B (a_2, b_2)$ \u3092\u3064\u306a\u3050\u66f2\u7dda\u3068\u3057\u307e\u3059\uff08Fig. 6-2\u53c2\u7167\uff09\uff0e $P(x, y)$ \u304a\u3088\u3073 $Q(x, y)$ \u3092\u66f2\u7dda C<\/em> \u4e0a\u306e\u3059\u3079\u3066\u306e\u70b9\u3092\u5b9a\u7fa9\u3059\u308b\u5358\u4e00\u5024\u95a2\u6570\u3068\u3057\u307e\u3059\uff0e $(x_1, y_1),\\ (x_2, y_2),\\ \\dots,\\ (x_{n-1}, y_{n-1})$ \u306b\u3088\u308a\u5f97\u3089\u308c\u305f n – 1<\/em> \u500b\u306e\u70b9\u3092\u9078\u629e\u3057\u3066 C<\/em> \u3092 n<\/em> \u500b\u306b\u7d30\u5206\u5316\u3057\u307e\u3059\uff0eCall $\\Delta x_k = x_k - x_{k-1}$ \u304a\u3088\u3073 $\\Delta y_k = y_k - y_{k-1},\\ k = 1,\\ 2,\\ \\dots\\ n$ \u3092\u547c\u3073\uff0cC<\/em> \u4e0a\u306b\u3042\u308a\u70b9 $(x_{k-1}, y_{k-1})$ \u304a\u3088\u3073\u70b9 $(x_k, y_k)$ \u306e\u9593\u306b\u3042\u308b\u3088\u3046\u306a\u70b9 $(\\xi_k, \\eta_k)$ \u3092\u60f3\u5b9a\u3057\u307e\u3059\uff0e\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u548c\u3092\u5f62\u6210\u3057\u307e\u3059\uff0e<\/p>\n
$\\displaystyle \\sum_{k=1}^{n}\\{P(\\xi_k, \\eta_k)\\Delta x_k + Q(\\xi_k, \\eta_k)\\Delta y_k\\}\\cdots(13)$ <\/p>\n
\u3000\u4eee\u306b\u6975\u9650\u304c\u5b58\u5728\u3059\u308b\u306a\u3089 $n\\rightarrow\\infty$ \u3068\u306a\u308b\u306b\u3064\u308c\u5168\u3066\u306e $\\Delta x_k,\\ \\Delta y$ \u306e\u91cf\u306f\u30bc\u30ed\u306b\u8fd1\u3065\u304d\uff0c\u3053\u306e\u548c\u306e\u6975\u9650\u3092 C<\/em> \u5468\u308a\u306e \u7dda\u7a4d\u5206<\/em> \u3068\u547c\u3073\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3057\u307e\u3059\uff0e<\/p>\n
$\\displaystyle \\int_C \\left[ P(x, y)dx + Q(x, y)dy \\right]$ \u307e\u305f\u306f $\\displaystyle \\int_{(a_1, b_1)}^{(a_2, b_2)}\\left[ Pdx + Qdy \\right]\\cdots(14)$ <\/p>\n
\u3000P<\/em> \u304a\u3088\u3073 Q<\/em> \u304c C<\/em> \u4e0a\u306e\u5168\u3066\u306e\u70b9\u306b\u3064\u3044\u3066\u9023\u7d9a\uff08\u307e\u305f\u306f\u533a\u9593\u7684\u306b\u9023\u7d9a\uff09\u306a\u3089\u3053\u306e\u6975\u9650\u306f\u5b58\u5728\u3057\u307e\u3059\uff0e\u305d\u306e\u7a4d\u5206\u5024\u306f\u4e00\u822c\u306b P<\/em>, Q<\/em>, \u7279\u306b\u66f2\u7dda C<\/em> \u306b\u4f9d\u5b58\u3057\uff0c\u307e\u305f $(a_1, b_1)$ \u304a\u3088\u3073 $(a_2, b_2)$ \u306e\u6975\u9650\u306b\u4f9d\u5b58\u3057\u307e\u3059\uff0e<\/p>\n
\u3000\u6b63\u78ba\u306b\u985e\u4f3c\u3057\u305f\u65b9\u6cd5\u3067 3 \u6b21\u5143\u7a7a\u9593\u306b\u304a\u3051\u308b\u66f2\u7dda C<\/em> \u5468\u308a\u306e\u7dda\u7a4d\u5206\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3067\u304d\u308b\u3067\u3057\u3087\u3046\uff0e<\/p>\n
$\\displaystyle \\lim\\limits_{n \\rightarrow\\infty}\\sum_{k=1}^{n}\\left\\{ A_1(\\xi_k, \\eta_k, \\zeta_k)\\Delta x_k + A_2(\\xi_k, \\eta_k, \\zeta_k)\\Delta y_k + A_3(\\xi_k, \\eta_k, \\zeta_k)\\Delta z_k \\right\\} \\\\ = \\int_C \\left[ A_1dx + A_2dy + A_3dz \\right] \\cdots(15)$ <\/p>\n
\u3053\u3053\u3067 $A_1$ , $A_2$ \u304a\u3088\u3073 $A_3$ \u306f $x$ , $y$ \u304a\u3088\u3073 $z$ \u306e\u95a2\u6570\u3067\u3059\uff0e<\/p>\n
\u3000\u4ed6\u306e\u7a2e\u985e\u306e\u7dda\u7a4d\u5206\uff0c\u7279\u306b\u66f2\u7dda\u306b\u4f9d\u5b58\u3059\u308b\u3082\u306e\u3082\u5b9a\u7fa9\u53ef\u80fd\u3067\u3059\uff0e\u4f8b\u3048\u3070\u4eee\u306b $\\Delta s_k$ \u304c\u4e0a\u56f3\u306e\u3088\u3046\u306b\u70b9 $(x_k, y_k)$ \u304a\u3088\u3073\u70b9 $(x_{k+1}, y_{k+1})$ \u9593\u306e\u66f2\u7dda C<\/em> \u306e\u5f27\u9577\u3092\u8a18\u8ff0\u3059\u308b\u306a\u3089<\/p>\n
$\\displaystyle \\lim\\limits_{n \\rightarrow \\infty} \\sum_{k=1}^{n} U(\\xi_k, \\eta_k)\\Delta s_k = \\int_C U(x, y)ds\\cdots(16)$ <\/p>\n
\u4e0a\u8a18\u306f\u66f2\u7dda C<\/em> \u5468\u308a\u306e $U(x, y)$ \u306e\u7dda\u7a4d\u5206\u3068\u547c\u3073\u307e\u3059\uff0e3\u6b21\u5143\u307e\u305f\u306f\u305d\u308c\u4ee5\u4e0a\u306e\u6b21\u5143\u3078\u306e\u62e1\u5f35\u3082\u53ef\u80fd\u3067\u3059\uff0e<\/p>\n
<\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u3000C \u3092 xy \u5e73\u9762\u306b\u304a\u3044\u3066 2 \u70b9 \u304a\u3088\u3073 \u3092\u3064\u306a\u3050\u66f2\u7dda\u3068\u3057\u307e\u3059\uff08Fig. 6-2\u53c2\u7167\uff09\uff0e \u304a\u3088\u3073 \u3092\u66f2\u7dda C \u4e0a\u306e\u3059\u3079\u3066\u306e\u70b9\u3092\u5b9a\u7fa9\u3059\u308b\u5358\u4e00\u5024\u95a2\u6570\u3068\u3057\u307e\u3059\uff0e \u306b\u3088\u308a\u5f97\u3089\u308c\u305f n – 1 \u500b\u306e\u70b9\u3092\u9078\u629e\u3057\u3066 C … <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5700\" class=\"more-link\"><span class=\"screen-reader-text\">“\u7dda\u7a4d\u5206” \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":6040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[125,83],"class_list":["post-5700","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","tag-125","tag-83"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5700","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5700"}],"version-history":[{"count":10,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5700\/revisions"}],"predecessor-version":[{"id":7826,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5700\/revisions\/7826"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/media\/6040"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5700"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

A (a_1, b_1) — Fig. 6-2<\/figcaption><\/figure>\n
\u3000C<\/em> \u3092 xy<\/em> \u5e73\u9762\u306b\u304a\u3044\u3066 2 \u70b9 $A (a_1, b_1)$ \u304a\u3088\u3073 $B (a_2, b_2)$ \u3092\u3064\u306a\u3050\u66f2\u7dda\u3068\u3057\u307e\u3059\uff08Fig. 6-2\u53c2\u7167\uff09\uff0e $P(x, y)$ \u304a\u3088\u3073 $Q(x, y)$ \u3092\u66f2\u7dda C<\/em> \u4e0a\u306e\u3059\u3079\u3066\u306e\u70b9\u3092\u5b9a\u7fa9\u3059\u308b\u5358\u4e00\u5024\u95a2\u6570\u3068\u3057\u307e\u3059\uff0e $(x_1, y_1),\\ (x_2, y_2),\\ \\dots,\\ (x_{n-1}, y_{n-1})$ \u306b\u3088\u308a\u5f97\u3089\u308c\u305f n – 1<\/em> \u500b\u306e\u70b9\u3092\u9078\u629e\u3057\u3066 C<\/em> \u3092 n<\/em> \u500b\u306b\u7d30\u5206\u5316\u3057\u307e\u3059\uff0eCall $\\Delta x_k = x_k - x_{k-1}$ \u304a\u3088\u3073 $\\Delta y_k = y_k - y_{k-1},\\ k = 1,\\ 2,\\ \\dots\\ n$ \u3092\u547c\u3073\uff0cC<\/em> \u4e0a\u306b\u3042\u308a\u70b9 $(x_{k-1}, y_{k-1})$ \u304a\u3088\u3073\u70b9 $(x_k, y_k)$ \u306e\u9593\u306b\u3042\u308b\u3088\u3046\u306a\u70b9 $(\\xi_k, \\eta_k)$ \u3092\u60f3\u5b9a\u3057\u307e\u3059\uff0e\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u548c\u3092\u5f62\u6210\u3057\u307e\u3059\uff0e<\/p>\n
$\\displaystyle \\sum_{k=1}^{n}\\{P(\\xi_k, \\eta_k)\\Delta x_k + Q(\\xi_k, \\eta_k)\\Delta y_k\\}\\cdots(13)$ <\/p>\n
\u3000\u4eee\u306b\u6975\u9650\u304c\u5b58\u5728\u3059\u308b\u306a\u3089 $n\\rightarrow\\infty$ \u3068\u306a\u308b\u306b\u3064\u308c\u5168\u3066\u306e $\\Delta x_k,\\ \\Delta y$ \u306e\u91cf\u306f\u30bc\u30ed\u306b\u8fd1\u3065\u304d\uff0c\u3053\u306e\u548c\u306e\u6975\u9650\u3092 C<\/em> \u5468\u308a\u306e \u7dda\u7a4d\u5206<\/em> \u3068\u547c\u3073\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3057\u307e\u3059\uff0e<\/p>\n
$\\displaystyle \\int_C \\left[ P(x, y)dx + Q(x, y)dy \\right]$ \u307e\u305f\u306f $\\displaystyle \\int_{(a_1, b_1)}^{(a_2, b_2)}\\left[ Pdx + Qdy \\right]\\cdots(14)$ <\/p>\n
\u3000P<\/em> \u304a\u3088\u3073 Q<\/em> \u304c C<\/em> \u4e0a\u306e\u5168\u3066\u306e\u70b9\u306b\u3064\u3044\u3066\u9023\u7d9a\uff08\u307e\u305f\u306f\u533a\u9593\u7684\u306b\u9023\u7d9a\uff09\u306a\u3089\u3053\u306e\u6975\u9650\u306f\u5b58\u5728\u3057\u307e\u3059\uff0e\u305d\u306e\u7a4d\u5206\u5024\u306f\u4e00\u822c\u306b P<\/em>, Q<\/em>, \u7279\u306b\u66f2\u7dda C<\/em> \u306b\u4f9d\u5b58\u3057\uff0c\u307e\u305f $(a_1, b_1)$ \u304a\u3088\u3073 $(a_2, b_2)$ \u306e\u6975\u9650\u306b\u4f9d\u5b58\u3057\u307e\u3059\uff0e<\/p>\n
\u3000\u6b63\u78ba\u306b\u985e\u4f3c\u3057\u305f\u65b9\u6cd5\u3067 3 \u6b21\u5143\u7a7a\u9593\u306b\u304a\u3051\u308b\u66f2\u7dda C<\/em> \u5468\u308a\u306e\u7dda\u7a4d\u5206\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3067\u304d\u308b\u3067\u3057\u3087\u3046\uff0e<\/p>\n
$\\displaystyle \\lim\\limits_{n \\rightarrow\\infty}\\sum_{k=1}^{n}\\left\\{ A_1(\\xi_k, \\eta_k, \\zeta_k)\\Delta x_k + A_2(\\xi_k, \\eta_k, \\zeta_k)\\Delta y_k + A_3(\\xi_k, \\eta_k, \\zeta_k)\\Delta z_k \\right\\} \\\\ = \\int_C \\left[ A_1dx + A_2dy + A_3dz \\right] \\cdots(15)$ <\/p>\n
\u3053\u3053\u3067 $A_1$ , $A_2$ \u304a\u3088\u3073 $A_3$ \u306f $x$ , $y$ \u304a\u3088\u3073 $z$ \u306e\u95a2\u6570\u3067\u3059\uff0e<\/p>\n
\u3000\u4ed6\u306e\u7a2e\u985e\u306e\u7dda\u7a4d\u5206\uff0c\u7279\u306b\u66f2\u7dda\u306b\u4f9d\u5b58\u3059\u308b\u3082\u306e\u3082\u5b9a\u7fa9\u53ef\u80fd\u3067\u3059\uff0e\u4f8b\u3048\u3070\u4eee\u306b $\\Delta s_k$ \u304c\u4e0a\u56f3\u306e\u3088\u3046\u306b\u70b9 $(x_k, y_k)$ \u304a\u3088\u3073\u70b9 $(x_{k+1}, y_{k+1})$ \u9593\u306e\u66f2\u7dda C<\/em> \u306e\u5f27\u9577\u3092\u8a18\u8ff0\u3059\u308b\u306a\u3089<\/p>\n
$\\displaystyle \\lim\\limits_{n \\rightarrow \\infty} \\sum_{k=1}^{n} U(\\xi_k, \\eta_k)\\Delta s_k = \\int_C U(x, y)ds\\cdots(16)$ <\/p>\n
\u4e0a\u8a18\u306f\u66f2\u7dda C<\/em> \u5468\u308a\u306e $U(x, y)$ \u306e\u7dda\u7a4d\u5206\u3068\u547c\u3073\u307e\u3059\uff0e3\u6b21\u5143\u307e\u305f\u306f\u305d\u308c\u4ee5\u4e0a\u306e\u6b21\u5143\u3078\u306e\u62e1\u5f35\u3082\u53ef\u80fd\u3067\u3059\uff0e<\/p>\n
<\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u3000C \u3092 xy \u5e73\u9762\u306b\u304a\u3044\u3066 2 \u70b9 \u304a\u3088\u3073 \u3092\u3064\u306a\u3050\u66f2\u7dda\u3068\u3057\u307e\u3059\uff08Fig. 6-2\u53c2\u7167\uff09\uff0e \u304a\u3088\u3073 \u3092\u66f2\u7dda C \u4e0a\u306e\u3059\u3079\u3066\u306e\u70b9\u3092\u5b9a\u7fa9\u3059\u308b\u5358\u4e00\u5024\u95a2\u6570\u3068\u3057\u307e\u3059\uff0e \u306b\u3088\u308a\u5f97\u3089\u308c\u305f n – 1 \u500b\u306e\u70b9\u3092\u9078\u629e\u3057\u3066 C … <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5700\" class=\"more-link\"><span class=\"screen-reader-text\">“\u7dda\u7a4d\u5206” \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":6040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[125,83],"class_list":["post-5700","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics","tag-125","tag-83"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5700","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5700"}],"version-history":[{"count":10,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5700\/revisions"}],"predecessor-version":[{"id":7826,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5700\/revisions\/7826"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/media\/6040"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5700"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}