{"id":5358,"date":"2014-04-16T06:00:56","date_gmt":"2014-04-15T21:00:56","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=5358"},"modified":"2014-09-10T16:36:44","modified_gmt":"2014-09-10T07:36:44","slug":"post-5358","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5358","title":{"rendered":"\u7279\u6b8a\u306a\u66f2\u7dda\u5ea7\u6a19"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><h4>1. \u5186\u67f1\u5ea7\u6a19\u7cfb <img src='https:\/\/s0.wp.com\/latex.php?latex=%28%5Crho%2C+%5Cphi%2C+z%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(\\rho, \\phi, z)' title='(\\rho, \\phi, z)' class='latex' \/><\/h4>\n<p><em>\u5909\u63db\u5f0f<\/em>: <img src='https:\/\/s0.wp.com\/latex.php?latex=+x+%3D+%5Crho%5Ccos%5Cphi+%2C%5C+y+%3D+%5Crho%5Csin%5Cphi+%2C%5C+z+%3D+z++&#038;bg=T&#038;fg=000000&#038;s=0' alt=' x = \\rho\\cos\\phi ,\\ y = \\rho\\sin\\phi ,\\ z = z  ' title=' x = \\rho\\cos\\phi ,\\ y = \\rho\\sin\\phi ,\\ z = z  ' class='latex' \/><\/p>\n<p>\u3053\u3053\u3067 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Crho+%5Cge+0+&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\rho \\ge 0 ' title='\\rho \\ge 0 ' class='latex' \/>, <img src='https:\/\/s0.wp.com\/latex.php?latex=+0+%5Cle+%5Cphi+%5Cle+2%5Cpi&#038;bg=T&#038;fg=000000&#038;s=0' alt=' 0 \\le \\phi \\le 2\\pi' title=' 0 \\le \\phi \\le 2\\pi' class='latex' \/>, <img src='https:\/\/s0.wp.com\/latex.php?latex=+-%5Cinfty+%3C+z+%3C+%5Cinfty+%26%2391%3B%2Flatex%26%2393%3B.++++++%3Cem%3E%E3%82%B9%E3%82%B1%E3%83%BC%E3%83%AB%E5%9B+%E5%AD%90%3C%2Fem%3E%3A+%5Blatex%5Dh_1+%3D+1%2C%5C+h_2+%3D+1%2C%5C+h_3+%3D+1&#038;bg=T&#038;fg=000000&#038;s=0' alt='' title='' class='latex' \/><\/p>\n<p><em>\u5f27\u9577\u8981\u7d20<\/em>: <img src='https:\/\/s0.wp.com\/latex.php?latex=+ds%5E2+%3D+d%5Crho%5E2+%2B+%5Crho%5E2+d%5Cphi%5E2+%2B+dz%5E2+&#038;bg=T&#038;fg=000000&#038;s=0' alt=' ds^2 = d\\rho^2 + \\rho^2 d\\phi^2 + dz^2 ' title=' ds^2 = d\\rho^2 + \\rho^2 d\\phi^2 + dz^2 ' class='latex' \/><\/p>\n<p><em>\u30e4\u30b3\u30d3\u30a2\u30f3<\/em>: <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cfrac%7B%5Cpartial%28x%2C+y%2C+z%29%7D%7B%5Cpartial%28%5Crho%2C+%5Cphi%2C+z%29%7D+%3D+%5Crho&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\frac{\\partial(x, y, z)}{\\partial(\\rho, \\phi, z)} = \\rho' title='\\displaystyle \\frac{\\partial(x, y, z)}{\\partial(\\rho, \\phi, z)} = \\rho' class='latex' \/><\/p>\n<p><em>\u4f53\u7a4d\u8981\u7d20<\/em>: <img src='https:\/\/s0.wp.com\/latex.php?latex=+dV+%3D+%5Crho+d%5Crho+d%5Cphi+dz+&#038;bg=T&#038;fg=000000&#038;s=0' alt=' dV = \\rho d\\rho d\\phi dz ' title=' dV = \\rho d\\rho d\\phi dz ' class='latex' \/><\/p>\n<p><em>\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3<\/em>: <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cnabla%5E2U+%3D+%5Cfrac%7B1%7D%7B%5Crho%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%5Crho%7D%5Cleft%28+%5Crho%5Cfrac%7B%5Cpartial+U%7D%7B%5Cpartial%5Crho%7D+%5Cright%29+%2B+%5Cfrac%7B1%7D%7B%5Crho%5E2%7D%5Cfrac%7B%5Cpartial%5E2U%7D%7B%5Cpartial%5Cphi%5E2%7D+%2B+%5Cfrac%7B%5Cpartial%5E2U%7D%7B%5Cpartial+z%5E2%7D++++%3D+%5Cfrac%7B%5Cpartial%5E2U%7D%7B%5Cpartial%5Crho%5E2%7D+%2B+%5Cfrac%7B1%7D%7B%5Crho%7D%5Cfrac%7B%5Cpartial+U%7D%7B%5Cpartial%5Crho%7D+%2B+%5Cfrac%7B1%7D%7B%5Crho%5E2%7D%5Cfrac%7B%5Cpartial%5E2U%7D%7B%5Cpartial%5Cphi%5E2%7D+%2B+%5Cfrac%7B%5Cpartial%5E2U%7D%7B%5Cpartial+z%5E2%7D+&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\nabla^2U = \\frac{1}{\\rho}\\frac{\\partial}{\\partial\\rho}\\left( \\rho\\frac{\\partial U}{\\partial\\rho} \\right) + \\frac{1}{\\rho^2}\\frac{\\partial^2U}{\\partial\\phi^2} + \\frac{\\partial^2U}{\\partial z^2}    = \\frac{\\partial^2U}{\\partial\\rho^2} + \\frac{1}{\\rho}\\frac{\\partial U}{\\partial\\rho} + \\frac{1}{\\rho^2}\\frac{\\partial^2U}{\\partial\\phi^2} + \\frac{\\partial^2U}{\\partial z^2} ' title='\\displaystyle \\nabla^2U = \\frac{1}{\\rho}\\frac{\\partial}{\\partial\\rho}\\left( \\rho\\frac{\\partial U}{\\partial\\rho} \\right) + \\frac{1}{\\rho^2}\\frac{\\partial^2U}{\\partial\\phi^2} + \\frac{\\partial^2U}{\\partial z^2}    = \\frac{\\partial^2U}{\\partial\\rho^2} + \\frac{1}{\\rho}\\frac{\\partial U}{\\partial\\rho} + \\frac{1}{\\rho^2}\\frac{\\partial^2U}{\\partial\\phi^2} + \\frac{\\partial^2U}{\\partial z^2} ' class='latex' \/><\/p>\n<p>\u3000<img src='https:\/\/s0.wp.com\/latex.php?latex=z&#038;bg=T&#038;fg=000000&#038;s=0' alt='z' title='z' class='latex' \/> \u4f9d\u5b58\u6027\u3092\u7701\u7565\u3057\u305f\u5e73\u9762\u5185\u3067\u306e\u6975\u5ea7\u6a19\u7cfb\u3067\u5bfe\u5fdc\u3059\u308b\u7d50\u679c\u304c\u5f97\u3089\u308c\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\uff0e\u305d\u306e\u3088\u3046\u306a\u5834\u5408\uff0c\u4f8b\u3048\u3070 <img src='https:\/\/s0.wp.com\/latex.php?latex=ds%5E2+%3D+d%5Crho%5E2+%2B+%5Crho%5E2d%5Cphi%5E2&#038;bg=T&#038;fg=000000&#038;s=0' alt='ds^2 = d\\rho^2 + \\rho^2d\\phi^2' title='ds^2 = d\\rho^2 + \\rho^2d\\phi^2' class='latex' \/> \u3053\u3053\u3067\u4f53\u7a4d\u8981\u7d20\u306f\u9762\u7a4d\u8981\u7d20 <img src='https:\/\/s0.wp.com\/latex.php?latex=dA+%3D+%5Crho+d%5Crho+d%5Cphi&#038;bg=T&#038;fg=000000&#038;s=0' alt='dA = \\rho d\\rho d\\phi' title='dA = \\rho d\\rho d\\phi' class='latex' \/> \u3067\u7f6e\u63db\u3055\u308c\u307e\u3059\uff0e<\/p>\n<h4>2. \u7403\u9762\u5ea7\u6a19\u7cfb <img src='https:\/\/s0.wp.com\/latex.php?latex=%28r%2C+%5Ctheta%2C+%5Cphi%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(r, \\theta, \\phi)' title='(r, \\theta, \\phi)' class='latex' \/><\/h4>\n<p><em>\u5909\u63db\u5f0f<\/em>: <img src='https:\/\/s0.wp.com\/latex.php?latex=x+%3D+r%5Csin%5Ctheta%2C%5C+y+%3D+r%5Csin%5Ctheta%5Csin%5Cphi%2C%5C+z+%3D+r%5Ccos%5Ctheta&#038;bg=T&#038;fg=000000&#038;s=0' alt='x = r\\sin\\theta,\\ y = r\\sin\\theta\\sin\\phi,\\ z = r\\cos\\theta' title='x = r\\sin\\theta,\\ y = r\\sin\\theta\\sin\\phi,\\ z = r\\cos\\theta' class='latex' \/><\/p>\n<p>\u3053\u3053\u3067 <img src='https:\/\/s0.wp.com\/latex.php?latex=r+%5Cge+0%2C%5C+0+%5Cle+%5Ctheta+%5Cle+%5Cpi%2C%5C+0+%5Cle+%5Cphi+%5Cle+2%5Cpi+&#038;bg=T&#038;fg=000000&#038;s=0' alt='r \\ge 0,\\ 0 \\le \\theta \\le \\pi,\\ 0 \\le \\phi \\le 2\\pi ' title='r \\ge 0,\\ 0 \\le \\theta \\le \\pi,\\ 0 \\le \\phi \\le 2\\pi ' class='latex' \/>. <\/p>\n<p><em>\u30b9\u30b1\u30fc\u30eb\u56e0\u5b50<\/em>: <img src='https:\/\/s0.wp.com\/latex.php?latex=h_1+%3D+1%2C%5C+h_2+%3D+r%2C%5C+h_3+%3D+r%5Csin%5Ctheta+&#038;bg=T&#038;fg=000000&#038;s=0' alt='h_1 = 1,\\ h_2 = r,\\ h_3 = r\\sin\\theta ' title='h_1 = 1,\\ h_2 = r,\\ h_3 = r\\sin\\theta ' class='latex' \/><\/p>\n<p><em>\u5f27\u9577\u8981\u7d20<\/em>: <img src='https:\/\/s0.wp.com\/latex.php?latex=+ds%5E2+%3D+dr%5E2+%2B+r%5E2d%5Ctheta%5E2+%2B+r%5E2%5Csin%5E2%5Ctheta+d%5Cphi%5E2+&#038;bg=T&#038;fg=000000&#038;s=0' alt=' ds^2 = dr^2 + r^2d\\theta^2 + r^2\\sin^2\\theta d\\phi^2 ' title=' ds^2 = dr^2 + r^2d\\theta^2 + r^2\\sin^2\\theta d\\phi^2 ' class='latex' \/><\/p>\n<p><em>\u30e4\u30b3\u30d3\u30a2\u30f3<\/em>: <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cfrac%7B%5Cpartial%28x%2C+y%2C+z%29%7D%7B%5Cpartial%28r%2C+%5Ctheta%2C+%5Cphi%29%7D+%3D+r%5E2%5Csin%5Ctheta+&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\frac{\\partial(x, y, z)}{\\partial(r, \\theta, \\phi)} = r^2\\sin\\theta ' title='\\displaystyle \\frac{\\partial(x, y, z)}{\\partial(r, \\theta, \\phi)} = r^2\\sin\\theta ' class='latex' \/><\/p>\n<p><em>\u4f53\u7a4d\u8981\u7d20<\/em>: <img src='https:\/\/s0.wp.com\/latex.php?latex=+dV+%3D+r%5E2%5Csin%5Ctheta+drd%5Ctheta+d%5Cphi+&#038;bg=T&#038;fg=000000&#038;s=0' alt=' dV = r^2\\sin\\theta drd\\theta d\\phi ' title=' dV = r^2\\sin\\theta drd\\theta d\\phi ' class='latex' \/><\/p>\n<p><em>\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3<\/em>: <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cnabla%5E2U+%3D+%5Cfrac%7B1%7D%7Br%5E2%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+r%7D%5Cleft%28r%5E2%5Cfrac%7B%5Cpartial+U%7D%7B%5Cpartial+r%7D%5Cright%29+%2B+%5Cfrac%7B1%7D%7Br%5E2%5Csin%5Ctheta%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%5Ctheta%7D%5Cleft%28%5Csin%5Ctheta%5Cfrac%7B%5Cpartial+U%7D%7B%5Cpartial%5Ctheta%7D%5Cright%29+%2B+%5Cfrac%7B1%7D%7Br%5E2%5Csin%5E2%5Ctheta%7D%5Cfrac%7B%5Cpartial%5E2U%7D%7B%5Cpartial%5Cphi%5E2%7D+&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\nabla^2U = \\frac{1}{r^2}\\frac{\\partial}{\\partial r}\\left(r^2\\frac{\\partial U}{\\partial r}\\right) + \\frac{1}{r^2\\sin\\theta}\\frac{\\partial}{\\partial\\theta}\\left(\\sin\\theta\\frac{\\partial U}{\\partial\\theta}\\right) + \\frac{1}{r^2\\sin^2\\theta}\\frac{\\partial^2U}{\\partial\\phi^2} ' title='\\displaystyle \\nabla^2U = \\frac{1}{r^2}\\frac{\\partial}{\\partial r}\\left(r^2\\frac{\\partial U}{\\partial r}\\right) + \\frac{1}{r^2\\sin\\theta}\\frac{\\partial}{\\partial\\theta}\\left(\\sin\\theta\\frac{\\partial U}{\\partial\\theta}\\right) + \\frac{1}{r^2\\sin^2\\theta}\\frac{\\partial^2U}{\\partial\\phi^2} ' class='latex' \/><\/p>\n<p>\u4ed6\u306e\u7a2e\u985e\u306e\u5ea7\u6a19\u7cfb\u3082\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>1. \u5186\u67f1\u5ea7\u6a19\u7cfb \u5909\u63db\u5f0f: \u3053\u3053\u3067 , , \u5f27\u9577\u8981\u7d20: \u30e4\u30b3\u30d3\u30a2\u30f3: \u4f53\u7a4d\u8981\u7d20: \u30e9\u30d7\u30e9\u30b7\u30a2\u30f3: \u3000 \u4f9d\u5b58\u6027\u3092\u7701\u7565\u3057\u305f\u5e73\u9762\u5185\u3067\u306e\u6975\u5ea7\u6a19\u7cfb\u3067\u5bfe\u5fdc\u3059\u308b\u7d50\u679c\u304c\u5f97\u3089\u308c\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\uff0e\u305d\u306e\u3088\u3046\u306a\u5834\u5408\uff0c\u4f8b\u3048\u3070 \u3053\u3053\u3067\u4f53\u7a4d\u8981 &hellip; <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5358\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;\u7279\u6b8a\u306a\u66f2\u7dda\u5ea7\u6a19&#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-5358","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\/5358","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=5358"}],"version-history":[{"count":3,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5358\/revisions"}],"predecessor-version":[{"id":6773,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/5358\/revisions\/6773"}],"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=5358"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5358"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5358"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}