﻿{"id":5778,"date":"2014-09-29T06:00:05","date_gmt":"2014-09-28T21:00:05","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=5778"},"modified":"2014-09-29T17:32:59","modified_gmt":"2014-09-29T08:32:59","slug":"post-5778","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5778","title":{"rendered":"\u9762\u7a4d\u5206"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><figure id=\"attachment_5776\" aria-describedby=\"caption-attachment-5776\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><a href=\"\/\/fujiitoshiki.com\/improvesociety\/wp-content\/uploads\/Fig6-3.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"\/\/fujiitoshiki.com\/improvesociety\/wp-content\/uploads\/Fig6-3-300x226.jpg\" alt=\"Fig. 6-3\" width=\"300\" height=\"226\" class=\"size-medium wp-image-5776\" srcset=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/wp-content\/uploads\/Fig6-3-300x226.jpg 300w, https:\/\/www.fujiitoshiki.com\/improvesociety\/wp-content\/uploads\/Fig6-3.jpg 425w\" sizes=\"auto, (max-width: 300px) 85vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-5776\" class=\"wp-caption-text\">Fig. 6-3<\/figcaption><\/figure>\n<p>\u3000<img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u3092 Fig. 6-3 \u306b\u793a\u3059\u3088\u3046\u306b <img src='https:\/\/s0.wp.com\/latex.php?latex=xy&#038;bg=T&#038;fg=000000&#038;s=0' alt='xy' title='xy' class='latex' \/> \u5e73\u9762\u3078\u306e\u5c04\u5f71 <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' \/> \u3092\u6709\u3059\u308b\u8868\u88cf\u306e\u3042\u308b\u9762\u3068\u3057\u307e\u3059\uff0e <img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u3092\u8868\u3059\u5f0f\u3092 <img src='https:\/\/s0.wp.com\/latex.php?latex=z+%3D+f%28x%2C+y%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='z = f(x, y)' title='z = f(x, y)' class='latex' \/> \u3068\u3057\uff0c <img src='https:\/\/s0.wp.com\/latex.php?latex=f&#038;bg=T&#038;fg=000000&#038;s=0' alt='f' title='f' class='latex' \/> \u306f\u5358\u4e00\u5024\u3067\uff0c<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' \/> \u306b\u304a\u3044\u3066\u5168\u3066\u306e <img src='https:\/\/s0.wp.com\/latex.php?latex=x&#038;bg=T&#038;fg=000000&#038;s=0' alt='x' title='x' class='latex' \/> \u304a\u3088\u3073 <img src='https:\/\/s0.wp.com\/latex.php?latex=y&#038;bg=T&#038;fg=000000&#038;s=0' alt='y' title='y' class='latex' \/> \u306b\u3064\u3044\u3066\u9023\u7d9a\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\uff0e <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' \/> \u3092 <img src='https:\/\/s0.wp.com\/latex.php?latex=n&#038;bg=T&#038;fg=000000&#038;s=0' alt='n' title='n' class='latex' \/> \u500b\u306e\u9818\u57df <img src='https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+A_p%2C%5C+p+%3D+1%2C%5C+2%2C%5C+%5Cdots%2C%5C+n&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\Delta A_p,\\ p = 1,\\ 2,\\ \\dots,\\ n' title='\\Delta A_p,\\ p = 1,\\ 2,\\ \\dots,\\ n' class='latex' \/> \u306b\u7d30\u5206\u5316\u3057\uff0c\u5404\u3005\u306e\u5c0f\u9818\u57df\u306e\u4e0a\u306b\u5782\u76f4\u306a\u67f1\u3092\u7acb\u3066\uff0c\u9818\u57df <img src='https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+S_p&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\Delta S_p' title='\\Delta S_p' class='latex' \/> \u306b\u304a\u3044\u3066 <img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u3068\u4ea4\u5dee\u3055\u305b\u307e\u3059\uff0e<\/p>\n<p>\u3000 <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' \/> \u3092\u5358\u4e00\u5024\u3067 <img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u4e0a\u306e\u3042\u3089\u3086\u308b\u70b9\u3067\u9023\u7d9a\u3067\u3042\u308b\u3068\u3057\u307e\u3059\uff0e\u6b21\u306e\u548c\u3092\u8003\u3048\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Csum_%7Bp%3D1%7D%5E%7Bn%7D%5Cphi%28%5Cxi_p%2C+%5Ceta_p%2C+%5Czeta_p%29%5CDelta+S_p+%5Ccdots%2829%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\sum_{p=1}^{n}\\phi(\\xi_p, \\eta_p, \\zeta_p)\\Delta S_p \\cdots(29)' title='\\displaystyle \\sum_{p=1}^{n}\\phi(\\xi_p, \\eta_p, \\zeta_p)\\Delta S_p \\cdots(29)' class='latex' \/><\/p>\n<p>\u3053\u3053\u3067 <img src='https:\/\/s0.wp.com\/latex.php?latex=%28%5Cxi_p%2C+%5Ceta_p%2C+%5Czeta_p%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(\\xi_p, \\eta_p, \\zeta_p)' title='(\\xi_p, \\eta_p, \\zeta_p)' class='latex' \/> \u306f <img src='https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+S_p&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\Delta S_p' title='\\Delta S_p' class='latex' \/> \u4e0a\u306e\u4efb\u610f\u306e\u70b9\u3067\u3059\uff0e\u4eee\u306b <img src='https:\/\/s0.wp.com\/latex.php?latex=n+%5Crightarrow+%5Cinfty&#038;bg=T&#038;fg=000000&#038;s=0' alt='n \\rightarrow \\infty' title='n \\rightarrow \\infty' class='latex' \/> \u306e\u6642\u5404\u3005\u306e <img src='https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+S_p+%5Crightarrow+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\Delta S_p \\rightarrow 0' title='\\Delta S_p \\rightarrow 0' class='latex' \/> \u3068\u306a\u308b\u3053\u306e\u548c\u306e\u6975\u9650\u304c\u5b58\u5728\u3059\u308b\u306a\u3089\uff0c\u7d50\u679c\u306e\u6975\u9650\u306f <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' \/> \u306e <img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u4e0a\u306e <em>\u9762\u7a4d\u5206<\/em> \u3068\u547c\u3070\u308c\uff0c\u4ee5\u4e0b\u306b\u3088\u308a\u6307\u5b9a\u3055\u308c\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cunderset%7BS%7D%7B%5Ciint%7D%5Cphi%28x%2C+y%2C+z%29dS%5Ccdots%2830%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\underset{S}{\\iint}\\phi(x, y, z)dS\\cdots(30)' title='\\displaystyle \\underset{S}{\\iint}\\phi(x, y, z)dS\\cdots(30)' class='latex' \/><\/p>\n<p>\u3000\u304a\u3088\u305d <img src='https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+S_p+%3D+%7C%5Csec%5Cgamma_p%7C%5CDelta+A_p&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\Delta S_p = |\\sec\\gamma_p|\\Delta A_p' title='\\Delta S_p = |\\sec\\gamma_p|\\Delta A_p' class='latex' \/> \u3067\u3042\u308b\u305f\u3081\uff0c\u3053\u3053\u3067 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cgamma_p&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\gamma_p' title='\\gamma_p' class='latex' \/> \u306f <img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u3078\u306e\u6cd5\u7dda\u304a\u3088\u3073 <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' \/> \u8ef8\u3068\u306e\u306a\u3059\u89d2\u3067\u3042\u308a\uff0c\u548c (29) \u306e\u6975\u9650\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cunderset%7B%5Ccal+R%7D%7B%5Ciint%7D%5Cphi%28x%2C+y%2C+z%29%7C%5Csec%5Cgamma%7CdA%5Ccdots%2831%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\underset{\\cal R}{\\iint}\\phi(x, y, z)|\\sec\\gamma|dA\\cdots(31)' title='\\displaystyle \\underset{\\cal R}{\\iint}\\phi(x, y, z)|\\sec\\gamma|dA\\cdots(31)' class='latex' \/><\/p>\n<p>\u3000 <img src='https:\/\/s0.wp.com\/latex.php?latex=%7C%5Csec%5Cgamma%7C&#038;bg=T&#038;fg=000000&#038;s=0' alt='|\\sec\\gamma|' title='|\\sec\\gamma|' class='latex' \/> \u306e\u5927\u304d\u3055\u306f\u4ee5\u4e0b\u3067\u5f97\u3089\u308c\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%7C%5Csec%5Cgamma%7C+%3D+%5Cfrac%7B1%7D%7B%7C%5Cbold%7Bn%7D_p%5Ccdot%5Cbold%7Bk%7D%7C%7D+%3D+%5Csqrt%7B1+%2B+%5Cleft%28+%5Cfrac%7B%5Cpartial+z%7D%7B%5Cpartial+x%7D+%5Cright%29%5E2+%2B+%5Cleft%28+%5Cfrac%7B%5Cpartial+z%7D%7B%5Cpartial+y%7D+%5Cright%29%5E2%7D%5Ccdots%2832%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle |\\sec\\gamma| = \\frac{1}{|\\bold{n}_p\\cdot\\bold{k}|} = \\sqrt{1 + \\left( \\frac{\\partial z}{\\partial x} \\right)^2 + \\left( \\frac{\\partial z}{\\partial y} \\right)^2}\\cdots(32)' title='\\displaystyle |\\sec\\gamma| = \\frac{1}{|\\bold{n}_p\\cdot\\bold{k}|} = \\sqrt{1 + \\left( \\frac{\\partial z}{\\partial x} \\right)^2 + \\left( \\frac{\\partial z}{\\partial y} \\right)^2}\\cdots(32)' class='latex' \/><\/p>\n<p>\u3000\u305d\u3053\u3067 <img src='https:\/\/s0.wp.com\/latex.php?latex=x+%3D+f%28x%2C+y%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='x = f(x, y)' title='x = f(x, y)' class='latex' \/> \u306f <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' \/> \u306b\u304a\u3044\u3066\u9023\u7d9a\uff08\u53c8\u306f\u533a\u9593\u7684\u306b\u9023\u7d9a\uff09\u306a\u5fae\u5206\u4fc2\u6570\u3092\u6709\u3057\u3066\u3044\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068 (31) \u306f\u76f4\u4ea4\u7cfb\u306b\u304a\u3044\u3066\u306f\u6b21\u306e\u5f62\u3067\u8a18\u8ff0\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cunderset%7B%5Ccal+R%7D%7B%5Ciint%7D%5Cphi%28x%2C+y%2C+z%29%5Csqrt%7B1+%2B+%5Cleft%28+%5Cfrac%7B%5Cpartial+z%7D%7B%5Cpartial+x%7D+%5Cright%29%5E2+%2B+%5Cleft%28+%5Cfrac%7B%5Cpartial+z%7D%7B%5Cpartial+y%7D+%5Cright%29%5E2%7Ddxdy+%5Ccdots%2833%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\underset{\\cal R}{\\iint}\\phi(x, y, z)\\sqrt{1 + \\left( \\frac{\\partial z}{\\partial x} \\right)^2 + \\left( \\frac{\\partial z}{\\partial y} \\right)^2}dxdy \\cdots(33)' title='\\displaystyle \\underset{\\cal R}{\\iint}\\phi(x, y, z)\\sqrt{1 + \\left( \\frac{\\partial z}{\\partial x} \\right)^2 + \\left( \\frac{\\partial z}{\\partial y} \\right)^2}dxdy \\cdots(33)' class='latex' \/><\/p>\n<p>\u3000 <img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u306e\u5f0f\u304c <img src='https:\/\/s0.wp.com\/latex.php?latex=F%28x%2C+y%2C+z%29+%3D+0&#038;bg=T&#038;fg=000000&#038;s=0' alt='F(x, y, z) = 0' title='F(x, y, z) = 0' class='latex' \/> \u306e\u5f62\u3067\u4e0e\u3048\u3089\u308c\u308b\u5834\u5408\u306f (33) \u306f\u6b21\u306e\u5f62\u3067\u8a18\u8ff0\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cunderset%7BS%7D%7B%5Ciint%7D%5Cphi%28x%2C+y%2C+z%29%5Cfrac%7B%5Csqrt%7B%28F_x%29%5E2+%2B+%28F_y%29%5E2+%2B+%28F_z%29%5E2%7D%7D%7B%7CF_z%7C%7Ddxdy%5Ccdots%2834%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\underset{S}{\\iint}\\phi(x, y, z)\\frac{\\sqrt{(F_x)^2 + (F_y)^2 + (F_z)^2}}{|F_z|}dxdy\\cdots(34)' title='\\displaystyle \\underset{S}{\\iint}\\phi(x, y, z)\\frac{\\sqrt{(F_x)^2 + (F_y)^2 + (F_z)^2}}{|F_z|}dxdy\\cdots(34)' class='latex' \/><\/p>\n<p>\u3000\u305d\u306e\u7d50\u679c (33) \u307e\u305f\u306f (34) \u306f (30) \u3092\u8a55\u4fa1\u3059\u308b\u306e\u306b\u7528\u3044\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p>\u3000\u4e0a\u8a18\u306b\u304a\u3044\u3066\u306f <img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u306f <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' \/> \u8ef8\u306b\u5e73\u884c\u306a\u3044\u304b\u306a\u308b\u7dda\u3082\u9762 <img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u3068\u305f\u3060 1 \u70b9\u306b\u304a\u3044\u3066\u4ea4\u5dee\u3059\u308b\u3088\u3046\u306a\u9762\u3067\u3042\u308b\u3053\u3068\u3092\u524d\u63d0\u3068\u3057\u3066\u3044\u307e\u3059\uff0e\u9762 <img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u304c\u3053\u306e\u30bf\u30a4\u30d7\u3067\u306a\u3044\u4f8b\u306b\u304a\u3044\u3066\u306f\uff0c\u666e\u901a <img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u3092 <img src='https:\/\/s0.wp.com\/latex.php?latex=S_1%2C%5C+S_2%2C%5C+%5Cdots&#038;bg=T&#038;fg=000000&#038;s=0' alt='S_1,\\ S_2,\\ \\dots' title='S_1,\\ S_2,\\ \\dots' class='latex' \/> \u306b\u5206\u5272\u3057\u3066\u3053\u306e\u30bf\u30a4\u30d7\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e\u305d\u3053\u3067\u9762 <img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u4e0a\u306e\u9762\u7a4d\u5206\u3092 <img src='https:\/\/s0.wp.com\/latex.php?latex=S_1%2C%5C+S_2%2C%5C+%5Cdots&#038;bg=T&#038;fg=000000&#038;s=0' alt='S_1,\\ S_2,\\ \\dots' title='S_1,\\ S_2,\\ \\dots' class='latex' \/> \u4e0a\u306e\u9762\u7a4d\u5206\u306e\u548c\u3068\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p>\u3000\u3053\u306e\u7d50\u679c\u306f <img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u304c <img src='https:\/\/s0.wp.com\/latex.php?latex=xy&#038;bg=T&#038;fg=000000&#038;s=0' alt='xy' title='xy' class='latex' \/> \u5e73\u9762 \u306b\u304a\u3051\u308b\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' \/> \u3078\u306e\u5c04\u5f71\u306e\u6642\u4fdd\u6301\u3055\u308c\u307e\u3059\uff0e\u5834\u5408\u306b\u3088\u3063\u3066\u306f <img src='https:\/\/s0.wp.com\/latex.php?latex=S&#038;bg=T&#038;fg=000000&#038;s=0' alt='S' title='S' class='latex' \/> \u3092 <img src='https:\/\/s0.wp.com\/latex.php?latex=yz&#038;bg=T&#038;fg=000000&#038;s=0' alt='yz' title='yz' class='latex' \/> \u307e\u305f\u306f <img src='https:\/\/s0.wp.com\/latex.php?latex=xz&#038;bg=T&#038;fg=000000&#038;s=0' alt='xz' title='xz' class='latex' \/> \u5e73\u9762\u306b\u5c04\u5f71\u3057\u305f\u307b\u3046\u304c\u826f\u3044\u3053\u3068\u3082\u3042\u308a\u307e\u3059\uff0e\u305d\u306e\u3088\u3046\u306a\u5834\u5408\u306f (30) \u306f (33) \u304a\u3088\u3073 (34) \u3092\u9069\u5207\u306b\u4fee\u6b63\u3059\u308b\u3053\u3068\u3067\u8a55\u4fa1\u3055\u308c\u307e\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 \u3092 Fig. 6-3 \u306b\u793a\u3059\u3088\u3046\u306b \u5e73\u9762\u3078\u306e\u5c04\u5f71 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