{"id":5190,"date":"2014-03-26T06:00:29","date_gmt":"2014-03-25T21:00:29","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=5190"},"modified":"2014-09-10T16:38:15","modified_gmt":"2014-09-10T07:38:15","slug":"post-5190","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5190","title":{"rendered":"\u52fe\u914d\uff0c\u767a\u6563\uff0c\u56de\u8ee2"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><p>\u3000\u4ee5\u4e0b\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u30d9\u30af\u30c8\u30eb\u6f14\u7b97\u5b50 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cnabla%5C+%28del%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\nabla\\ (del)' title='\\nabla\\ (del)' class='latex' \/> \u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cnabla+%5Cequiv+%5Cbold%7Bi%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+x%7D+%2B+%5Cbold%7Bj%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+y%7D+%2B+%5Cbold%7Bk%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+z%7D%5Ccdots%2813%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\nabla \\equiv \\bold{i}\\frac{\\partial}{\\partial x} + \\bold{j}\\frac{\\partial}{\\partial y} + \\bold{k}\\frac{\\partial}{\\partial z}\\cdots(13)' title='\\displaystyle \\nabla \\equiv \\bold{i}\\frac{\\partial}{\\partial x} + \\bold{j}\\frac{\\partial}{\\partial y} + \\bold{k}\\frac{\\partial}{\\partial z}\\cdots(13)' class='latex' \/><\/p>\n<p>\u3000\u4eee\u306b <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cphi%28x%2C+y%2C+z%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\phi(x, y, z)' title='\\phi(x, y, z)' class='latex' \/> \u304a\u3088\u3073 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cbold%7BA%7D%28x%2C+y%2C+z%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\bold{A}(x, y, z)' title='\\bold{A}(x, y, z)' class='latex' \/> \u304c\uff08\u591a\u304f\u306e\u4f8b\u306b\u304a\u3044\u3066\u5fc5\u8981\u6027\u3088\u308a\u3082\u5f37\u3044\u72b6\u614b\u306b\u3042\u308b\uff09\u3042\u308b\u5730\u70b9\u306b\u304a\u3044\u3066\u4e00\u968e\u306e\u504f\u5fae\u5206\u3092\u6709\u3059\u308b\u5834\u5408\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff0e<\/p>\n<h4>1. \u52fe\u914d<\/h4>\n<p>\u3000 &phi; \u306e <em>\u52fe\u914d<\/em> \u306f\u4ee5\u4e0b\u306e\u5b9a\u7fa9\u3067\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+grad%5Cphi+%3D+%5Cnabla%5Cphi+%3D+%5Cleft%28%5Cbold%7Bi%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+x%7D+%2B+%5Cbold%7Bj%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+y%7D+%2B+%5Cbold%7Bk%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+z%7D%5Cright%29%5Cphi%5C%5C++++%3D+%5Cbold%7Bi%7D%5Cfrac%7B%5Cpartial%5Cphi%7D%7B%5Cpartial+x%7D+%2B+%5Cbold%7Bj%7D%5Cfrac%7B%5Cpartial%5Cphi%7D%7B%5Cpartial+y%7D+%2B+%5Cbold%7Bk%7D%5Cfrac%7B%5Cpartial%5Cphi%7D%7B%5Cpartial+z%7D%5C%5C++++%3D+%5Cfrac%7B%5Cpartial%5Cphi%7D%7B%5Cpartial+x%7D%5Cbold%7Bi%7D+%2B+%5Cfrac%7B%5Cpartial%5Cphi%7D%7B%5Cpartial+y%7D%5Cbold%7Bj%7D+%2B+%5Cfrac%7B%5Cpartial%5Cphi%7D%7B%5Cpartial+z%7D%5Cbold%7Bk%7D%5Ccdots%2814%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle grad\\phi = \\nabla\\phi = \\left(\\bold{i}\\frac{\\partial}{\\partial x} + \\bold{j}\\frac{\\partial}{\\partial y} + \\bold{k}\\frac{\\partial}{\\partial z}\\right)\\phi\\\\    = \\bold{i}\\frac{\\partial\\phi}{\\partial x} + \\bold{j}\\frac{\\partial\\phi}{\\partial y} + \\bold{k}\\frac{\\partial\\phi}{\\partial z}\\\\    = \\frac{\\partial\\phi}{\\partial x}\\bold{i} + \\frac{\\partial\\phi}{\\partial y}\\bold{j} + \\frac{\\partial\\phi}{\\partial z}\\bold{k}\\cdots(14)' title='\\displaystyle grad\\phi = \\nabla\\phi = \\left(\\bold{i}\\frac{\\partial}{\\partial x} + \\bold{j}\\frac{\\partial}{\\partial y} + \\bold{k}\\frac{\\partial}{\\partial z}\\right)\\phi\\\\    = \\bold{i}\\frac{\\partial\\phi}{\\partial x} + \\bold{j}\\frac{\\partial\\phi}{\\partial y} + \\bold{k}\\frac{\\partial\\phi}{\\partial z}\\\\    = \\frac{\\partial\\phi}{\\partial x}\\bold{i} + \\frac{\\partial\\phi}{\\partial y}\\bold{j} + \\frac{\\partial\\phi}{\\partial z}\\bold{k}\\cdots(14)' class='latex' \/><\/p>\n<p>\u3000\u4eee\u306b <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cphi%28x%2C+y%2C+z%29+%3D+c&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\phi(x, y, z) = c' title='\\phi(x, y, z) = c' class='latex' \/> \u304c\u8868\u9762\u306e\u65b9\u7a0b\u5f0f\u306e\u5834\u5408\uff0c <img src='https:\/\/s0.wp.com\/latex.php?latex=+%5Cnabla%5Cphi&#038;bg=T&#038;fg=000000&#038;s=0' alt=' \\nabla\\phi' title=' \\nabla\\phi' class='latex' \/> \u306f\u3053\u306e\u8868\u9762\u306b\u5bfe\u3057\u3066\u5782\u76f4\u3067\u3042\u308b\u3053\u3068\u306f\u8208\u5473\u6df1\u3044\u89e3\u91c8\u3067\u3059\uff0e<\/p>\n<h4>2. \u767a\u6563<\/h4>\n<p>\u3000<img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cbold%7BA%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\bold{A}' title='\\bold{A}' class='latex' \/> \u306e <em>\u767a\u6563<\/em> \u306f\u4ee5\u4e0b\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+div%5Cbold%7BA%7D+%3D+%5Cnabla%5Ccdot%5Cbold%7BA%7D+%3D+%5Cleft%28%5Cbold%7Bi%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+x%7D+%2B+%5Cbold%7Bj%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+y%7D+%2B+%5Cbold%7Bk%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+z%7D%5Cright%29%5Ccdot%28A_1%5Cbold%7Bi%7D+%2B+A_2%5Cbold%7Bj%7D+%2B+A_3%5Cbold%7Bk%7D%29%5C%5C+%3D+%5Cfrac%7B%5Cpartial+A_1%7D%7B%5Cpartial+x%7D+%2B+%5Cfrac%7B%5Cpartial+A_2%7D%7B%5Cpartial+y%7D+%2B+%5Cfrac%7B%5Cpartial+A_3%7D%7B%5Cpartial+z%7D%5Ccdots%2815%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle div\\bold{A} = \\nabla\\cdot\\bold{A} = \\left(\\bold{i}\\frac{\\partial}{\\partial x} + \\bold{j}\\frac{\\partial}{\\partial y} + \\bold{k}\\frac{\\partial}{\\partial z}\\right)\\cdot(A_1\\bold{i} + A_2\\bold{j} + A_3\\bold{k})\\\\ = \\frac{\\partial A_1}{\\partial x} + \\frac{\\partial A_2}{\\partial y} + \\frac{\\partial A_3}{\\partial z}\\cdots(15)' title='\\displaystyle div\\bold{A} = \\nabla\\cdot\\bold{A} = \\left(\\bold{i}\\frac{\\partial}{\\partial x} + \\bold{j}\\frac{\\partial}{\\partial y} + \\bold{k}\\frac{\\partial}{\\partial z}\\right)\\cdot(A_1\\bold{i} + A_2\\bold{j} + A_3\\bold{k})\\\\ = \\frac{\\partial A_1}{\\partial x} + \\frac{\\partial A_2}{\\partial y} + \\frac{\\partial A_3}{\\partial z}\\cdots(15)' class='latex' \/><\/p>\n<h4>3. \u56de\u8ee2<\/h4>\n<p>\u3000<img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cbold%7BA%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\bold{A}' title='\\bold{A}' class='latex' \/> \u306e <em>\u56de\u8ee2<\/em> \u306f\u4ee5\u4e0b\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+curl%5Cbold%7BA%7D+%3D+%5Cnabla%5Ctimes%5Cbold%7BA%7D+%3D+%5Cleft%28%5Cbold%7Bi%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+x%7D+%2B+%5Cbold%7Bj%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+y%7D+%2B+%5Cbold%7Bk%7D%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+z%7D%5Cright%29%5Ctimes%28A_1%5Cbold%7Bi%7D+%2B+A_2%5Cbold%7Bj%7D+%2B+A_3%5Cbold%7Bk%7D%29%5C%5C++++%3D+%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D+%5Cbold%7Bi%7D+%26+%5Cbold%7Bj%7D+%26+%5Cbold%7Bk%7D+%5C%5C+%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+x%7D+%26+%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+y%7D+%26+%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+z%7D+%5C%5C+A_1+%26+A_2+%26+A_3+%5Cend%7Barray%7D%5Cright%7C+%5C%5C+++%3D+%5Cbold%7Bi%7D%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D+%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+y%7D+%26+%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+z%7D+%5C%5C+A_2+%26+A_3+%5Cend%7Barray%7D%5Cright%7C+-+%5Cbold%7Bj%7D%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D+%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+z%7D+%26+%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+z%7D+%5C%5C+A_1+%26+A_3+%5Cend%7Barray%7D%5Cright%7C+%2B+%5Cbold%7Bk%7D%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D+%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+x%7D+%26+%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+y%7D+%5C%5C+A_1+%26+A_2+%5Cend%7Barray%7D%5Cright%7C%5C%5C+++%3D+%5Cleft%28%5Cfrac%7B%5Cpartial+A_3%7D%7B%5Cpartial+y%7D+-+%5Cfrac%7B%5Cpartial+A_2%7D%7B%5Cpartial+z%7D%5Cright%29%5Cbold%7Bi%7D+%2B+%5Cleft%28%5Cfrac%7B%5Cpartial+A_1%7D%7B%5Cpartial+z%7D+-+%5Cfrac%7B%5Cpartial+A_3%7D%7B%5Cpartial+x%7D%5Cright%29%5Cbold%7Bj%7D+%2B+%5Cleft%28%5Cfrac%7B%5Cpartial+A_2%7D%7B%5Cpartial+x%7D+-+%5Cfrac%7B%5Cpartial+A_1%7D%7B%5Cpartial+y%7D%5Cright%29%5Cbold%7Bk%7D%5Ccdots%2816%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle curl\\bold{A} = \\nabla\\times\\bold{A} = \\left(\\bold{i}\\frac{\\partial}{\\partial x} + \\bold{j}\\frac{\\partial}{\\partial y} + \\bold{k}\\frac{\\partial}{\\partial z}\\right)\\times(A_1\\bold{i} + A_2\\bold{j} + A_3\\bold{k})\\\\    = \\left|\\begin{array}{ccc} \\bold{i} &amp; \\bold{j} &amp; \\bold{k} \\\\ \\frac{\\partial}{\\partial x} &amp; \\frac{\\partial}{\\partial y} &amp; \\frac{\\partial}{\\partial z} \\\\ A_1 &amp; A_2 &amp; A_3 \\end{array}\\right| \\\\   = \\bold{i}\\left|\\begin{array}{cc} \\frac{\\partial}{\\partial y} &amp; \\frac{\\partial}{\\partial z} \\\\ A_2 &amp; A_3 \\end{array}\\right| - \\bold{j}\\left|\\begin{array}{cc} \\frac{\\partial}{\\partial z} &amp; \\frac{\\partial}{\\partial z} \\\\ A_1 &amp; A_3 \\end{array}\\right| + \\bold{k}\\left|\\begin{array}{cc} \\frac{\\partial}{\\partial x} &amp; \\frac{\\partial}{\\partial y} \\\\ A_1 &amp; A_2 \\end{array}\\right|\\\\   = \\left(\\frac{\\partial A_3}{\\partial y} - \\frac{\\partial A_2}{\\partial z}\\right)\\bold{i} + \\left(\\frac{\\partial A_1}{\\partial z} - \\frac{\\partial A_3}{\\partial x}\\right)\\bold{j} + \\left(\\frac{\\partial A_2}{\\partial x} - \\frac{\\partial A_1}{\\partial y}\\right)\\bold{k}\\cdots(16)' title='\\displaystyle curl\\bold{A} = \\nabla\\times\\bold{A} = \\left(\\bold{i}\\frac{\\partial}{\\partial x} + \\bold{j}\\frac{\\partial}{\\partial y} + \\bold{k}\\frac{\\partial}{\\partial z}\\right)\\times(A_1\\bold{i} + A_2\\bold{j} + A_3\\bold{k})\\\\    = \\left|\\begin{array}{ccc} \\bold{i} &amp; \\bold{j} &amp; \\bold{k} \\\\ \\frac{\\partial}{\\partial x} &amp; \\frac{\\partial}{\\partial y} &amp; \\frac{\\partial}{\\partial z} \\\\ A_1 &amp; A_2 &amp; A_3 \\end{array}\\right| \\\\   = \\bold{i}\\left|\\begin{array}{cc} \\frac{\\partial}{\\partial y} &amp; \\frac{\\partial}{\\partial z} \\\\ A_2 &amp; A_3 \\end{array}\\right| - \\bold{j}\\left|\\begin{array}{cc} \\frac{\\partial}{\\partial z} &amp; \\frac{\\partial}{\\partial z} \\\\ A_1 &amp; A_3 \\end{array}\\right| + \\bold{k}\\left|\\begin{array}{cc} \\frac{\\partial}{\\partial x} &amp; \\frac{\\partial}{\\partial y} \\\\ A_1 &amp; A_2 \\end{array}\\right|\\\\   = \\left(\\frac{\\partial A_3}{\\partial y} - \\frac{\\partial A_2}{\\partial z}\\right)\\bold{i} + \\left(\\frac{\\partial A_1}{\\partial z} - \\frac{\\partial A_3}{\\partial x}\\right)\\bold{j} + \\left(\\frac{\\partial A_2}{\\partial x} - \\frac{\\partial A_1}{\\partial y}\\right)\\bold{k}\\cdots(16)' class='latex' \/><\/p>\n<p>\u3000\u884c\u5217\u5f0f\uff0c\u6f14\u7b97\u5b50 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cpartial%2F%5Cpartial+x&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\partial\/\\partial x' title='\\partial\/\\partial x' class='latex' \/>, <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cpartial%2F%5Cpartial+y&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\partial\/\\partial y' title='\\partial\/\\partial y' class='latex' \/>, <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cpartial%2F%5Cpartial+z&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\partial\/\\partial z' title='\\partial\/\\partial z' class='latex' \/> \u306b\u304a\u3044\u3066\u306f\u5fc5\u305a <img src='https:\/\/s0.wp.com\/latex.php?latex=A_1&#038;bg=T&#038;fg=000000&#038;s=0' alt='A_1' title='A_1' class='latex' \/>, <img src='https:\/\/s0.wp.com\/latex.php?latex=A_2&#038;bg=T&#038;fg=000000&#038;s=0' alt='A_2' title='A_2' class='latex' \/>, <img src='https:\/\/s0.wp.com\/latex.php?latex=A_3&#038;bg=T&#038;fg=000000&#038;s=0' alt='A_3' title='A_3' class='latex' \/> \u306e\u524d\u306b\u7f6e\u304b\u306d\u3070\u306a\u3089\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\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\u4ee5\u4e0b\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u30d9\u30af\u30c8\u30eb\u6f14\u7b97\u5b50 \u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\uff0e \u3000\u4eee\u306b \u304a\u3088\u3073 \u304c\uff08\u591a\u304f\u306e\u4f8b\u306b\u304a\u3044\u3066\u5fc5\u8981\u6027\u3088\u308a\u3082\u5f37\u3044\u72b6\u614b\u306b\u3042\u308b\uff09\u3042\u308b\u5730\u70b9\u306b\u304a\u3044\u3066\u4e00\u968e\u306e\u504f\u5fae\u5206\u3092\u6709\u3059\u308b\u5834\u5408\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff0e 1. \u52fe\u914d \u3000 &phi; 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