{"id":5693,"date":"2014-08-04T06:00:55","date_gmt":"2014-08-03T21:00:55","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=5693"},"modified":"2017-04-27T09:16:04","modified_gmt":"2017-04-27T00:16:04","slug":"post-5693","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5693","title":{"rendered":"\u591a\u91cd\u7a4d\u5206\u306e\u5909\u6570\u5909\u63db"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><p>\u3000\u9818\u57df <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Ccal+R&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\cal R' title='\\cal R' class='latex' \/> \u4e0a\u306e\u591a\u91cd\u7a4d\u5206\u3092\u8a55\u4fa1\u3059\u308b\u306b\u3042\u305f\u308a\uff0c\u76f4\u4ea4\u7cfb\u4ee5\u5916\u306e\u5ea7\u6a19\uff0c\u4f8b\u3048\u3070\u7b2c5\u7ae0\u3067\u8003\u616e\u3057\u305f\u3088\u3046\u306a\u66f2\u7dda\u5ea7\u6a19\u3092\u3057\u3070\u3057\u3070\u4fbf\u5229\u306b\u7528\u3044\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\uff0e<\/p>\n<p>\u3000\u4eee\u306b <img src='https:\/\/s0.wp.com\/latex.php?latex=%28u%2C+v%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(u, v)' title='(u, v)' class='latex' \/> \u3092\u3042\u308b\u5e73\u9762\u4e0a\u306e\u70b9\u306e\u66f2\u7dda\u5ea7\u6a19\u3068\u3059\u308b\u3068\uff0c<em>xy<\/em> \u5e73\u9762\u306e\u70b9 <img src='https:\/\/s0.wp.com\/latex.php?latex=%28x%2C+y%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(x, y)' title='(x, y)' class='latex' \/> \u3092 <em>uv<\/em> \u5e73\u9762\u306e\u70b9 <img src='https:\/\/s0.wp.com\/latex.php?latex=%28u%2C+v%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(u, v)' title='(u, v)' class='latex' \/> \u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3059\u308b\u5909\u63db\u5f0f\u306e\u30bb\u30c3\u30c8 <img src='https:\/\/s0.wp.com\/latex.php?latex=x+%3D+f%28u%2C+v%29%2C%5C+y+%3D+g%28u%2C+v%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='x = f(u, v),\\ y = g(u, v)' title='x = f(u, v),\\ y = g(u, v)' class='latex' \/> \u304c\u5f97\u3089\u308c\u308b\u306f\u305a\u3067\u3059\uff0e\u305d\u306e\u5834\u5408 <em>xy<\/em> \u5e73\u9762\u306e\u9818\u57df <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Ccal+R&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\cal R' title='\\cal R' class='latex' \/> \u306f <em>uv<\/em> \u5e73\u9762\u306e\u9818\u57df <img src='https:\/\/s0.wp.com\/latex.php?latex=%7B%5Ccal+R%7D%27&#038;bg=T&#038;fg=000000&#038;s=0' alt='{\\cal R}&#039;' title='{\\cal R}&#039;' class='latex' \/> \u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3055\u308c\u307e\u3059\uff0e\u3053\u3053\u3067\u6b21\u306e\u5f0f\u3092\u5f97\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cunderset%7B%5Ccal+R%7D%7B%5Ciint%7DF%28x%2C+y%29dxdy+%3D+%5Cunderset%7B%7B%5Ccal+R%7D%27%7D%7B%5Ciint%7D+G%28u%2C+v%29%5Cleft%7C%5Cfrac%7B%5Cpartial+%28x%2Cy%29%7D%7B%5Cpartial+%28u%2C+v%29%7D%5Cright%7C+dudv+%5Ccdots%289%29+&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\underset{\\cal R}{\\iint}F(x, y)dxdy = \\underset{{\\cal R}&#039;}{\\iint} G(u, v)\\left|\\frac{\\partial (x,y)}{\\partial (u, v)}\\right| dudv \\cdots(9) ' title='\\displaystyle \\underset{\\cal R}{\\iint}F(x, y)dxdy = \\underset{{\\cal R}&#039;}{\\iint} G(u, v)\\left|\\frac{\\partial (x,y)}{\\partial (u, v)}\\right| dudv \\cdots(9) ' class='latex' \/><\/p>\n<p>\u3053\u3053\u3067 <img src='https:\/\/s0.wp.com\/latex.php?latex=G%28u%2C+v%29+%5Cequiv+F%5C%7Bf%28u%2Cv%29%2C+g%28u%2Cv%29%5C%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='G(u, v) \\equiv F\\{f(u,v), g(u,v)\\}' title='G(u, v) \\equiv F\\{f(u,v), g(u,v)\\}' class='latex' \/> \u304a\u3088\u3073<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cfrac%7B%5Cpartial+%28x%2C+y%29%7D%7B%5Cpartial+%28u%2C+v%29%7D+%5Cequiv+%5Cleft%7C+%5Cbegin%7Barray%7D%7Bcc%7D+%5Cfrac%7B%5Cpartial+x%7D%7B%5Cpartial+u%7D+%26+%5Cfrac%7B%5Cpartial+x%7D%7B%5Cpartial+v%7D+%5C%5C+%5Cfrac%7B%5Cpartial+y%7D%7B%5Cpartial+u%7D+%26+%5Cfrac%7B%5Cpartial+y%7D%7B%5Cpartial+v%7D+%5Cend%7Barray%7D+%5Cright%7C+%5Ccdots+%2810%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\frac{\\partial (x, y)}{\\partial (u, v)} \\equiv \\left| \\begin{array}{cc} \\frac{\\partial x}{\\partial u} &amp; \\frac{\\partial x}{\\partial v} \\\\ \\frac{\\partial y}{\\partial u} &amp; \\frac{\\partial y}{\\partial v} \\end{array} \\right| \\cdots (10)' title='\\displaystyle \\frac{\\partial (x, y)}{\\partial (u, v)} \\equiv \\left| \\begin{array}{cc} \\frac{\\partial x}{\\partial u} &amp; \\frac{\\partial x}{\\partial v} \\\\ \\frac{\\partial y}{\\partial u} &amp; \\frac{\\partial y}{\\partial v} \\end{array} \\right| \\cdots (10)' class='latex' \/><\/p>\n<p>\u306f <em>u<\/em> \u304a\u3088\u3073 <em>v<\/em> \u306b\u3064\u3044\u3066\u306e <em>x<\/em> \u304a\u3088\u3073 <em>y<\/em> \u306e <em>\u30e4\u30b3\u30d3\u30a2\u30f3<\/em> \u3067\u3059\uff0e<\/p>\n<p>\u3000\u540c\u69d8\u306b <img src='https:\/\/s0.wp.com\/latex.php?latex=%28u%2C+v%2C+w%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(u, v, w)' title='(u, v, w)' class='latex' \/> \u30923\u6b21\u5143\u306b\u304a\u3051\u308b\u66f2\u7dda\u5ea7\u6a19\u3068\u3059\u308b\u306a\u3089 <img src='https:\/\/s0.wp.com\/latex.php?latex=x+%3D+f%28u%2C+v%2C+w%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='x = f(u, v, w)' title='x = f(u, v, w)' class='latex' \/>, <img src='https:\/\/s0.wp.com\/latex.php?latex=y+%3D+g%28u%2C+v%2C+w%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='y = g(u, v, w)' title='y = g(u, v, w)' class='latex' \/>, <img src='https:\/\/s0.wp.com\/latex.php?latex=z+%3D+h%28u%2C+v%2C+w%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='z = h(u, v, w)' title='z = h(u, v, w)' class='latex' \/> \u3068\u3044\u3046\u5909\u6570\u5909\u63db\u5f0f\u30bb\u30c3\u30c8\u304c\u5f97\u3089\u308c\uff0c\u4e0b\u8a18\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3057\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cunderset%7B%5Ccal+R%7D%7B%5Ciiint%7DF%28x%2C+y%2C+z%29dxdydz+%3D+%5Cunderset%7B%7B%5Ccal+R%7D%27%7D%7B%5Ciiint%7D+G%28u%2C+v%2C+w%29+%5Cleft%7C+%5Cfrac%7B%5Cpartial+%28x%2C+y%2C+z%29%7D%7B%5Cpartial+%28u%2C+v%2C+w%29%7D+%5Cright%7Cdudvdw+%5Ccdots%2811%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\underset{\\cal R}{\\iiint}F(x, y, z)dxdydz = \\underset{{\\cal R}&#039;}{\\iiint} G(u, v, w) \\left| \\frac{\\partial (x, y, z)}{\\partial (u, v, w)} \\right|dudvdw \\cdots(11)' title='\\displaystyle \\underset{\\cal R}{\\iiint}F(x, y, z)dxdydz = \\underset{{\\cal R}&#039;}{\\iiint} G(u, v, w) \\left| \\frac{\\partial (x, y, z)}{\\partial (u, v, w)} \\right|dudvdw \\cdots(11)' class='latex' \/><\/p>\n<p>\u3053\u3053\u3067 <img src='https:\/\/s0.wp.com\/latex.php?latex=G%28u%2C+v%2C+w%29+%5Cequiv+F%5C%7Bf%28u%2C+v%2C+w%29%2C+g%28u%2C+v%2C+w%29%2C+h%28u%2C+v%2C+w%29%5C%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='G(u, v, w) \\equiv F\\{f(u, v, w), g(u, v, w), h(u, v, w)\\}' title='G(u, v, w) \\equiv F\\{f(u, v, w), g(u, v, w), h(u, v, w)\\}' class='latex' \/> \u304a\u3088\u3073<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cfrac%7B%5Cpartial+%28x%2C+y%2C+z%29%7D%7B%5Cpartial+%28u%2C+v%2C+w%29%7D+%5Cequiv+%5Cleft%7C+%5Cbegin%7Barray%7D%7Bccc%7D+%5Cfrac%7B%5Cpartial+x%7D%7B%5Cpartial+u%7D+%26+%5Cfrac%7B%5Cpartial+x%7D%7B%5Cpartial+v%7D+%26+%5Cfrac%7B%5Cpartial+x%7D%7B%5Cpartial+w%7D+%5C%5C+%5Cfrac%7B%5Cpartial+y%7D%7B%5Cpartial+u%7D+%26+%5Cfrac%7B%5Cpartial+y%7D%7B%5Cpartial+v%7D+%26+%5Cfrac%7B%5Cpartial+y%7D%7B%5Cpartial+w%7D+%5C%5C+%5Cfrac%7B%5Cpartial+z%7D%7B%5Cpartial+u%7D+%26+%5Cfrac%7B%5Cpartial+z%7D%7B%5Cpartial+v%7D+%26+%5Cfrac%7B%5Cpartial+z%7D%7B%5Cpartial+w%7D+%5Cend%7Barray%7D+%5Cright%7C%5Ccdots%2812%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\frac{\\partial (x, y, z)}{\\partial (u, v, w)} \\equiv \\left| \\begin{array}{ccc} \\frac{\\partial x}{\\partial u} &amp; \\frac{\\partial x}{\\partial v} &amp; \\frac{\\partial x}{\\partial w} \\\\ \\frac{\\partial y}{\\partial u} &amp; \\frac{\\partial y}{\\partial v} &amp; \\frac{\\partial y}{\\partial w} \\\\ \\frac{\\partial z}{\\partial u} &amp; \\frac{\\partial z}{\\partial v} &amp; \\frac{\\partial z}{\\partial w} \\end{array} \\right|\\cdots(12)' title='\\displaystyle \\frac{\\partial (x, y, z)}{\\partial (u, v, w)} \\equiv \\left| \\begin{array}{ccc} \\frac{\\partial x}{\\partial u} &amp; \\frac{\\partial x}{\\partial v} &amp; \\frac{\\partial x}{\\partial w} \\\\ \\frac{\\partial y}{\\partial u} &amp; \\frac{\\partial y}{\\partial v} &amp; \\frac{\\partial y}{\\partial w} \\\\ \\frac{\\partial z}{\\partial u} &amp; \\frac{\\partial z}{\\partial v} &amp; \\frac{\\partial z}{\\partial w} \\end{array} \\right|\\cdots(12)' class='latex' \/><\/p>\n<p>\u4e0a\u8a18\u306f <em>u<\/em>, <em>v<\/em> and <em>w<\/em> \u306b\u95a2\u3059\u308b <em>x<\/em>, <em>y<\/em> \u304a\u3088\u3073 <em>z<\/em> \u306e <em>\u30e4\u30b3\u30d3\u30a2\u30f3<\/em> \u3067\u3059\uff0e<\/p>\n<p>\u3000\u305d\u306e\u7d50\u679c (9) \u304a\u3088\u3073 (11) \u306f\u4e8c\u91cd\u7a4d\u5206\u53ca\u3073\u4e09\u91cd\u7a4d\u5206\u306e\u5909\u6570\u5909\u63db\u306b\u5bfe\u5fdc\u3057\u307e\u3059\uff0e<\/p>\n<p>\u3000\u3088\u308a\u9ad8\u6b21\u3078\u306e\u4e00\u822c\u5316\u3082\u5bb9\u6613\u306b\u53ef\u80fd\u3067\u3059\uff0e<\/p>\n<p><iframe src=\"\/\/rcm-fe.amazon-adsystem.com\/e\/cm?lt1=_blank&#038;bc1=000000&#038;IS2=1&#038;bg1=FFFFFF&#038;fc1=000000&#038;lc1=0000FF&#038;t=fujiitoshiki-22&#038;o=9&#038;p=8&#038;l=as4&#038;m=amazon&#038;f=ifr&#038;ref=ss_til&#038;asins=0071635408\" style=\"width:120px;height:240px;\" scrolling=\"no\" marginwidth=\"0\" marginheight=\"0\" frameborder=\"0\"><\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u3000\u9818\u57df \u4e0a\u306e\u591a\u91cd\u7a4d\u5206\u3092\u8a55\u4fa1\u3059\u308b\u306b\u3042\u305f\u308a\uff0c\u76f4\u4ea4\u7cfb\u4ee5\u5916\u306e\u5ea7\u6a19\uff0c\u4f8b\u3048\u3070\u7b2c5\u7ae0\u3067\u8003\u616e\u3057\u305f\u3088\u3046\u306a\u66f2\u7dda\u5ea7\u6a19\u3092\u3057\u3070\u3057\u3070\u4fbf\u5229\u306b\u7528\u3044\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\uff0e \u3000\u4eee\u306b \u3092\u3042\u308b\u5e73\u9762\u4e0a\u306e\u70b9\u306e\u66f2\u7dda\u5ea7\u6a19\u3068\u3059\u308b\u3068\uff0cxy \u5e73\u9762\u306e\u70b9 \u3092 uv \u5e73\u9762\u306e\u70b9 \u306b\u30de\u30c3 &hellip; <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5693\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;\u591a\u91cd\u7a4d\u5206\u306e\u5909\u6570\u5909\u63db&#8221; \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":[],"class_list":["post-5693","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5693","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=5693"}],"version-history":[{"count":8,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5693\/revisions"}],"predecessor-version":[{"id":7684,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5693\/revisions\/7684"}],"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=5693"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5693"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5693"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}