{"id":1624,"date":"2023-05-08T19:02:44","date_gmt":"2023-05-08T11:02:44","guid":{"rendered":"http:\/\/zhang.mba\/?p=1624"},"modified":"2023-05-09T14:39:20","modified_gmt":"2023-05-09T06:39:20","slug":"er-zhong-ji-fen","status":"publish","type":"post","link":"https:\/\/zhang.mba\/index.php\/2023\/05\/08\/19\/02\/44\/1624\/er-zhong-ji-fen\/%e9%ab%98%e7%ad%89%e6%95%b0%e5%ad%a6\/zhangzhiqi\/","title":{"rendered":"\u4e8c\u91cd\u79ef\u5206"},"content":{"rendered":"

## \u4e8c\u91cd\u79ef\u5206\u4ecb\u7ecd
\n\u4e8c\u91cd\u79ef\u5206\u662f\u4e00\u79cd\u6570\u5b66\u5de5\u5177\uff0c\u7528\u4e8e\u8ba1\u7b97\u5e73\u9762\u4e0a\u67d0\u4e2a\u533a\u57df\u5185\u7684\u67d0\u79cd\u7269\u7406\u91cf\uff0c\u6bd4\u5982\u9762\u79ef\u3001\u91cd\u5fc3\u3001\u8d28\u5fc3\u7b49\u3002\u53ef\u4ee5\u5c06\u8fd9\u4e2a\u533a\u57df\u770b\u6210\u4e00\u4e2a\u5e73\u9762\u5185\u7684\u4e8c\u7ef4\u56fe\u5f62\uff0c\u6bd4\u5982\u77e9\u5f62\u3001\u4e09\u89d2\u5f62\u3001\u5706\u5f62\u7b49\u3002<\/p>\n

\u4e8c\u91cd\u79ef\u5206\u7684\u8ba1\u7b97\u65b9\u6cd5\u7c7b\u4f3c\u4e8e\u4e00\u5143\u79ef\u5206\uff0c\u4f46\u662f\u9700\u8981\u5bf9\u4e24\u4e2a\u81ea\u53d8\u91cf\u8fdb\u884c\u79ef\u5206\u3002\u4e3a\u4e86\u65b9\u4fbf\u7406\u89e3\uff0c\u53ef\u4ee5\u5c06\u5176\u5206\u89e3\u4e3a\u4e24\u4e2a\u6b65\u9aa4\uff1a<\/p>\n

\u9996\u5148\uff0c\u5c06\u4e8c\u7ef4\u56fe\u5f62\u5206\u6210\u8bb8\u591a\u5c0f\u7684\u9762\u79ef\u5143\u7d20\uff0c\u6bcf\u4e2a\u9762\u79ef\u5143\u7d20\u7684\u9762\u79ef\u53ef\u4ee5\u770b\u6210\u662f\u4e00\u4e2a\u5fae\u5c0f\u7684\u77e9\u5f62\uff0c\u5176\u9762\u79ef\u53ef\u4ee5\u7528\u5fae\u79ef\u5206\u4e2d\u7684\u5fae\u5143\u6982\u5ff5\u6765\u63cf\u8ff0\u3002<\/p>\n

\u7136\u540e\uff0c\u5bf9\u6bcf\u4e2a\u5fae\u5c0f\u7684\u9762\u79ef\u5143\u7d20\u8fdb\u884c\u79ef\u5206\uff0c\u5c06\u5b83\u4eec\u7684\u8d21\u732e\u7d2f\u52a0\u8d77\u6765\uff0c\u5c31\u53ef\u4ee5\u5f97\u5230\u6574\u4e2a\u533a\u57df\u5185\u7684\u7269\u7406\u91cf\u3002<\/p>\n

\u5177\u4f53\u6765\u8bf4\uff0c\u53ef\u4ee5\u5c06\u4e8c\u91cd\u79ef\u5206\u8868\u793a\u4e3a\uff1a<\/p>\n

\u222cf(x,y)dxdy<\/p>\n

\u5176\u4e2d\uff0cf(x,y)\u662f\u8981\u6c42\u79ef\u5206\u7684\u51fd\u6570\uff0c\u8868\u793a\u5728\u6bcf\u4e2a\u5c0f\u7684\u9762\u79ef\u5143\u7d20\u4e0a\u7684\u53d6\u503c\u3002dx\u548cdy\u5206\u522b\u8868\u793a\u5bf9x\u548cy\u8fdb\u884c\u7684\u79ef\u5206\u53d8\u91cf\u3002\u8fd9\u4e2a\u79ef\u5206\u53ef\u4ee5\u770b\u505a\u662f\u5728\u4e8c\u7ef4\u5e73\u9762\u4e0a\u5bf9f(x,y)\u8fdb\u884c\u79ef\u5206\u7684\u8fc7\u7a0b\uff0c\u5176\u4e2d\u6bcf\u4e2a\u5fae\u5c0f\u7684\u9762\u79ef\u5143\u7d20\u5bf9\u79ef\u5206\u7ed3\u679c\u90fd\u6709\u4e00\u5b9a\u7684\u8d21\u732e\u3002<\/p>\n

\u4e8c\u91cd\u79ef\u5206\u7684\u8ba1\u7b97\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u6700\u5e38\u7528\u7684\u662f\u57fa\u4e8e\u7d2f\u6b21\u79ef\u5206\u7684\u65b9\u6cd5\u3002\u8fd9\u79cd\u65b9\u6cd5\u5c06\u4e8c\u91cd\u79ef\u5206\u95ee\u9898\u8f6c\u5316\u4e3a\u4e24\u4e2a\u4e00\u5143\u79ef\u5206\u7684\u95ee\u9898\uff0c\u5148\u5bf9\u5176\u4e2d\u4e00\u4e2a\u53d8\u91cf\u8fdb\u884c\u79ef\u5206\uff0c\u518d\u5bf9\u53e6\u4e00\u4e2a\u53d8\u91cf\u8fdb\u884c\u79ef\u5206\uff0c\u4ece\u800c\u5f97\u5230\u6700\u7ec8\u7684\u79ef\u5206\u503c\u3002
\n## \u4e3e\u4f8b<\/p>\n

\u5f53\u60f3\u8981\u8ba1\u7b97\u5e73\u9762\u4e0a\u67d0\u4e2a\u533a\u57df\u7684\u9762\u79ef\u65f6\uff0c\u53ef\u4ee5\u4f7f\u7528\u4e8c\u91cd\u79ef\u5206\u6765\u6c42\u89e3\u3002\u5047\u8bbe\u8981\u8ba1\u7b97\u4e00\u4e2a\u77e9\u5f62\u533a\u57df\u7684\u9762\u79ef\uff0c\u5176\u5de6\u4e0b\u89d2\u5750\u6807\u4e3a$(a,b)$\uff0c\u53f3\u4e0a\u89d2\u5750\u6807\u4e3a$(c,d)$\uff0c\u5219\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8fdb\u884c\u8ba1\u7b97\uff1a<\/p>\n

$$\\iint_R dxdy$$<\/p>\n

\u5176\u4e2d\uff0c$R$\u8868\u793a\u77e9\u5f62\u533a\u57df\uff0c$dx$\u548c$dy$\u5206\u522b\u8868\u793a\u5bf9$x$\u548c$y$\u8fdb\u884c\u7684\u79ef\u5206\u53d8\u91cf\uff0c$dxdy$\u8868\u793a\u5bf9\u6bcf\u4e2a\u5fae\u5c0f\u7684\u9762\u79ef\u5143\u7d20\u8fdb\u884c\u79ef\u5206\u3002<\/p>\n

\u4e3a\u4e86\u6c42\u89e3\u8fd9\u4e2a\u79ef\u5206\uff0c\u53ef\u4ee5\u91c7\u7528\u7d2f\u6b21\u79ef\u5206\u7684\u65b9\u6cd5\uff0c\u5373\u5148\u5bf9$x$\u8fdb\u884c\u79ef\u5206\uff0c\u518d\u5bf9$y$\u8fdb\u884c\u79ef\u5206\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u53ef\u4ee5\u5c06\u4e0a\u5f0f\u6539\u5199\u4e3a\uff1a<\/p>\n

$$\\int_a^c\\int_b^d dxdy$$<\/p>\n

\u5176\u4e2d\uff0c\u7b2c\u4e00\u4e2a\u79ef\u5206\u8868\u793a\u5bf9$x$\u5728$a$\u5230$c$\u4e4b\u95f4\u8fdb\u884c\u79ef\u5206\uff0c\u7b2c\u4e8c\u4e2a\u79ef\u5206\u8868\u793a\u5bf9$y$\u5728$b$\u5230$d$\u4e4b\u95f4\u8fdb\u884c\u79ef\u5206\u3002\u7531\u4e8e$dxdy$\u8868\u793a\u6bcf\u4e2a\u5fae\u5c0f\u7684\u9762\u79ef\u5143\u7d20\uff0c\u6240\u4ee5\u79ef\u5206\u7684\u7ed3\u679c\u5c31\u662f\u77e9\u5f62\u533a\u57df\u7684\u9762\u79ef\u3002<\/p>\n

\u4f8b\u5982\uff0c\u5982\u679c\u8981\u8ba1\u7b97\u5de6\u4e0b\u89d2\u5750\u6807\u4e3a$(0,0)$\uff0c\u53f3\u4e0a\u89d2\u5750\u6807\u4e3a$(2,3)$\u7684\u77e9\u5f62\u533a\u57df\u7684\u9762\u79ef\uff0c\u90a3\u4e48\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u8ba1\u7b97\u8fc7\u7a0b\uff1a<\/p>\n

$$\\int_0^2\\int_0^3 dxdy = \\int_0^2 [xy]_0^3 dx = \\int_0^2 3x dx = \\frac{3}{2}(2)^2 = 6$$<\/p>\n

\u56e0\u6b64\uff0c\u8fd9\u4e2a\u77e9\u5f62\u533a\u57df\u7684\u9762\u79ef\u4e3a6\u5e73\u65b9\u5355\u4f4d\u3002<\/p>\n\n

<\/div>","protected":false},"excerpt":{"rendered":"

## \u4e8c\u91cd\u79ef\u5206\u4ecb\u7ecd \u4e8c\u91cd\u79ef\u5206\u662f\u4e00\u79cd\u6570\u5b66\u5de5\u5177\uff0c\u7528\u4e8e\u8ba1\u7b97\u5e73\u9762\u4e0a\u67d0\u4e2a\u533a\u57df\u5185\u7684\u67d0\u79cd\u7269\u7406\u91cf\uff0c\u6bd4\u5982\u9762\u79ef\u3001\u91cd\u5fc3\u3001\u8d28\u5fc3\u7b49\u3002\u53ef\u4ee5\u5c06\u8fd9\u4e2a\u533a\u57df\u770b\u6210\u4e00\u4e2a\u5e73\u9762\u5185\u7684\u4e8c\u7ef4\u56fe\u5f62\uff0c\u6bd4\u5982\u77e9\u5f62\u3001\u4e09\u89d2\u5f62\u3001\u5706\u5f62\u7b49\u3002 \u4e8c\u91cd\u79ef\u5206\u7684\u8ba1\u7b97\u65b9\u6cd5\u7c7b\u4f3c\u4e8e\u4e00\u5143\u79ef\u5206\uff0c\u4f46\u662f\u9700\u8981\u5bf9\u4e24\u4e2a\u81ea\u53d8\u91cf\u8fdb\u884c\u79ef\u5206\u3002\u4e3a …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0},"categories":[20],"tags":[59],"_links":{"self":[{"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/posts\/1624"}],"collection":[{"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/comments?post=1624"}],"version-history":[{"count":0,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/posts\/1624\/revisions"}],"wp:attachment":[{"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/media?parent=1624"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/categories?post=1624"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zhang.mba\/index.php\/wp-json\/wp\/v2\/tags?post=1624"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}