{"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":"<div class=\"theContentWrap-ccc\"><figure id=\"attachment_5660\" aria-describedby=\"caption-attachment-5660\" style=\"width: 300px\" class=\"wp-caption aligncenter\"><a href=\"\/\/fujiitoshiki.com\/improvesociety\/wp-content\/uploads\/Fig6-2.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"\/\/fujiitoshiki.com\/improvesociety\/wp-content\/uploads\/Fig6-2-300x223.jpg\" alt=\"Fig. 6-2\" width=\"300\" height=\"223\" class=\"size-medium wp-image-5660\" srcset=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/wp-content\/uploads\/Fig6-2-300x223.jpg 300w, https:\/\/www.fujiitoshiki.com\/improvesociety\/wp-content\/uploads\/Fig6-2.jpg 312w\" sizes=\"auto, (max-width: 300px) 85vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-5660\" class=\"wp-caption-text\">Fig. 6-2<\/figcaption><\/figure>\n<p>\u3000<em>C<\/em> \u3092 <em>xy<\/em> \u5e73\u9762\u306b\u304a\u3044\u3066 2 \u70b9 <img src='https:\/\/s0.wp.com\/latex.php?latex=A+%28a_1%2C+b_1%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='A (a_1, b_1)' title='A (a_1, b_1)' class='latex' \/> \u304a\u3088\u3073 <img src='https:\/\/s0.wp.com\/latex.php?latex=B+%28a_2%2C+b_2%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='B (a_2, b_2)' title='B (a_2, b_2)' class='latex' \/> \u3092\u3064\u306a\u3050\u66f2\u7dda\u3068\u3057\u307e\u3059\uff08Fig. 6-2\u53c2\u7167\uff09\uff0e<img src='https:\/\/s0.wp.com\/latex.php?latex=P%28x%2C+y%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='P(x, y)' title='P(x, y)' class='latex' \/> \u304a\u3088\u3073 <img src='https:\/\/s0.wp.com\/latex.php?latex=Q%28x%2C+y%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='Q(x, y)' title='Q(x, y)' class='latex' \/> \u3092\u66f2\u7dda <em>C<\/em> \u4e0a\u306e\u3059\u3079\u3066\u306e\u70b9\u3092\u5b9a\u7fa9\u3059\u308b\u5358\u4e00\u5024\u95a2\u6570\u3068\u3057\u307e\u3059\uff0e <img src='https:\/\/s0.wp.com\/latex.php?latex=%28x_1%2C+y_1%29%2C%5C+%28x_2%2C+y_2%29%2C%5C+%5Cdots%2C%5C+%28x_%7Bn-1%7D%2C+y_%7Bn-1%7D%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(x_1, y_1),\\ (x_2, y_2),\\ \\dots,\\ (x_{n-1}, y_{n-1})' title='(x_1, y_1),\\ (x_2, y_2),\\ \\dots,\\ (x_{n-1}, y_{n-1})' class='latex' \/> \u306b\u3088\u308a\u5f97\u3089\u308c\u305f <em>n &#8211; 1<\/em> \u500b\u306e\u70b9\u3092\u9078\u629e\u3057\u3066 <em>C<\/em> \u3092 <em>n<\/em> \u500b\u306b\u7d30\u5206\u5316\u3057\u307e\u3059\uff0eCall <img src='https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+x_k+%3D+x_k+-+x_%7Bk-1%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\Delta x_k = x_k - x_{k-1}' title='\\Delta x_k = x_k - x_{k-1}' class='latex' \/> \u304a\u3088\u3073 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+y_k+%3D+y_k+-+y_%7Bk-1%7D%2C%5C+k+%3D+1%2C%5C+2%2C%5C+%5Cdots%5C+n&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\Delta y_k = y_k - y_{k-1},\\ k = 1,\\ 2,\\ \\dots\\ n' title='\\Delta y_k = y_k - y_{k-1},\\ k = 1,\\ 2,\\ \\dots\\ n' class='latex' \/> \u3092\u547c\u3073\uff0c<em>C<\/em> \u4e0a\u306b\u3042\u308a\u70b9 <img src='https:\/\/s0.wp.com\/latex.php?latex=%28x_%7Bk-1%7D%2C+y_%7Bk-1%7D%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(x_{k-1}, y_{k-1})' title='(x_{k-1}, y_{k-1})' class='latex' \/> \u304a\u3088\u3073\u70b9 <img src='https:\/\/s0.wp.com\/latex.php?latex=%28x_k%2C+y_k%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(x_k, y_k)' title='(x_k, y_k)' class='latex' \/> \u306e\u9593\u306b\u3042\u308b\u3088\u3046\u306a\u70b9 <img src='https:\/\/s0.wp.com\/latex.php?latex=%28%5Cxi_k%2C+%5Ceta_k%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(\\xi_k, \\eta_k)' title='(\\xi_k, \\eta_k)' class='latex' \/> \u3092\u60f3\u5b9a\u3057\u307e\u3059\uff0e\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u548c\u3092\u5f62\u6210\u3057\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Csum_%7Bk%3D1%7D%5E%7Bn%7D%5C%7BP%28%5Cxi_k%2C+%5Ceta_k%29%5CDelta+x_k+%2B+Q%28%5Cxi_k%2C+%5Ceta_k%29%5CDelta+y_k%5C%7D%5Ccdots%2813%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\sum_{k=1}^{n}\\{P(\\xi_k, \\eta_k)\\Delta x_k + Q(\\xi_k, \\eta_k)\\Delta y_k\\}\\cdots(13)' title='\\displaystyle \\sum_{k=1}^{n}\\{P(\\xi_k, \\eta_k)\\Delta x_k + Q(\\xi_k, \\eta_k)\\Delta y_k\\}\\cdots(13)' class='latex' \/><\/p>\n<p>\u3000\u4eee\u306b\u6975\u9650\u304c\u5b58\u5728\u3059\u308b\u306a\u3089 <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' \/> \u3068\u306a\u308b\u306b\u3064\u308c\u5168\u3066\u306e <img src='https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+x_k%2C%5C+%5CDelta+y&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\Delta x_k,\\ \\Delta y' title='\\Delta x_k,\\ \\Delta y' class='latex' \/> \u306e\u91cf\u306f\u30bc\u30ed\u306b\u8fd1\u3065\u304d\uff0c\u3053\u306e\u548c\u306e\u6975\u9650\u3092 <em>C<\/em> \u5468\u308a\u306e <em>\u7dda\u7a4d\u5206<\/em> \u3068\u547c\u3073\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3057\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cint_C+%5Cleft%5B+P%28x%2C+y%29dx+%2B+Q%28x%2C+y%29dy+%5Cright%5D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\int_C \\left[ P(x, y)dx + Q(x, y)dy \\right]' title='\\displaystyle \\int_C \\left[ P(x, y)dx + Q(x, y)dy \\right]' class='latex' \/> \u307e\u305f\u306f <img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cint_%7B%28a_1%2C+b_1%29%7D%5E%7B%28a_2%2C+b_2%29%7D%5Cleft%5B+Pdx+%2B+Qdy+%5Cright%5D%5Ccdots%2814%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\int_{(a_1, b_1)}^{(a_2, b_2)}\\left[ Pdx + Qdy \\right]\\cdots(14)' title='\\displaystyle \\int_{(a_1, b_1)}^{(a_2, b_2)}\\left[ Pdx + Qdy \\right]\\cdots(14)' class='latex' \/><\/p>\n<p>\u3000<em>P<\/em> \u304a\u3088\u3073 <em>Q<\/em> \u304c <em>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 <em>P<\/em>, <em>Q<\/em>, \u7279\u306b\u66f2\u7dda <em>C<\/em> \u306b\u4f9d\u5b58\u3057\uff0c\u307e\u305f <img src='https:\/\/s0.wp.com\/latex.php?latex=%28a_1%2C+b_1%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(a_1, b_1)' title='(a_1, b_1)' class='latex' \/> \u304a\u3088\u3073 <img src='https:\/\/s0.wp.com\/latex.php?latex=%28a_2%2C+b_2%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(a_2, b_2)' title='(a_2, b_2)' class='latex' \/> \u306e\u6975\u9650\u306b\u4f9d\u5b58\u3057\u307e\u3059\uff0e<\/p>\n<p>\u3000\u6b63\u78ba\u306b\u985e\u4f3c\u3057\u305f\u65b9\u6cd5\u3067 3 \u6b21\u5143\u7a7a\u9593\u306b\u304a\u3051\u308b\u66f2\u7dda <em>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<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Clim%5Climits_%7Bn+%5Crightarrow%5Cinfty%7D%5Csum_%7Bk%3D1%7D%5E%7Bn%7D%5Cleft%5C%7B+A_1%28%5Cxi_k%2C+%5Ceta_k%2C+%5Czeta_k%29%5CDelta+x_k+%2B+A_2%28%5Cxi_k%2C+%5Ceta_k%2C+%5Czeta_k%29%5CDelta+y_k+%2B+A_3%28%5Cxi_k%2C+%5Ceta_k%2C+%5Czeta_k%29%5CDelta+z_k++%5Cright%5C%7D+%5C%5C+%3D+%5Cint_C+%5Cleft%5B+A_1dx+%2B+A_2dy+%2B+A_3dz+%5Cright%5D+%5Ccdots%2815%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\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)' title='\\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)' class='latex' \/><\/p>\n<p>\u3053\u3053\u3067 <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' \/> \u304a\u3088\u3073 <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' \/> \u306f <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' \/>, <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' \/> \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' \/> \u306e\u95a2\u6570\u3067\u3059\uff0e<\/p>\n<p>\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 <img src='https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+s_k&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\Delta s_k' title='\\Delta s_k' class='latex' \/> \u304c\u4e0a\u56f3\u306e\u3088\u3046\u306b\u70b9 <img src='https:\/\/s0.wp.com\/latex.php?latex=%28x_k%2C+y_k%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(x_k, y_k)' title='(x_k, y_k)' class='latex' \/> \u304a\u3088\u3073\u70b9 <img src='https:\/\/s0.wp.com\/latex.php?latex=%28x_%7Bk%2B1%7D%2C+y_%7Bk%2B1%7D%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='(x_{k+1}, y_{k+1})' title='(x_{k+1}, y_{k+1})' class='latex' \/> \u9593\u306e\u66f2\u7dda <em>C<\/em> \u306e\u5f27\u9577\u3092\u8a18\u8ff0\u3059\u308b\u306a\u3089<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Clim%5Climits_%7Bn+%5Crightarrow+%5Cinfty%7D+%5Csum_%7Bk%3D1%7D%5E%7Bn%7D+U%28%5Cxi_k%2C+%5Ceta_k%29%5CDelta+s_k+%3D+%5Cint_C+U%28x%2C+y%29ds%5Ccdots%2816%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\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)' title='\\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)' class='latex' \/><\/p>\n<p>\u4e0a\u8a18\u306f\u66f2\u7dda <em>C<\/em> \u5468\u308a\u306e <img src='https:\/\/s0.wp.com\/latex.php?latex=U%28x%2C+y%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='U(x, y)' title='U(x, y)' class='latex' \/> \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<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>\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 &#8211; 1 \u500b\u306e\u70b9\u3092\u9078\u629e\u3057\u3066 C &hellip; <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5700\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;\u7dda\u7a4d\u5206&#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":{"_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":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.9 - aioseo.com -->\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"admin\"\/>\n\t<meta name=\"keywords\" content=\"\u7dda\u7a4d\u5206,\u533a\u9593\u7684\u306b\u9023\u7d9a\" \/>\n\t<link rel=\"canonical\" href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=5700\" \/>\n\t<meta name=\"generator\" content=\"All 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