{"id":276,"date":"2023-07-29T07:35:15","date_gmt":"2023-07-28T23:35:15","guid":{"rendered":"http:\/\/8.130.122.109\/?p=276"},"modified":"2023-12-10T19:44:59","modified_gmt":"2023-12-10T11:44:59","slug":"%e5%be%ae%e7%a7%af%e5%88%86%e8%ae%b2%e4%b9%89","status":"publish","type":"post","link":"http:\/\/wangheran.com\/?p=276","title":{"rendered":"\u6781\u7b80\u5185\u5316\u5fae\u79ef\u5206\uff1a\u6838\u5fc3\u6982\u5ff5\u4e0e\u601d\u60f3"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_61 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor: pointer\">\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" 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title=\"\u6781\u9650\u662f\u4e00\u79cd\u7ebf\u6027\u8fd0\u7b97\">\u6781\u9650\u662f\u4e00\u79cd\u7ebf\u6027\u8fd0\u7b97<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"http:\/\/wangheran.com\/?p=276\/#%E6%9C%AA%E5%AE%9A%E5%BC%8F%E6%9E%81%E9%99%90%E7%9A%84%E8%AE%A1%E7%AE%97\" title=\"\u672a\u5b9a\u5f0f\u6781\u9650\u7684\u8ba1\u7b97\">\u672a\u5b9a\u5f0f\u6781\u9650\u7684\u8ba1\u7b97<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"http:\/\/wangheran.com\/?p=276\/#%E4%BD%BF%E7%94%A8MATLAB%E8%AE%A1%E7%AE%97%E6%9E%81%E9%99%90\" title=\"\u4f7f\u7528MATLAB\u8ba1\u7b97\u6781\u9650\">\u4f7f\u7528MATLAB\u8ba1\u7b97\u6781\u9650<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"http:\/\/wangheran.com\/?p=276\/#%E5%AF%BC%E6%95%B0%E4%B8%8E%E5%BE%AE%E5%88%86\" 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class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"http:\/\/wangheran.com\/?p=276\/#%E5%AE%9A%E7%A7%AF%E5%88%86%EF%BC%9A%E6%9C%89%E9%99%90%E8%8C%83%E5%9B%B4%E5%86%85%E7%9A%84%E6%B1%82%E5%92%8C\" title=\"\u5b9a\u79ef\u5206\uff1a\u6709\u9650\u8303\u56f4\u5185\u7684\u6c42\u548c\">\u5b9a\u79ef\u5206\uff1a\u6709\u9650\u8303\u56f4\u5185\u7684\u6c42\u548c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"http:\/\/wangheran.com\/?p=276\/#%E5%AE%9A%E7%A7%AF%E5%88%86%EF%BC%9A%E5%8E%9F%E5%9B%A0%E5%8E%86%E7%BB%8F%E6%97%B6%E9%97%B4%E4%BA%A7%E7%94%9F%E7%9A%84%E4%BD%9C%E7%94%A8\" title=\"\u5b9a\u79ef\u5206\uff1a\u539f\u56e0\u5386\u7ecf\u65f6\u95f4\u4ea7\u751f\u7684\u4f5c\u7528\">\u5b9a\u79ef\u5206\uff1a\u539f\u56e0\u5386\u7ecf\u65f6\u95f4\u4ea7\u751f\u7684\u4f5c\u7528<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"http:\/\/wangheran.com\/?p=276\/#%E5%AE%9A%E7%A7%AF%E5%88%86%E7%9A%84MATLAB%E6%B1%82%E8%A7%A3\" title=\"\u5b9a\u79ef\u5206\u7684MATLAB\u6c42\u89e3\">\u5b9a\u79ef\u5206\u7684MATLAB\u6c42\u89e3<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-28\" href=\"http:\/\/wangheran.com\/?p=276\/#%E5%82%85%E9%87%8C%E5%8F%B6%E5%B1%95%E5%BC%80%EF%BC%9A%E9%A2%91%E5%9F%9F%E4%B8%8B%E7%9A%84%E8%B0%90%E6%B3%A2%E4%BB%BF%E7%9C%9F%E7%B3%BB%E7%BB%9F\" title=\"\u5085\u91cc\u53f6\u5c55\u5f00\uff1a\u9891\u57df\u4e0b\u7684\u8c10\u6ce2\u4eff\u771f\u7cfb\u7edf\">\u5085\u91cc\u53f6\u5c55\u5f00\uff1a\u9891\u57df\u4e0b\u7684\u8c10\u6ce2\u4eff\u771f\u7cfb\u7edf<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-29\" href=\"http:\/\/wangheran.com\/?p=276\/#%E8%B0%90%E6%B3%A2%EF%BC%9A%E8%87%AA%E7%84%B6%E4%B9%8B%E9%81%93\" title=\"\u8c10\u6ce2\uff1a\u81ea\u7136\u4e4b\u9053\">\u8c10\u6ce2\uff1a\u81ea\u7136\u4e4b\u9053<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-30\" href=\"http:\/\/wangheran.com\/?p=276\/#%E8%B0%90%E6%B3%A2%EF%BC%9A%E5%91%BD%E8%BF%90%E5%90%AF%E8%BF%AA\" title=\"\u8c10\u6ce2\uff1a\u547d\u8fd0\u542f\u8fea\">\u8c10\u6ce2\uff1a\u547d\u8fd0\u542f\u8fea<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-31\" href=\"http:\/\/wangheran.com\/?p=276\/#%E5%82%85%E9%87%8C%E5%8F%B6%E5%88%86%E8%A7%A3%EF%BC%9A%E4%BB%BB%E6%84%8F%E6%B3%A2%E9%83%BD%E7%94%B1%E8%B0%90%E6%B3%A2%E7%BB%84%E6%88%90\" title=\"\u5085\u91cc\u53f6\u5206\u89e3\uff1a\u4efb\u610f\u6ce2\u90fd\u7531\u8c10\u6ce2\u7ec4\u6210\">\u5085\u91cc\u53f6\u5206\u89e3\uff1a\u4efb\u610f\u6ce2\u90fd\u7531\u8c10\u6ce2\u7ec4\u6210<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-32\" href=\"http:\/\/wangheran.com\/?p=276\/#%E5%82%85%E9%87%8C%E5%8F%B6%E5%88%86%E8%A7%A3%EF%BC%9A%E9%A2%91%E5%9F%9F%E4%B8%8A%E7%9A%84%E8%B0%90%E6%B3%A2%E5%8F%A0%E5%8A%A0%E4%BB%BF%E7%9C%9F%E7%B3%BB%E7%BB%9F\" title=\"\u5085\u91cc\u53f6\u5206\u89e3\uff1a\u9891\u57df\u4e0a\u7684\u8c10\u6ce2\u53e0\u52a0\u4eff\u771f\u7cfb\u7edf\">\u5085\u91cc\u53f6\u5206\u89e3\uff1a\u9891\u57df\u4e0a\u7684\u8c10\u6ce2\u53e0\u52a0\u4eff\u771f\u7cfb\u7edf<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-33\" href=\"http:\/\/wangheran.com\/?p=276\/#%E6%8A%8A%E6%B3%A2%E6%8C%AF%E5%8A%A8%E5%90%91%E9%A2%91%E5%9F%9F%E5%88%86%E8%A7%A3%E5%90%8E%E7%9A%84%E5%BA%94%E7%94%A8\" title=\"\u628a\u6ce2(\u632f\u52a8)\u5411\u9891\u57df\u5206\u89e3\u540e\u7684\u5e94\u7528\">\u628a\u6ce2(\u632f\u52a8)\u5411\u9891\u57df\u5206\u89e3\u540e\u7684\u5e94\u7528<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-34\" href=\"http:\/\/wangheran.com\/?p=276\/#%E5%82%85%E9%87%8C%E5%8F%B6%E5%B1%95%E5%BC%80%E7%9A%84MATLAB%E6%BA%90%E7%A0%81\" title=\"\u5085\u91cc\u53f6\u5c55\u5f00\u7684MATLAB\u6e90\u7801\">\u5085\u91cc\u53f6\u5c55\u5f00\u7684MATLAB\u6e90\u7801<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-35\" href=\"http:\/\/wangheran.com\/?p=276\/#%E4%B8%A4%E7%A7%8D%E4%BB%BF%E7%9C%9F%E7%B3%BB%E7%BB%9F%EF%BC%9A%E6%B3%B0%E5%8B%92%E4%B8%8E%E5%82%85%E9%87%8C%E5%8F%B6\" title=\"\u4e24\u79cd\u4eff\u771f\u7cfb\u7edf\uff1a\u6cf0\u52d2\u4e0e\u5085\u91cc\u53f6\">\u4e24\u79cd\u4eff\u771f\u7cfb\u7edf\uff1a\u6cf0\u52d2\u4e0e\u5085\u91cc\u53f6<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-36\" href=\"http:\/\/wangheran.com\/?p=276\/#%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E5%B0%B1%E6%98%AF%E5%9B%A0%E6%9E%9C%E5%85%B3%E7%B3%BB\" title=\"\u5fae\u5206\u65b9\u7a0b\u5c31\u662f\u56e0\u679c\u5173\u7cfb\">\u5fae\u5206\u65b9\u7a0b\u5c31\u662f\u56e0\u679c\u5173\u7cfb<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-37\" href=\"http:\/\/wangheran.com\/?p=276\/#%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%EF%BC%9A%E7%8E%B0%E4%BB%A3%E7%A7%91%E5%AD%A6%E7%9A%84%E5%9F%BA%E7%9F%B3\" title=\"\u5fae\u5206\u65b9\u7a0b\uff1a\u73b0\u4ee3\u79d1\u5b66\u7684\u57fa\u77f3\">\u5fae\u5206\u65b9\u7a0b\uff1a\u73b0\u4ee3\u79d1\u5b66\u7684\u57fa\u77f3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-38\" href=\"http:\/\/wangheran.com\/?p=276\/#%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E8%A7%A3%E6%9E%90%E8%A7%A3\" title=\"\u5fae\u5206\u65b9\u7a0b\u89e3\u6790\u89e3\">\u5fae\u5206\u65b9\u7a0b\u89e3\u6790\u89e3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-39\" href=\"http:\/\/wangheran.com\/?p=276\/#%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E6%95%B0%E5%80%BC%E8%A7%A3\" title=\"\u5fae\u5206\u65b9\u7a0b\u6570\u503c\u89e3\">\u5fae\u5206\u65b9\u7a0b\u6570\u503c\u89e3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-40\" href=\"http:\/\/wangheran.com\/?p=276\/#%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E9%80%A0%E5%B0%B1%E4%BA%86%E6%9C%89%E9%99%90%E5%85%83%E6%B3%95\" title=\"\u5fae\u5206\u65b9\u7a0b\u9020\u5c31\u4e86\u6709\u9650\u5143\u6cd5\">\u5fae\u5206\u65b9\u7a0b\u9020\u5c31\u4e86\u6709\u9650\u5143\u6cd5<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-41\" href=\"http:\/\/wangheran.com\/?p=276\/#%E6%80%9D%E6%83%B3%E6%80%BB%E7%BB%93\" title=\"\u601d\u60f3\u603b\u7ed3\">\u601d\u60f3\u603b\u7ed3<\/a><\/li><\/ul><\/nav><\/div>\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u5b66\u4e60\u77e5\u8bc6\u7684\u5c42\u6b21\u662f\uff1a\u63a5\u89e6 \u2192 \u7406\u89e3 \u2192 \u5185\u5316 \u2192 \u5e94\u7528 \u2192 \u638c\u63e1\u3002<\/p>\n<cite>\u4eba\u4e0e\u4eba\u4e4b\u95f4\u7684\u533a\u522b\u4e3b\u8981\u4ea7\u751f\u5728\u2014\u2014\u201c\u5185\u5316\u201d\u73af\u8282\u3002<\/cite><\/blockquote>\n\n\n\n<h1 class=\"wp-block-heading has-text-align-center\"><span class=\"ez-toc-section\" id=\"%E8%BF%9E%E7%BB%AD%E4%B8%8E%E6%97%A0%E7%A9%B7\"><\/span>\u8fde\u7eed\u4e0e\u65e0\u7a77<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%BE%AE%E7%A7%AF%E5%88%86_%E5%BE%AE%E5%88%86_%E7%A7%AF%E5%88%86\"><\/span><strong>\u5fae\u79ef\u5206 = \u5fae\u5206 + \u79ef\u5206<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5fae\u5206\uff1a\u628a\u7814\u7a76\u7684\u5bf9\u8c61\u5206\u89e3\u6210\u975e\u5e38\u975e\u5e38\u5fae\u5c0f\u7684\u5355\u5143\u53bb\u7814\u7a76\uff1b<\/strong>\uff08\u6ce8\u610f\uff0c\u6bcf\u4e2a\u5fae\u5c0f\u5355\u5143\u8981\u5177\u5907\u5168\u5c40\u6027\u8d28\uff0c\u201c\u5168\u606f\u201d\uff09<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u79ef\u5206\uff1a\u628a\u521a\u624d\u7814\u7a76\u5b8c\u7684\u975e\u5e38\u5fae\u5c0f\u7684\u5355\u5143\uff0c\u518d\u79ef\u7d2f\u5728\u4e00\u8d77\u5f97\u5230\u7ed3\u679c\u3002<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7c7b\u4f3c\u4e8e\u201c\u5206\u6790\u201d\u4e0e\u201c\u7efc\u5408\u201d\u7684\u5173\u7cfb\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" width=\"640\" height=\"364\" src=\"http:\/\/8.130.122.109\/wp-content\/uploads\/2023\/08\/image-7.png\" alt=\"\" class=\"wp-image-417\" style=\"width:312px;height:177px\" srcset=\"http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-7.png 640w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-7-300x171.png 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E8%8B%B1%E6%96%87_Calculus%EF%BC%9A%E2%80%9C%E8%AE%A1%E7%AE%97%E6%96%B9%E6%B3%95%E2%80%9D\"><\/span><strong>\u82f1\u6587 Calculus\uff1a\u201c\u8ba1\u7b97\u65b9\u6cd5<\/strong>\u201d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u548c\u6211\u4eec\u5e38\u8bf4\u7684<strong>\u8ba1\u7b97\u5668<\/strong>\u2014\u2014calculator \u975e\u5e38\u50cf\uff0c\u5176\u5b9e\uff0c\u5b83\u7684\u539f\u610f\u5c31\u662f\u201c\u8ba1\u7b97\u65b9\u6cd5\u201d\u7684\u610f\u601d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\uff0c\u6700\u521d\uff0c\u5b8c\u6574\u7684\u5fae\u79ef\u5206\u82f1\u6587\u8981\u8fd9\u4e48\u8bf4\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>differential and integral calculus<\/strong> \uff08<strong>\u201c\u5fae\u5206\u548c\u79ef\u5206\u7684\u8ba1\u7b97\u65b9\u6cd5\u201d<\/strong>\uff09<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u53e6\u5916\u4e5f\u53ef\u4ee5\u8fd9\u4e48\u8bf4\uff1a<strong>infinitesimal calculus<\/strong> \uff08<strong>\u201c\u7814\u7a76\u65e0\u7a77\u5c0f\u91cf\u7684\u8ba1\u7b97\u65b9\u6cd5\u201d<\/strong>\uff09<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E8%BF%9E%E7%BB%AD%E6%80%A7%EF%BC%9A%E8%87%AA%E7%84%B6%E8%A7%84%E5%BE%8B%E4%B9%8B%E5%A4%A7%E9%81%93\"><\/span>\u8fde\u7eed\u6027\uff1a\u81ea\u7136\u89c4\u5f8b\u4e4b\u5927\u9053<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u201c\u8fde\u7eed\u201d<\/strong>\u662f\u7814\u7a76\u5fae\u79ef\u5206\u7684\u91cd\u8981\u524d\u63d0\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u7ecf\u5178\u7684\u7269\u7406\u4e16\u754c\u4e2d\uff0c\u4e00\u5207\u90fd\u662f\u8fde\u7eed\u7684\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u91cc\uff0c\u6211\u4eec\u5047\u88c5\u4e0d\u77e5\u9053\u201c\u91cf\u5b50\u4e16\u754c\u201d\uff0c\u53ea\u7814\u7a76\u201c<strong>\u8fde\u7eed\u51fd\u6570<\/strong>\u201d\uff08<strong>Continuous function<\/strong>\uff09\u2014\u2014<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p26.toutiaoimg.com\/large\/pgc-image\/501c640be1ef4b83917a06d086cd7e8b\" alt=\"\" style=\"width:396px;height:268px\"\/><figcaption class=\"wp-element-caption\">\u65e0\u8bba\u600e\u4e48\u653e\u5927\uff0c\u4ecd\u7136\u662f\u4e00\u6bb5\u8fde\u7eed\u7684\u7ebf<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fde\u7eed\u51fd\u6570\u4e00\u822c\u8868\u793a\u4e3a\uff1a\\(f\\left( x \\right) \\in C\\)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%97%A0%E7%A9%B7%EF%BC%9A%E6%98%AF%E4%B8%80%E4%B8%AA%E5%8A%A8%E6%80%81%E7%9A%84%E6%A6%82%E5%BF%B5\"><\/span>\u65e0\u7a77\uff1a\u662f\u4e00\u4e2a\u52a8\u6001\u7684\u6982\u5ff5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u201c\u65e0\u7a77\u201d\u662f\u5fae\u79ef\u5206\u7684\u6838\u5fc3\u6982\u5ff5\u3002<\/strong><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u201c\u4e00\u5c3a\u4e4b\u68f0\uff0c\u65e5\u53d6\u5176\u534a\uff0c\u4e07\u4e16\u4e0d\u7aed\u3002\u201d <\/p>\n<cite>\u2014\u2014 \u300a\u5e84\u5b50 \u00b7 \u5929\u4e0b\u300b<\/cite><\/blockquote>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p26.toutiaoimg.com\/large\/pgc-image\/ef515ac628ff41edafb8c476b378755f\" alt=\"\" style=\"width:444px;height:112px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u53f3\u8fb9\u7684\u5f0f\u5b50\uff0c\u201c\u65e0\u9650\u8d8b\u8fd1\u201d\u4e8e 1\u3002\u8fd9\u662f\u4e00\u4e2a\u201c\u52a8\u6001\u8fc7\u7a0b\u201d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u65e0\u7a77\u5c0f\uff0c\u662f\u4e00\u4e2a\u201c\u53d8\u91cf\u201d\uff0c\u662f\u4e00\u4e2a\u65e0\u9650\u8d8b\u8fd1\u4e8e0\u7684\u4e00\u4e2a\u201c\u8fc7\u7a0b\u201d\u3002<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u8c13\u201c\u9ad8\u9636\u65e0\u7a77\u5c0f\u201d\uff0c\u65e0\u975e\u5c31\u662f\u5b83\u201c<strong>\u8d8b\u8fd1\u4e8e0\u7684\u2018\u901f\u5ea6\u2019\u66f4\u5feb<\/strong>\u201d\u5457\u3002\uff08\u6b64\u5904\u6709\u6df1\u610f\uff0c\u4e0e\u540e\u9762\u7684\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u6709\u8054\u7cfb\uff09<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E2%80%9C%E6%97%A0%E7%A9%B7%E8%A7%86%E8%A7%92%E2%80%9D%E7%9C%8B%E9%97%AE%E9%A2%98\"><\/span>\u201c\u65e0\u7a77\u89c6\u89d2\u201d\u770b\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b1 <strong>\u5728\u4e00\u4e2a\u65e0\u7a77\u5c0f\u7684\u8303\u56f4\u91cc\uff0c\u6240\u6709\u66f2\u7ebf\u90fd\u662f\u76f4\u7ebf\uff1a<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p26.toutiaoimg.com\/large\/pgc-image\/47553986bca24ed2a217e86c048cd0c7\" alt=\"\" style=\"width:464px;height:218px\"\/><\/figure>\n\n\n\n<p class=\"has-text-align-left wp-block-paragraph\">\u4f8b2 <strong>\u5272\u5706\u672f<\/strong><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u201c\u5272\u4e4b\u5f25\u7ec6\uff0c\u6240\u5931\u5f25\u5c11\uff0c\u5272\u4e4b\u53c8\u5272\uff0c\u4ee5\u81f3\u4e8e\u4e0d\u53ef\u5272\uff0c\u5219\u4e0e\u5706\u5408\u4f53\uff0c\u800c\u65e0\u6240\u5931\u77e3\u3002\u201d <\/p>\n<cite>\u2014\u2014 \u5218\u5fbd \u300a\u4e5d\u7ae0\u7b97\u672f\u6ce8\u300b\uff08263\u5e74\uff09<\/cite><\/blockquote>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p26.toutiaoimg.com\/large\/pgc-image\/facada0c3e274cf7bb5e8c1defd5f054\" alt=\"\" style=\"width:456px;height:195px\"\/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-text-align-center\"><span class=\"ez-toc-section\" id=\"%E6%9E%81%E9%99%90\"><\/span>\u6781\u9650<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%9E%81%E9%99%90%E6%98%AF%E6%97%A0%E9%99%90%E9%80%BC%E8%BF%91%E7%9A%84%E8%BF%87%E7%A8%8B\"><\/span>\u6781\u9650\u662f\u65e0\u9650\u903c\u8fd1\u7684\u8fc7\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8fd9\u4e2a\u8fc7\u7a0b\u7684\u201c\u7ec8\u70b9\u201d\u6c38\u8fdc\u8fbe\u4e0d\u5230\uff0c\u4f46\u662f\u65e0\u6bd4\u8d8b\u8fd1\u7684\u90a3\u4e2a\u503c\uff0c\u5c31\u662f\u201c\u6781\u9650\u503c\u201d<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bd4\u5982\uff0c\\(\\lim_{x\\rightarrow x_0} f\\left( x \\right) \\) \u8868\u793a \u53d8\u91cf <em>x<\/em> \u5411 <em>x<\/em><sub>0<\/sub> \u70b9\u65e0\u9650\u903c\u8fd1\uff0c<em>f<\/em>(<em>x<\/em>) \u65e0\u9650\u8d8b\u8fd1\u7684\u90a3\u4e2a\u503c\uff0c\u5c31\u662f\u6781\u9650\u503c\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0a\u6587\u8bb2\u7684<strong>\u65e0\u7a77\u5c0f\u672c\u8eab\u662f\u4e00\u4e2a&#8221;\u8fc7\u7a0b&#8221;\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u7684\u6781\u9650\uff0c\u5c31\u662f0<\/strong>\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%9E%81%E9%99%90%E6%98%AF%E4%B8%80%E7%A7%8D%E7%BA%BF%E6%80%A7%E8%BF%90%E7%AE%97\"><\/span>\u6781\u9650\u662f\u4e00\u79cd\u7ebf\u6027\u8fd0\u7b97<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" width=\"640\" height=\"359\" src=\"http:\/\/8.130.122.109\/wp-content\/uploads\/2023\/08\/image-4.png\" alt=\"\" class=\"wp-image-370\" style=\"width:366px;height:205px\" srcset=\"http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-4.png 640w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-4-300x168.png 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\infty \/A=\\infty \\)<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u201c\u543e\u751f\u4e5f\u6709\u6daf\uff0c\u800c\u77e5\u4e5f\u65e0\u6daf\u3002\u4ee5\u6709\u6daf\u968f\u65e0\u6daf\uff0c\u6b86\u5df2\uff01\u201d <\/p>\n<cite>\u2014\u2014\u300a\u5e84\u5b50 \u00b7 \u517b\u751f\u4e3b\u300b<\/cite><\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\u77e5\u8bc6\u662f\u65e0\u7a77\u7684\uff0c\u800c\u751f\u547d\u5374\u53ea\u6709\u90a3\u4e48\u51e0\u5929\uff0c\u6240\u4ee5\u7b97\u4e0b\u6765\uff0c\u60f3\u8981\u5b66\u5b8c\u6240\u6709\u77e5\u8bc6\uff0c\u6bcf\u5929\u5fc5\u987b\u4e5f\u5b66\u65e0\u7a77\u591a\u7684\u77e5\u8bc6\uff0c\u90a3\u8fd8\u5f97\u4e86\uff01<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%9C%AA%E5%AE%9A%E5%BC%8F%E6%9E%81%E9%99%90%E7%9A%84%E8%AE%A1%E7%AE%97\"><\/span><strong>\u672a\u5b9a\u5f0f\u6781\u9650\u7684\u8ba1\u7b97<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u6307\u4e24\u79cd\u60c5\u51b5\uff1a\\(0\/0 \\) \u548c \\(\\infty \/ \\infty \\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0a\u6587\u8bf4\uff0c\u6781\u9650\u662f\u4e00\u4e2a\u8fc7\u7a0b\uff0c\u90a3\u4e48\u6781\u9650\u4e4b\u95f4\u7684\u6bd4\u8f83\uff0c\u5176\u5b9e\u662f\u5728\u6bd4\u8f83\u8c01\u7684\u901f\u5ea6\u5feb\uff0c\u8fd9\u5c31\u662f\u201c\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u201d\uff08\u6c42\u5bfc\u540e\u518d\u6bd4\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6216 \u4f7f\u7528\u56e0\u5f0f\u5206\u89e3\/\u5316\u7b80\u2014\u2014<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" width=\"1024\" height=\"294\" src=\"http:\/\/8.130.122.109\/wp-content\/uploads\/2023\/08\/image-3-1024x294.png\" alt=\"\" class=\"wp-image-364\" style=\"width:580px;height:166px\" srcset=\"http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-3-1024x294.png 1024w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-3-300x86.png 300w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-3-768x220.png 768w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-3.png 1175w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u6216 \u66ff\u6362\u53d8\u91cf\u6216\u4f7f\u7528\u7b49\u4ef7\u65e0\u7a77\u5c0f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E4%BD%BF%E7%94%A8MATLAB%E8%AE%A1%E7%AE%97%E6%9E%81%E9%99%90\"><\/span>\u4f7f\u7528MATLAB\u8ba1\u7b97\u6781\u9650<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>limit(fun,x,x0) % \u6c42\u51fd\u6570fun\u5173\u4e8ex\u5728x0\u70b9\u5904\u7684\u6781\u9650\nlimit(fun,x,x0,'left') % \u6c42\u5de6\u6781\u9650\nlimit(fun,x,x0,'right') % \u6c42\u53f3\u6781\u9650<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u4e0d\u662f\u8d8b\u8fd1\u4e8e <em>x<\/em><sub>0<\/sub>\uff0c\u800c\u662f\u8d8b\u8fd1\u4e8e\u65e0\u7a77\uff0c\u5c31\u4f7f\u7528 <strong>inf \u4ee3\u8868\u65e0\u7a77<\/strong>\uff0c\u4ee3\u66ffx0\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u6781\u9650\u4e0d\u5b58\u5728\uff0cMATLAB\u4f1a\u5410\u51fa\u4e00\u4e2a\u201cNaN\u201d\u5b57\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">limit \u51fd\u6570\u4e5f\u80fd\u4f7f\u7528\u7b26\u53f7\uff0c\u6bd4\u5982\u2014\u2014<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>syms x a b; % \u628ax a b\u90fd\u5b9a\u4e49\u4e3a\u7b26\u53f7\nf=x*(1+a\/x)^x*sin(b\/x); % \u8f93\u5165\u51fd\u6570\nL=limit(f,x,inf) % \u6c42\u6781\u9650<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-text-align-center\"><span class=\"ez-toc-section\" id=\"%E5%AF%BC%E6%95%B0%E4%B8%8E%E5%BE%AE%E5%88%86\"><\/span>\u5bfc\u6570\u4e0e\u5fae\u5206<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%AF%BC%E6%95%B0%E4%B9%8B%E2%80%9C%E5%AF%BC%E2%80%9D%E2%80%94%E2%80%94%E5%B0%8E\"><\/span>\u5bfc\u6570\u4e4b\u201c\u5bfc\u201d\u2014\u2014\u5c0e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u7ec4\u4e2a\u8bcd\u770b\u4e00\u770b\uff1a<strong>\u5bfc<\/strong>\u81f4\u3001\u5f15<strong>\u5bfc<\/strong>\u3001<strong>\u5bfc<\/strong>\u5411<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u201c\u5584\u6218\u8005\uff0c\u56e0\u5176\u52bf\u800c\u5229<strong>\u5bfc<\/strong>\u4e4b\u3002\u201d<\/p>\n<cite>\u2014\u2014\u300a\u53f2\u8bb0\u00b7\u5b59\u5b50\u5434\u8d77\u5217\u4f20\u300b<\/cite><\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\u201c\u5bfc\u201d\u5c31\u662f\u201c<strong>\u65b9\u5411<\/strong>\u201d\uff0c\u5bfc\u6570\u5c31\u662f\u8868\u793a\u51fd\u6570\u201c\u8fd0\u884c\u7684\u65b9\u5411\u201d\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" width=\"150\" height=\"150\" src=\"http:\/\/8.130.122.109\/wp-content\/uploads\/2023\/08\/image-12.png\" alt=\"\" class=\"wp-image-453\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%AF%BC%E6%95%B0%E6%98%AF%E2%80%9C%E5%87%BD%E6%95%B0%E7%9A%84%E5%8E%9F%E5%9B%A0%E2%80%9D\"><\/span>\u5bfc\u6570\u662f\u201c\u51fd\u6570\u7684\u539f\u56e0\u201d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u201c\u5bfc\u6570\u201d\u662f\u51fd\u6570\u7684\u539f\u56e0\uff08\u53d8\u5316\u7684\u6765\u6e90\uff09\uff0c\u51fd\u6570\u662f\u201c\u5bfc\u6570\u201d\u7684\u7ed3\u679c\u3002<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p3.toutiaoimg.com\/large\/pgc-image\/08bb0ce017db4635ab991cc78e0d56bf\" alt=\"\" style=\"width:431px;height:186px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u901f\u5ea6\u662f\u4f4d\u79fb\u7684\u5bfc\u6570\uff0c\u901f\u5ea6<strong>\u5bfc\u81f4<\/strong>\u4e86\u4f4d\u79fb\uff1b\u52a0\u901f\u5ea6\u662f\u901f\u5ea6\u7684\u5bfc\u6570\uff0c\u52a0\u901f\u5ea6<strong>\u5bfc\u81f4<\/strong>\u4e86\u901f\u5ea6\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7528\u3010\u5bfc\u6570\u601d\u7ef4\u3011\u6765\u5206\u6790\u95ee\u9898\uff0c\u53ef\u4ee5\u627e\u5230\u4e8b\u7269\u53d8\u5316\u7684\u539f\u56e0\uff0c\u63a7\u5236\u4e8b\u7269\u7684\u53d1\u5c55\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u201c\u7269\u6709\u672c\u672b\uff0c\u4e8b\u6709\u7ec8\u59cb\uff0c\u77e5\u6240\u5148\u540e\uff0c\u5219\u8fd1\u9053\u77e3\u3002\u201c <\/p>\n<cite>\u2014\u2014\u300a\u5927\u5b66\u300b<\/cite><\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%90%86%E8%A7%A3%E4%B9%98%E6%B3%95%E5%AF%BC%E6%95%B0%E6%B1%82%E5%AF%BC%E6%B3%95%E5%88%99\"><\/span>\u7406\u89e3\u4e58\u6cd5\u5bfc\u6570\u6c42\u5bfc\u6cd5\u5219<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\\((uv)\\prime=u\\prime v+u v\\prime\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6211\u4eec\u628a <em>u<\/em>\u3001<em>v<\/em> \u770b\u6210\u662f\u4e00\u4e2a\u77e9\u5f62\u7684\u8fb9\u957f\uff0c\u5219 <strong>(<em>uv<\/em>)&#8217; \u5c31\u662f\u6307\u8fb9\u957f <em>u<\/em> \u548c <em>v<\/em> \u540c\u65f6\u53d8\u5316\uff0c\u6240\u5f15\u8d77\u7684\u9762\u79ef\u53d8\u5316\u91cf\u3002<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p26.toutiaoimg.com\/large\/pgc-image\/1e0facdc00494a87962f45cf0c34e93f\" alt=\"\" style=\"width:454px;height:171px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u77e9\u5f62\u7684\u9762\u79ef\u53d8\u5316\u91cf\u8fd8\u6709\u89d2\u843d\u91cc\u7684\u4e00\u5c0f\u5757\uff0c\u4f46\u662f<strong>\u592a\u5c0f\u4e86\uff0c\u5c0f\u5230\u76f4\u63a5\u820d\u53bb<\/strong>\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%AF%BC%E6%95%B0%E7%9A%84MATLAB%E6%B1%82%E8%A7%A3\"><\/span>\u5bfc\u6570\u7684MATLAB\u6c42\u89e3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>y=diff(fun,x) % \u6c42\u51fd\u6570 fun \u5173\u4e8e x \u7684\u5bfc\u6570\n\ny=diff(fun,x,n) % \u6c42\u51fd\u6570 fun \u5173\u4e8e x \u7684 n \u9636\u5bfc\u6570<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%BE%AE%E5%88%86%EF%BC%9A%E5%90%8C%E6%A0%B7%E4%B9%9F%E6%98%AF%E5%8A%A8%E6%80%81%E6%A6%82%E5%BF%B5\"><\/span>\u5fae\u5206\uff1a\u540c\u6837\u4e5f\u662f\u52a8\u6001\u6982\u5ff5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5fae\u5206\u5c31\u662f<strong>\u5dee\u5206\u7684\u3010\u65e0\u7a77\u5c0f\u8fc7\u7a0b<\/strong>\u3011\uff0c\u81ea\u53d8\u91cf <em>x<\/em> \u7684\u5fae\u5206\u4e3a\uff1a<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(\\mathrm{d}x\\,\\,=\\,\\,\\Delta x\\left| _{\\Delta x\\rightarrow 0} \\right. \\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u65f6\uff0c\u56e0\u53d8\u91cf <em>y<\/em> \u7684\u5fae\u5206\u4e3a\uff1a<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(\\mathrm{d}y=f&#8217;\\left( x \\right) \\mathrm{\u00b7d}x\\)<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" width=\"1024\" height=\"875\" src=\"http:\/\/8.130.122.109\/wp-content\/uploads\/2023\/08\/image-6-1024x875.png\" alt=\"\" class=\"wp-image-405\" style=\"width:368px;height:314px\" srcset=\"http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-6-1024x875.png 1024w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-6-300x256.png 300w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-6-768x656.png 768w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-6-1536x1312.png 1536w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-6.png 1920w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u53ef\u4ee5\u8bf4\uff0cd<em>y<\/em> \u662f \u0394<em>y<\/em> \u7684\u201c<strong>\u7ebf\u6027\u4e3b\u90e8<\/strong>\u201d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6ce8\u610f\u54c8~ \u4e0d\u8981\u89c9\u5f97\u8fd9\u91cc\u9762\u6709\u4e00\u4e2a\u201c\u8bef\u5dee\u201d\uff0c\u8fd9\u662f\u201c\u9759\u6001\u89c6\u89d2\u201d\u4e0b\u770b\u5230\u7684\uff0c\u800c\u5fae\u5206\u662f\u4e00\u4e2a\u52a8\u6001\u7684\u65e0\u7a77\u5c0f\u8fc7\u7a0b\uff0c\u662f\u5b8c\u5168\u6ca1\u6709\u8bef\u5dee\u7684\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-text-align-center\"><span class=\"ez-toc-section\" id=\"%E6%B3%B0%E5%8B%92%E5%B1%95%E5%BC%80%EF%BC%9A%E5%A4%9A%E9%A1%B9%E5%BC%8F%E4%BB%BF%E7%9C%9F%E7%B3%BB%E7%BB%9F\"><\/span>\u6cf0\u52d2\u5c55\u5f00\uff1a\u591a\u9879\u5f0f\u4eff\u771f\u7cfb\u7edf<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%B3%B0%E5%8B%92%E5%B1%95%E5%BC%80%E5%85%AC%E5%BC%8F%E5%88%9D%E6%8E%A2\"><\/span>\u6cf0\u52d2\u5c55\u5f00\u516c\u5f0f\u521d\u63a2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(f\\left( x \\right) =\\sum_{n=0}^{\\infty}{\\frac{f^{\\left( n \\right)}\\left( x_0 \\right)}{n!}\\left( x-x_0 \\right) ^n}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u89c2\u5bdf\u540e\uff0c\u53d1\u73b0\u6709\u51e0\u4e2a\u7279\u70b9\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u4e00\u4e2a\u51fd\u6570\uff0c\u65e0\u8bba\u5b83\u662f\u4ec0\u4e48\u201c\u58f3\u201d\uff0c\u90fd\u53ef\u4ee5\u5206\u89e3\u4e3a\u201c\u591a\u9879\u5f0f\u4e4b\u548c\u201d\u7684\u5f62\u5f0f\uff1b<\/strong><\/li>\n\n\n\n<li><strong>\u5206\u89e3\u65f6\uff0c\u53ef\u4ee5\u9009\u62e9\u4e00\u4e2a\u57fa\u7840\u70b9 <em>x<\/em><sub>0<\/sub>\uff1b<\/strong><\/li>\n\n\n\n<li><strong>\u9879\u8d8a\u591a\uff0c\u5c31\u8d8a\u63a5\u8fd1\u539f\u51fd\u6570\uff0c\u65e0\u7a77\u591a\u9879\u65f6\u53d6\u7b49\u53f7\uff1b<\/strong><\/li>\n\n\n\n<li><strong>\u8d8a\u9760\u524d\uff0c\u8d8a\u4e3b\u8981\uff0c\u6bcf\u4e00\u9879\u7684\u4f5c\u7528\uff0c\u8981\u88abn!\u524a\u5f31\u3002<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bd4\u5982\u6b63\u5f26\u51fd\u6570\u5728 0 \u5904\u5206\u89e3\u2014\u2014<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(\\sin \\left( x \\right) =x-\\frac{x^3}{3!}+\\frac{x^5}{5!}-\\frac{x^7}{7!}+\\cdots \\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff08\u5076\u6570\u9879\u7684\u5bfc\u6570\u5747\u4e3a0\uff0c\u56e0\u6b64\u4e0d\u5728\u516c\u5f0f\u4e2d\uff09<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7528MATLAB\u753b\u4e00\u4e0b\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>x=-6:0.01:6;\ny3=x-x.^3\/factorial(3);\ny5=y3+x.^5\/factorial(5);\ny7=y5-x.^7\/factorial(7);\nplot(x,sin(x),x,y3,x,y5,x,y7)\nylim(&#091;-1.5 1.5])\n<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" width=\"731\" height=\"577\" src=\"http:\/\/8.130.122.109\/wp-content\/uploads\/2023\/08\/image-9.png\" alt=\"\" class=\"wp-image-423\" style=\"width:527px;height:416px\" srcset=\"http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-9.png 731w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-9-300x237.png 300w\" sizes=\"(max-width: 731px) 100vw, 731px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u53ea\u8981\u9879\u6570 n \u6709\u9650\uff0c\u5c31\u4e00\u5b9a\u6709\u8bef\u5dee\uff0c\u8bef\u5dee\u9879\u4e3a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" width=\"1024\" height=\"158\" src=\"http:\/\/8.130.122.109\/wp-content\/uploads\/2023\/08\/image-10-1024x158.png\" alt=\"\" class=\"wp-image-425\" style=\"width:519px;height:79px\" srcset=\"http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-10-1024x158.png 1024w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-10-300x46.png 300w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-10-768x118.png 768w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-10.png 1284w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%B3%B0%E5%8B%92%E5%B1%95%E5%BC%80%E7%9A%84%E5%93%B2%E5%AD%A6%E7%90%86%E8%A7%A3\"><\/span>\u6cf0\u52d2\u5c55\u5f00\u7684\u54f2\u5b66\u7406\u89e3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5148\u53ea\u5c55\u5f00\u524d2\u9879\uff0c\u89e3\u91ca\u4e3a\uff1a<strong><em>x<\/em> \u5904\u7684\u51fd\u6570\u503c\uff0c\u7ea6\u7b49\u4e8e <em>x<\/em><sub>0<\/sub> \u5904\u7684\u51fd\u6570\u503c\uff0c\u518d\u52a0\u4e0a\u7531\u5bfc\u6570\u5f15\u8d77\u7684\u53d8\u5316\u91cf<\/strong>\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p9.toutiaoimg.com\/large\/pgc-image\/ca6468e2eea34c95b3b5f5baaf2aded9\" alt=\"\" style=\"width:576px;height:178px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u662f\u5bf9\u672a\u6765\u60c5\u51b5\u7684\u4eff\u771f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u51e0\u4f55\u8868\u8fbe\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p26.toutiaoimg.com\/large\/pgc-image\/d5bc0bb81d924681ab77417eee9ba8cc\" alt=\"\" style=\"width:484px;height:244px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7531\u4e8e\u539f\u56e0\uff08\u5bfc\u6570\uff09\u53ea\u662f\u201c\u5f53\u524d\u201d\u7684\u539f\u56e0\uff0c\u6240\u4ee5\u4eff\u771f\u9884\u6d4b\u7684\u7ed3\u679c\u80af\u5b9a\u4e0d\u5b8c\u5168\u51c6\u786e\uff1b\u4e0d\u8fc7\uff0c\u53ea\u8981\u65f6\u95f4\u8db3\u591f\u77ed\uff0c\u4eff\u771f\u5c31\u8db3\u591f\u51c6\u786e<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8c\u9636\u5bfc\u6570\u5462\uff1f\u5c31\u662f<strong>\u539f\u56e0\u7684\u539f\u56e0<\/strong>\uff0c\u5373\u201c<strong>\u95f4\u63a5\u539f\u56e0<\/strong>\u201d\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p3.toutiaoimg.com\/large\/pgc-image\/f29dc3e175604d53853c80f97b91d65f\" alt=\"\" style=\"width:566px;height:156px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7ed3\u679c \u2248 \u73b0\u72b6 + \u76f4\u63a5\u539f\u56e0\u5f15\u53d1\u7684\u53d8\u5316 + \u539f\u56e0\u7684\u539f\u56e0\u5f15\u53d1\u7684\u53d8\u5316+&#8230;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8003\u8651\u5f97\u8d8a\u591a\uff0c\u5c31\u8d8a\u51c6\u786e<\/strong>\u3001<strong>\u8d8a\u957f\u8fdc\u3002<\/strong><\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u201c\u592b\u672a\u6218\u800c\u5e99\u7b97\u80dc\u8005\uff0c\u5f97\u7b97\u591a\u4e5f\uff0c\u672a\u6218\u800c\u5e99\u7b97\u4e0d\u80dc\u8005\uff0c\u5f97\u7b97\u5c11\u4e5f\u3002<strong>\u591a\u7b97\u80dc<\/strong>\uff0c\u5c11\u7b97\u4e0d\u80dc\uff0c\u800c\u51b5\u4e8e\u65e0\u7b97\u4e4e!&#8221;<\/p>\n<cite>\u2014\u2014\u300a\u5b59\u5b50\u5175\u6cd5\u300b<\/cite><\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%B3%B0%E5%8B%92%E5%85%AC%E5%BC%8F%E7%9A%84%E6%8F%90%E9%86%92%EF%BC%9A%E6%9C%AC%E6%9C%AB%E4%B8%BB%E6%AC%A1%E4%B9%8B%E5%88%86\"><\/span>\u6cf0\u52d2\u516c\u5f0f\u7684\u63d0\u9192\uff1a\u672c\u672b\/\u4e3b\u6b21\u4e4b\u5206<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u516c\u5f0f\u76f4\u63a5\u5c55\u73b0\u4e86\u5206\u6790\u95ee\u9898\u7684\u6b65\u9aa4\uff1a<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\u73b0\u72b6<em>f<\/em> (<em>x<\/em><sub>0<\/sub>) \u2192 \u4e3b\u56e0<em>f<\/em> &#8216;(<em>x<\/em><sub>0<\/sub>) \u2192 \u6b21\u56e0<em>f<\/em> &#8220;(<em>x<\/em><sub>0<\/sub>)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9884\u6d4b\u7684\u7b2c\u4e00\u8981\u52a1\u662f\u8981\u5206\u6e05\u201c\u672c\u672b\u201d\uff0c\u73b0\u72b6\u4e3a\u672c\uff0c\u53d8\u5316\u4e3a\u672b\uff1b\u5f15\u8d77\u53d8\u5316\u7684\u539f\u56e0\u5f88\u591a\uff0c\u4e5f\u8981\u5148\u5206\u201c\u4e3b\u6b21\u201d\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u201c\u6c42\u4e4b\u5176\u672c\uff0c\u7ecf\u65ec\u5fc5\u5f97\uff1b\u6c42\u4e4b\u5176\u672b\uff0c\u52b3\u800c\u65e0\u529f\u3002\u201d<\/p>\n<cite>\u2014\u2014\u300a\u5415\u6c0f\u6625\u79cb\u300b<\/cite><\/blockquote>\n\n\n\n<h1 class=\"wp-block-heading has-text-align-center\"><span class=\"ez-toc-section\" id=\"%E7%A7%AF%E5%88%86%E4%B8%BA%E2%80%9C%E6%9E%9C%E2%80%9D%EF%BC%9A%E6%98%AF%E2%80%9C%E5%9B%A0%E2%80%9D%E7%9A%84%E9%99%8D%E7%BB%B4%E6%8A%95%E5%BD%B1\"><\/span>\u79ef\u5206\u4e3a\u201c\u679c\u201d\uff1a\u662f\u201c\u56e0\u201d\u7684\u964d\u7ef4\u6295\u5f71<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%EF%BC%9A%E6%B1%82%E5%AF%BC%E7%9A%84%E9%80%86%E8%BF%87%E7%A8%8B\"><\/span>\u4e0d\u5b9a\u79ef\u5206\uff1a\u6c42\u5bfc\u7684\u9006\u8fc7\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u51fd\u6570 <em>F<\/em> (<em>x<\/em>) \u7684\u5bfc\u51fd\u6570\u4e3a <em>F<\/em> &#8216;(<em>x<\/em>) = <em>f<\/em> (<em>x<\/em>)\uff0c\u5219\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>f<\/em> (x) \u662f <em>F<\/em> (<em>x<\/em>) \u7684\u5bfc\u51fd\u6570\uff1b<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>F<\/em> (<em>x<\/em>) \u662f <em>f<\/em> (<em>x<\/em>) \u7684\u539f\u51fd\u6570\u3002<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6ce8\u610f\u54c8\uff0c<strong><em>F<\/em> (<em>x<\/em>) + <em>C<\/em>(\u5e38\u6570) \u7684\u5bfc\u6570\u4e5f\u662f<\/strong> <em>f<\/em>(<em>x<\/em>)\uff0c\u6240\u4ee5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>f<\/em> (<em>x<\/em>) \u6709\u4e00\u65cf\u539f\u51fd\u6570\u2014\u2014 <em>F<\/em>(<em>x<\/em>) + <em>C<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(\\left( F\\left( x \\right) +\\mathrm{C} \\right) &#8216;\\,\\,=\\,\\,f\\left( x \\right) \\,\\, \\text{\u6216} \\int{f\\left( x \\right)}\\mathrm{d}x\\,\\,=\\,\\,F\\left( x \\right) +\\mathrm{C}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8ba1\u7b97\u7684\u8bdd\uff0c\u6709\u201c\u6362\u5143\u79ef\u5206\u6cd5\u201d\u548c\u201c\u5206\u90e8\u79ef\u5206\u6cd5\u201d\u7b49\u65b9\u6cd5\uff0cMATLAB\u53ea\u9700\u4e00\u53e5\u8bdd\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>F=int(fun,x) % \u6c42\u51fd\u6570fun\u5173\u4e8ex\u7684\u4e0d\u5b9a\u79ef\u5206<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E7%9B%B8%E5%90%8C%E5%8E%9F%E5%9B%A0%E5%AF%BC%E8%87%B4%E4%B8%8D%E5%90%8C%E7%BB%93%E6%9E%9C\"><\/span>\u76f8\u540c\u539f\u56e0\u5bfc\u81f4\u4e0d\u540c\u7ed3\u679c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e00\u4e2a\u5bfc\u51fd\u6570\u5bf9\u5e94\u4e00\u7c07\u539f\u51fd\u6570\uff0c\u8fd9\u662f\u56e0\u4e3a\uff0c\u73b0\u72b6(C)\u4e0d\u540c\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u79cd\u5173\u7cfb\u7c7b\u4f3c\u4e8e\u201c\u6295\u5f71\u201d\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/i2.100024.xyz\/2023\/12\/10\/w3mwpe.webp\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0b\u9762\u662f\u4e00\u70b9\u4e2a\u4eba\u7406\u89e3\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f4e\u7ef4\u4e16\u754c\u7684\u539f\u51fd\u6570 \u662f \u9ad8\u7ef4\u4e16\u754c\u7684\u5bfc\u51fd\u6570 \u7684\u6295\u5f71\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u539f\u56e0\u5728\u9ad8\u7ef4\uff0c\u7ed3\u679c\u5728\u4f4e\u7ef4\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bd4\u5982\uff0c\u5c0f\u8f66\u7684\u901f\u5ea6 <em>v<\/em>\uff0c\u76f8\u5bf9\u4e8e\u4f4d\u79fb <em>s<\/em> \u662f\u4e00\u4e2a<strong>\u9ad8\u7ef4\u4e16\u754c\u7684\u4fe1\u606f<\/strong>\uff0c\u56e0\u4e3a\u5b83\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u51b3\u5b9a\u4e86\u4f4e\u7ef4\u4fe1\u606f\u4f4d\u79fb <em>s<\/em> \u7684\u53d8\u5316\uff1b<\/strong><\/li>\n\n\n\n<li><strong>\u201c\u4e0d\u76f4\u89c2\u201d\uff0c\u5982\u679c\u4e0d\u6295\u5f71\u4f4e\u7ef4\u7684\u4f4d\u79fb\u4fe1\u606f\uff0c\u6211\u4eec\u751a\u81f3\u4e0d\u6613\u7406\u89e3\uff1b<\/strong><\/li>\n\n\n\n<li><strong>\u8868\u8fbe\u7b80\u5355\uff0c\u201c\u9ad8\u7ef4\u7684\u8868\u8fbe\u53cd\u800c\u7b80\u5355\u201d\u3002<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u63d0\u793a\u6211\u4eec\u5efa\u7acb\u3010\u5347\u7ef4\u601d\u7ef4\u3011\uff0c\u53ef\u4ee5\u89e3\u51b3\u8bb8\u591a\u5b9e\u9645\u95ee\u9898\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%AE%9A%E7%A7%AF%E5%88%86%EF%BC%9A%E6%9C%89%E9%99%90%E8%8C%83%E5%9B%B4%E5%86%85%E7%9A%84%E6%B1%82%E5%92%8C\"><\/span>\u5b9a\u79ef\u5206\uff1a\u6709\u9650\u8303\u56f4\u5185\u7684\u6c42\u548c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u4f55\u6c42\u4e00\u4e2a\u66f2\u7ebf <em>f<\/em>(<em>x<\/em>) \u5305\u56f4\u7684\u9762\u79ef\uff1f<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p3.toutiaoimg.com\/large\/pgc-image\/7d13c3bbec71496f8ce6ef9b5669078d\" alt=\"\" style=\"width:598px;height:141px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5206\u5272\u65e0\u9650\u5c0f\uff0c\u518d\u52a0\u8d77\u6765\uff0c\u5c31\u662f\u201c<strong>\u5b9a\u79ef\u5206<\/strong>\u201d\u3002\u5b9a\u79ef\u5206\u6c42\u7684\u662f\u201c\u66f2\u7ebf\u4e0b\u9762\u79ef\u201d\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p3.toutiaoimg.com\/large\/pgc-image\/62c67dad3e874a90a0d27930d89272ae\" alt=\"\" style=\"width:424px;height:124px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u79ef\u5206\u5c31\u662f\u6c42\u548c<\/strong>\uff0c\u79ef\u5206\u53f7\u5c31\u662f\u4e00\u4e2a\u62c9\u957f\u7684 S (<strong>sum<\/strong>)\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%AE%9A%E7%A7%AF%E5%88%86%EF%BC%9A%E5%8E%9F%E5%9B%A0%E5%8E%86%E7%BB%8F%E6%97%B6%E9%97%B4%E4%BA%A7%E7%94%9F%E7%9A%84%E4%BD%9C%E7%94%A8\"><\/span>\u5b9a\u79ef\u5206\uff1a\u539f\u56e0\u5386\u7ecf\u65f6\u95f4\u4ea7\u751f\u7684\u4f5c\u7528<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ece\u5b9a\u79ef\u5206\u7684\u57fa\u672c\u5b9a\u7406\u5c31\u53ef\u89c1\u7aef\u502a\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p3.toutiaoimg.com\/large\/pgc-image\/e2b9eb4c8a8348c8a0cff6c1ad157a33\" alt=\"\" style=\"width:356px;height:115px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b9a\u79ef\u5206\uff0c\u662f\u5728\u8ba1\u7b97\u201c<strong>\u5f71\u54cd<\/strong>\u201d\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5b9a\u79ef\u5206 \u662f\u201c\u539f\u56e0\u201d <em>f<\/em>(<em>x<\/em>) \u7ecf\u8fc7\u4e00\u6bb5\u8fc7\u7a0b\uff08\u4ecea\u5230b\uff09\u6240\u9020\u6210\u7684\u7ed3\u679c\u6539\u53d8(\u5f71\u54cd)\u3002<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p26.toutiaoimg.com\/large\/pgc-image\/08bad4eebca64b628ade4debc8d82ca9\" alt=\"\" style=\"width:391px;height:177px\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%AE%9A%E7%A7%AF%E5%88%86%E7%9A%84MATLAB%E6%B1%82%E8%A7%A3\"><\/span>\u5b9a\u79ef\u5206\u7684MATLAB\u6c42\u89e3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>F=int(fun,x,a,b) % \u6c42\u51fd\u6570fun\u5173\u4e8ex\u7684\u4ecea\u5230b\u7684\u4e0d\u5b9a\u79ef\u5206<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u662f<strong>\u65e0\u7a77\u79ef\u5206<\/strong>\u5462\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5373a\u6216b\u4e2d\u81f3\u5c11\u4e00\u4e2a\u662f\u65e0\u7a77\u91cf\u7684\u79ef\u5206\uff0c\u4e66\u672c\u4e0a\u79f0\u4e3a\u5e7f\u4e49\u79ef\u5206\u6216\u53cd\u5e38\u79ef\u5206\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u90a3\u5c31\u76f4\u63a5\u628aa\u6216b\u6362\u6210 inf\uff0c\u5c31OK\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-text-align-center\"><span class=\"ez-toc-section\" id=\"%E5%82%85%E9%87%8C%E5%8F%B6%E5%B1%95%E5%BC%80%EF%BC%9A%E9%A2%91%E5%9F%9F%E4%B8%8B%E7%9A%84%E8%B0%90%E6%B3%A2%E4%BB%BF%E7%9C%9F%E7%B3%BB%E7%BB%9F\"><\/span>\u5085\u91cc\u53f6\u5c55\u5f00\uff1a\u9891\u57df\u4e0b\u7684\u8c10\u6ce2\u4eff\u771f\u7cfb\u7edf<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b63\u5f26\u6ce2\u51fd\u6570\u4e0e\u4f59\u5f26\u6ce2\u51fd\u6570\uff0c\u7edf\u4e00\u79f0\u4e3a\uff1a<strong>\u8c10\u6ce2\u51fd\u6570<\/strong>\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p9.toutiaoimg.com\/large\/pgc-image\/66ff50dc4697432d8a7e02732db54465\" alt=\"\" style=\"width:336px;height:202px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u660e\u660e\u5c31\u662f\u540c\u4e00\u4e2a\u51fd\u6570\uff0c\u53ea\u4e0d\u8fc7\u201c\u76f8\u4f4d\u201d\u4e0d\u540c\u800c\u5df2<\/strong>\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u8c10\uff0c\u548c\u4e5f\u3002<\/p>\n<cite>\u2014\u2014\u300a\u5c14\u96c5\u300b<\/cite><\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E8%B0%90%E6%B3%A2%EF%BC%9A%E8%87%AA%E7%84%B6%E4%B9%8B%E9%81%93\"><\/span>\u8c10\u6ce2\uff1a\u81ea\u7136\u4e4b\u9053<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e16\u754c\u7531\u6ce2\u7ec4\u6210\uff1a\u58f0\u6ce2\u3001\u5149\u6ce2\u3001\u7535\u78c1\u6ce2\u3001\u5730\u9707\u6ce2\u3001\u5e94\u529b\u6ce2\u3001\u5f15\u529b\u6ce2 &#8230;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/i2.100024.xyz\/2023\/12\/10\/fj798n.webp\" alt=\"\" style=\"width:864px;height:auto\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u8c10\u6ce2\u662f\u6240\u6709\u6ce2\u4e2d\uff0c\u6700\u201c\u548c\u8c10\u201d\u7684\uff0c\u5b83\u6709\u4e00\u4e2a\u91cd\u5927\u7684\u7279\u6027\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8c10\u6ce2\u7684\u5bfc\u51fd\u6570\u8fd8\u662f\u8c10\u6ce2\uff0c\u8c10\u6ce2\u7684\u539f\u51fd\u6570\u8fd8\u662f\u8c10\u6ce2\uff01<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bd4\u5982\uff0csin'(<em>x<\/em>) = cos(<em>x<\/em>) = sin(<em>x<\/em>+pi\/2)\uff0c\u610f\u601d\u662f\uff0c\u6b63\u5f26\u7684\u5bfc\u51fd\u6570\u8fd8\u662f\u6b63\u5f26\uff0c\u53ea\u4e0d\u8fc7\u5bfc\u51fd\u6570\u8981\u65e9\u4e86 \u03c0\/2\uff081\/4\u4e2a\u5468\u671f\uff09\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E8%B0%90%E6%B3%A2%EF%BC%9A%E5%91%BD%E8%BF%90%E5%90%AF%E8%BF%AA\"><\/span>\u8c10\u6ce2\uff1a\u547d\u8fd0\u542f\u8fea<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e2d\u56fd\u4eba\u5728\u57fa\u56e0\u91cc\u5df2\u7ecf\u523b\u5165\u4e86\u5bf9\u4e8e\u8c10\u6ce2\u7684\u7406\u89e3\uff0c\u300a\u6613 \u00b7 \u4e7e\u300b\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p3.toutiaoimg.com\/large\/pgc-image\/2ac5762b41a74bd9a8ca7d4656915ca9\" alt=\"\" style=\"width:412px;height:280px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u4eba\u5728\u9006\u5883\u4e2d\u4e3a\u4ec0\u4e48\u80fd\u575a\u6301\u4f4f\uff1f\u5c31\u662f\u56e0\u4e3a\u4ed6\u770b\u5230\u4e86\u547d\u8fd0\u7684\u5468\u671f\u3002<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7269\u6781\u5fc5\u53cd\uff0c\u5426\u6781\u6cf0\u6765\uff0c\u53cd\u8005\u9053\u4e4b\u52a8\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u7978\u516e \u798f\u4e4b\u6240\u501a \u798f\u516e \u7978\u4e4b\u6240\u4f0f<\/p>\n<cite>\u2014\u2014\u300a\u9053\u5fb7\u7ecf\u300b<\/cite><\/blockquote>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/i2.100024.xyz\/2023\/12\/10\/w4ekqn.webp\" alt=\"\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%82%85%E9%87%8C%E5%8F%B6%E5%88%86%E8%A7%A3%EF%BC%9A%E4%BB%BB%E6%84%8F%E6%B3%A2%E9%83%BD%E7%94%B1%E8%B0%90%E6%B3%A2%E7%BB%84%E6%88%90\"><\/span><strong>\u5085\u91cc\u53f6\u5206\u89e3<\/strong>\uff1a\u4efb\u610f\u6ce2\u90fd\u7531\u8c10\u6ce2\u7ec4\u6210<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u201c\u6ce2\u201d\u7684\u672c\u8d28\u5373\u662f\u201c<strong>\u5468\u671f\u51fd\u6570<\/strong>\u201d\uff0c\u5468\u671f\u7684\u5012\u6570\u5373\u4e3a\u9891\u7387\uff0c\u4efb\u610f\u4e00\u79cd\u6ce2\uff0c\u662f\u5426\u80fd\u5206\u89e3\u6210\u4e0d\u540c\u9891\u7387\u7684\u8c10\u6ce2\u7684\u53e0\u52a0\u5462\uff1f<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(f\\left( x \\right) =\\sum_{n=0}^{\\infty}{\\left( a_n\\cos nx+b_n\\sin nx \\right)}\\)<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(a_n=\\frac{1}{\\pi}\\int_{-\\pi}^{\\pi}{f\\left( x \\right) \\cos nx\\mathrm{d}x}\\quad b_n=\\frac{1}{\\pi}\\int_{-\\pi}^{\\pi}{f\\left( x \\right) \\sin nx\\mathrm{d}x}\\)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%82%85%E9%87%8C%E5%8F%B6%E5%88%86%E8%A7%A3%EF%BC%9A%E9%A2%91%E5%9F%9F%E4%B8%8A%E7%9A%84%E8%B0%90%E6%B3%A2%E5%8F%A0%E5%8A%A0%E4%BB%BF%E7%9C%9F%E7%B3%BB%E7%BB%9F\"><\/span><strong>\u5085\u91cc\u53f6\u5206\u89e3<\/strong>\uff1a\u9891\u57df\u4e0a\u7684\u8c10\u6ce2\u53e0\u52a0\u4eff\u771f\u7cfb\u7edf<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bd4\u5982\uff0c\u65b9\u6ce2\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p26.toutiaoimg.com\/large\/pgc-image\/9e67e6d7d4804b7596719ec86845fb26\" alt=\"\" style=\"width:377px;height:135px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u53e0\u52a0\u9879\u8d8a\u591a\uff0c\u8d8a\u63a5\u8fd1\u539f\u59cb\u65b9\u6ce2\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/p3.toutiaoimg.com\/large\/pgc-image\/31fafaa8265449bb9736afaccf839511\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u5b9e\uff0c\u8fd9<strong>\u8ddf\u6cf0\u52d2\u5c55\u5f00\u662f\u4e00\u81f4\u7684\uff0c\u8d8a\u5230\u540e\u9762\u7684\u9879\uff0c\u8d77\u4f5c\u7528\u5c31\u8d8a\u5c0f<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u53f3\u8fb9\u90a3\u4e00\u5217\u53eb\u4f5c\uff1a<strong>\u9891\u8c31<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u628a\u65f6\u57df\u7684\u4fe1\u606f\uff0c\u53d8\u6210\u9891\u57df\u4fe1\u606f\u4e86\u3002\u56fe\u4e2d\u8868\u793a\u4e86\u6bcf\u4e00\u8c10\u6ce2\u9879\u7684\u9891\u7387\uff08\u6a2a\u8f74\uff09\u548c\u5e45\u503c\uff08\u7eb5\u8f74\uff09\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" src=\"https:\/\/i2.100024.xyz\/2023\/12\/10\/w5iovz.gif\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5085\u91cc\u53f6\u5c55\u5f00\uff0c\u662f\u901a\u8fc7\u4e0d\u540c\u9891\u7387\u8c10\u6ce2\u53e0\u52a0\u7684\u65b9\u5f0f\uff0c\u5bf9\u4efb\u610f\u5468\u671f\u51fd\u6570\u8fdb\u884c\u4eff\u771f\u7684\u7cfb\u7edf\u3002<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E6%8A%8A%E6%B3%A2%E6%8C%AF%E5%8A%A8%E5%90%91%E9%A2%91%E5%9F%9F%E5%88%86%E8%A7%A3%E5%90%8E%E7%9A%84%E5%BA%94%E7%94%A8\"><\/span>\u628a\u6ce2(\u632f\u52a8)\u5411\u9891\u57df\u5206\u89e3\u540e\u7684\u5e94\u7528<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b1 \u6bd4\u5982\u4e00\u53f0\u673a\u5668\uff0c\u53d1\u751f\u4e86\u4e0d\u597d\u7684\u632f\u52a8\uff0c\u90a3\u5c31\u628a\u632f\u52a8\u4fe1\u53f7\u5085\u91cc\u53f6\u5206\u89e3\u51fa\u6765\uff0c\u627e\u5230\u51fa\u95ee\u9898\u7684\u9891\u7387\uff0c\u7136\u540e\u518d\u67e5\u54ea\u4e2a\u632f\u52a8\u6e90\u662f\u8fd9\u4e2a\u9891\u7387\u5440\uff0c\u5c31\u627e\u5230\u95ee\u9898\u6240\u5728\u4e86\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b2 \u6709\u9650\u5143\u53ef\u4ee5\u8ba1\u7b97\u96f6\u4ef6\u7684\u5404\u9636\u6a21\u6001\u7684\u9891\u7387\u632f\u578b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img decoding=\"async\" src=\"http:\/\/p26.toutiaoimg.com\/large\/pgc-image\/edcf21b6195e445fa7ba46eeedfdb252\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b3 \u4e00\u4e2a\u4f4e\u9891\u4fe1\u53f7\uff0c\u63ba\u5165\u4e86\u4e00\u4e9b\u9ad8\u9891\u7684\u566a\u97f3\uff0c\u90a3\u4e48\u53ef\u4ee5\u91c7\u7528\u5085\u91cc\u53f6\u5206\u89e3\u7684\u65b9\u6cd5\uff0c\u5206\u89e3\u540e\u76f4\u63a5\u5c06\u9ad8\u9891\u7684\u90e8\u5206\u820d\u53bb\uff0c\u8fd9\u5c31\u53eb<strong>\u4f4e\u901a\u6ee4\u6ce2<\/strong>\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%82%85%E9%87%8C%E5%8F%B6%E5%B1%95%E5%BC%80%E7%9A%84MATLAB%E6%BA%90%E7%A0%81\"><\/span>\u5085\u91cc\u53f6\u5c55\u5f00\u7684MATLAB\u6e90\u7801<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728MATLAB\u4e2d\uff0c\u6ca1\u6709\u5085\u91cc\u53f6\u5c55\u5f00\u7684\u76f4\u63a5\u51fd\u6570\uff0c\u4f46\u662f\u6211\u4eec\u53ef\u4ee5\u4f9d\u7167\u516c\u5f0f\u5199\u4e00\u4e2a\u51fa\u6765:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>&#091;A,B,F] = fseries(f,x,p,a,b) % \u8c03\u7528\u683c\u5f0f\n% \u4ee5\u4e0b\u4e3a\u51fd\u6570\u4f53\nfunction &#091;A,B,F] = fseries(f,x,p,a,b)\nif nargin==3, a=-pi; b=pi; end\nL=(b-a)\/2;\nif a+b, f=subs(f,x,x+L+a);end\nA=int(f,x,-L,L)\/L; B=&#091;]; F=A\/2;\nfor n=1:p\n  an=int(f*cos(n*pi*x\/L),x,-L,L)\/L;\n  bn=int(f*sin(n*pi*x\/L),x,-L,L)\/L;\n  A=&#091;A,an]; B=&#091;B,bn];\n  F=F+an*cos(n*pi*x\/L)+bn*sin(n*pi*x\/L);\nend\nif a+b, F=subs(F,x,x-L-a);end<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E4%B8%A4%E7%A7%8D%E4%BB%BF%E7%9C%9F%E7%B3%BB%E7%BB%9F%EF%BC%9A%E6%B3%B0%E5%8B%92%E4%B8%8E%E5%82%85%E9%87%8C%E5%8F%B6\"><\/span>\u4e24\u79cd\u4eff\u771f\u7cfb\u7edf\uff1a\u6cf0\u52d2\u4e0e\u5085\u91cc\u53f6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e24\u8005\u90fd\u662f\u4eff\u771f\u7cfb\u7edf\uff0c\u90fd\u662f\u9879\u6570\u8d8a\u591a\uff0c\u8bef\u5dee\u8d8a\u5c0f\uff0c\u4f46\u662f\u4e5f\u6709\u533a\u522b\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u6cf0\u52d2<\/strong> <strong>\u5206\u6790\u8fd0\u52a8\u7684\u56e0\u679c<\/strong>\uff1a\u7740\u773c\u4e8e\u4ece\u4e00\u70b9 <em>x<\/em><sub>0<\/sub> \u5c55\u5f00\uff0c\u79bb\u8be5\u70b9\u8d8a\u8fdc\u8bef\u5dee\u8d8a\u5927\uff0c\u7528\u591a\u9879\u5f0f\u63ed\u793a\u8fd0\u52a8\u7684\u91cf\u5316\u89c4\u5f8b\uff1b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5085\u91cc\u53f6<\/strong> <strong>\u5206\u6790\u9891\u7387\u7684\u6784\u6210<\/strong>\uff1a\u7740\u773c\u4e8e\u5168\u5c40\u5468\u671f\u6027\uff0c\u4ece\u9891\u57df\u7684\u89d2\u5ea6<strong>\u627e\u5230\u539f\u51fd\u6570\u7684\u9ad8\u7ef4\u7279\u5f81<\/strong>\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-text-align-center\"><span class=\"ez-toc-section\" id=\"%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E5%B0%B1%E6%98%AF%E5%9B%A0%E6%9E%9C%E5%85%B3%E7%B3%BB\"><\/span>\u5fae\u5206\u65b9\u7a0b\u5c31\u662f\u56e0\u679c\u5173\u7cfb<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5fae\u5206\u65b9\u7a0b<\/strong>\uff08<strong>Differential equation<\/strong>\uff0c<strong>DE<\/strong>\uff09\u8868\u793a\u7684\u662f\u539f\u51fd\u6570(\u679c)\u4e0e\u5bfc\u51fd\u6570(\u56e0)\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bd4\u5982\uff0c<strong><em>y<\/em>&#8216; = 1<\/strong>\uff0c\u5c31\u662f\u6700\u7b80\u5355\u7684\u5fae\u5206\u65b9\u7a0b\u4e86\u3002\u662f<strong>\u4e00\u9636\u5fae\u5206\u65b9\u7a0b<\/strong>\uff08\u6700\u9ad8\u9636\u5bfc\u6570\u7684\u9636\u6570\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u89e3\u662f\uff1a<em>y<\/em> = <em>x <\/em>+ C<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u518d\u52a0\u4e00\u4e2a\u6761\u4ef6\uff08\u521d\u59cb\u6761\u4ef6\uff09\uff1a<em>y<\/em>(0) = 0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u6837\uff0c\u89e3\u5c31\u53ea\u80fd\u662f <em>y <\/em>= <em>x<\/em> \u4e86\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%EF%BC%9A%E7%8E%B0%E4%BB%A3%E7%A7%91%E5%AD%A6%E7%9A%84%E5%9F%BA%E7%9F%B3\"><\/span>\u5fae\u5206\u65b9\u7a0b\uff1a\u73b0\u4ee3\u79d1\u5b66\u7684\u57fa\u77f3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5927\u81f4\u4e0a\u53ef\u4ee5\u8fd9\u4e48\u8bf4\uff0c\u4e00\u4e2a\u5b66\u79d1\u662f\u4e0d\u662f\u79d1\u5b66\uff0c\u5c31\u662f\u770b\u6709\u6ca1\u6709\u5fae\u5206\u65b9\u7a0b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56e0\u4e3a\uff0c\u7814\u7a76\u4e00\u4e2a\u91cf\u7684\u5bfc\u6570\u7684\u89c4\u5f8b\uff0c\u624d\u6709\u53ef\u80fd\u4ece\u6839\u672c\u4e0a\u7406\u89e3\u8fd9\u4e2a\u91cf\u7684\u89c4\u5f8b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5fae\u5206\u65b9\u7a0b\uff0c\u5c55\u793a\u7684\u5c31\u662f\u539f\u51fd\u6570(\u679c)\u4e0e\u5bfc\u51fd\u6570(\u56e0)\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E8%A7%A3%E6%9E%90%E8%A7%A3\"><\/span>\u5fae\u5206\u65b9\u7a0b\u89e3\u6790\u89e3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8b\u5b9e\u4e0a\uff0c\u5fae\u5206\u65b9\u7a0b\u4e0d\u592a\u597d\u89e3\uff0c\u6559\u6750\u4e0a\u4e00\u822c\u4e5f\u5c31<strong>\u5217\u4e3e\u4e86\u51e0\u79cd\u5f88\u7279\u6b8a\u7684\u5fae\u5206\u65b9\u7a0b\u7684\u89e3\u6cd5<\/strong>\uff0c\u4f46\u5176\u5b9e\u771f\u5230\u4e86\u4f7f\u7528\u5fae\u5206\u65b9\u7a0b\u7684\u65f6\u5019\uff0c\u5f80\u5f80\u4e0d\u5728\u8fd9\u51e0\u79cd\u5217\u4e3e\u7684\u8303\u56f4\u4e4b\u5185\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">&#8220;\u541b\u5b50\u751f\u975e\u5f02\u4e5f\uff0c\u5584\u5047\u4e8e\u7269\u4e5f&#8221;<\/p>\n<cite>\u2014\u2014\u300a\u529d\u5b66\u300b<\/cite><\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">MATLAB\u6c42\u89e3\u5fae\u5206\u65b9\u7a0b\uff0c\u4e00\u822c\u7528 dsolve \u51fd\u6570\u5c31\u80fd\u641e\u5b9a\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b1\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" width=\"304\" height=\"112\" src=\"http:\/\/8.130.122.109\/wp-content\/uploads\/2023\/08\/image-15.png\" alt=\"\" class=\"wp-image-469\" style=\"width:208px;height:77px\" srcset=\"http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-15.png 304w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-15-300x111.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>syms y(t) a % \u7b26\u53f7\neqn = diff(y,t) == a*y % \u51fd\u6570\ncond = y(0) == 5; % \u6761\u4ef6\nySol(t) = dsolve(eqn,cond) % \u89e3<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" width=\"317\" height=\"90\" src=\"http:\/\/8.130.122.109\/wp-content\/uploads\/2023\/08\/image-16.png\" alt=\"\" class=\"wp-image-470\" style=\"width:227px;height:64px\" srcset=\"http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-16.png 317w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-16-300x85.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b2\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" width=\"305\" height=\"135\" src=\"http:\/\/8.130.122.109\/wp-content\/uploads\/2023\/08\/image-17.png\" alt=\"\" class=\"wp-image-471\" style=\"width:177px;height:78px\" srcset=\"http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-17.png 305w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-17-300x133.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>syms y(t) a \neqn = diff(y,t,2) == a*y\nySol(t) = dsolve(eqn)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" width=\"596\" height=\"108\" src=\"http:\/\/8.130.122.109\/wp-content\/uploads\/2023\/08\/image-18.png\" alt=\"\" class=\"wp-image-472\" style=\"width:377px;height:68px\" srcset=\"http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-18.png 596w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-18-300x54.png 300w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E6%95%B0%E5%80%BC%E8%A7%A3\"><\/span>\u5fae\u5206\u65b9\u7a0b\u6570\u503c\u89e3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u5b9e\uff0c<strong>\u8bb8\u591a\u5fae\u5206\u65b9\u7a0b\u6839\u672c\u6c42\u4e0d\u51fa\u89e3\u6790\u89e3\uff0c\u53ea\u80fd\u6c42\u51fa\u6570\u503c\u89e3\u3002<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5565\u53eb\u6570\u503c\u89e3\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5c31\u662f\u8bf4\uff0c<strong>\u867d\u7136\u6c42\u4e0d\u51fa\u51fd\u6570\u7684\u8868\u8fbe\u5f0f\uff0c\u4f46\u662f\u6211\u80fd\u77e5\u9053\u51fd\u6570\u5728\u5404\u5904\u7684\u503c\uff0c\u8fd9\u4e2a\u503c\u4e0d\u662f\u7edd\u5bf9\u51c6\u786e\uff0c\u4f46\u662f\u5728\u4e00\u5b9a\u7684\u7cbe\u5ea6\u8303\u56f4\u5185<\/strong>\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">MATLAB\u4e2d\u6700\u5e38\u7528\u7684\u89e3\u5e38\u5fae\u5206\u65b9\u7a0b(ODE)\u7684\u51fd\u6570\u4e3a ode45\uff08\u56db\u9636\u4e94\u7ea7\u53d8\u6b65\u957f\u7b97\u6cd5\uff09\u2014\u2014<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f8b\uff0c\u89e3\u65b9\u7a0b\uff1a<em>y <\/em>&#8216; = 2<em>t<\/em><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>tspan = &#091;0 5]; % \u6c42\u89e3\u8303\u56f4\ny0 = 0; % \u521d\u503c\u6761\u4ef6\n&#091;t,y] = ode45(@(t,y) 2*t, tspan, y0); % \u65b9\u7a0b\u4ee5\u51fd\u6570\u53e5\u67c4\u5f62\u5f0f\u6765\u5b9a\u4e49\nplot(t,y,'-o')<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" src=\"http:\/\/p3.toutiaoimg.com\/large\/pgc-image\/7e82b06088e54cf59e84b91a940e57c5\" alt=\"\" style=\"width:412px;height:322px\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u6ca1\u6709\u8868\u8fbe\u5f0f\uff0c\u53ea\u6709\u7531\u70b9\u7ec4\u6210\u7684\u201c\u6570\u503c\u89e3\u201d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u975e\u5f97\u5199\u6210\u8868\u8fbe\u5f0f\u7684\u5f62\u5f0f\uff0c\u4e5f\u597d\u529e\uff0c<strong>\u62df\u5408<\/strong>\u56de\u53bb\u5457\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E9%80%A0%E5%B0%B1%E4%BA%86%E6%9C%89%E9%99%90%E5%85%83%E6%B3%95\"><\/span>\u5fae\u5206\u65b9\u7a0b\u9020\u5c31\u4e86\u6709\u9650\u5143\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5927\u540d\u9f0e\u9f0e\u7684\u201c\u6709\u9650\u5143\u6cd5\u201d\uff08FEM\uff0cFinite Element Method\uff09\uff0c\u5176\u5b9e\u53ea\u662f\u4e00\u79cd\u6c42\u89e3\u5fae\u5206\u65b9\u7a0b\u7684\u6570\u503c\u89e3\u6cd5\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" width=\"350\" height=\"274\" src=\"http:\/\/8.130.122.109\/wp-content\/uploads\/2023\/08\/image-19.png\" alt=\"\" class=\"wp-image-477\" srcset=\"http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-19.png 350w, http:\/\/wangheran.com\/wp-content\/uploads\/2023\/08\/image-19-300x235.png 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u8c13\u201c\u4eff\u771f\u201d\uff0c\u5c31\u662f\u5bf9\u6a21\u578b\u7684\u8ba1\u7b97\u3002FEM\u7684\u5143\u6a21\u578b\uff0c\u5c31\u662f\u5fae\u5206\u65b9\u7a0b\uff0c\u4e5f\u5c31\u662f\u4e8b\u7269\u4e4b\u95f4\u7684\u56e0\u679c\u5173\u7cfb\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-text-align-center\"><span class=\"ez-toc-section\" id=\"%E6%80%9D%E6%83%B3%E6%80%BB%E7%BB%93\"><\/span>\u601d\u60f3\u603b\u7ed3<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">\u201c\u65e0\u7a77\u201d\u662f\u5fae\u79ef\u5206\u7684\u57fa\u7840\u6838\u5fc3\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u201c\u5bfc\u6570\u201d\u662f\u51fd\u6570\u7684\u539f\u56e0\uff0c\u51fd\u6570\u662f\u201c\u5bfc\u6570\u201d\u7684\u7ed3\u679c\u3002<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6cf0\u52d2\u5c55\u5f00\uff1a\u591a\u9879\u5f0f\u4eff\u771f\u7cfb\u7edf\uff0c\u63d0\u9192\u6211\u4eec\u672c\u672b\/\u4e3b\u6b21\u4e4b\u5206\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5085\u91cc\u53f6\u5c55\u5f00\uff1a\u9891\u57df\u4e0b\u7684\u8c10\u6ce2\u4eff\u771f\u7cfb\u7edf\uff0c\u63d0\u9192\u6211\u4eec\u5728\u9891\u57df\u4e2d\u5bfb\u627e\u672c\u8d28\u7279\u5f81\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5fae\u5206\u65b9\u7a0b\u5c31\u662f\u56e0\u679c\u5173\u7cfb<\/strong>\uff0c\u662f\u73b0\u4ee3\u79d1\u5b66\u7684\u57fa\u7840\u6838\u5fc3\uff0c\u4e5f\u9020\u5c31\u4e86\u6709\u9650\u5143\u6cd5\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u201c\u4f60\u6700\u597d\u5b66\u5b66\u5fae\u79ef\u5206\uff0c\u5b83\u662f\u4e0a\u5e1d\u7684\u8bed\u8a00\u3002\u201d&nbsp;<\/p>\n<cite>\u2014\u2014 \u8d39\u66fc<\/cite><\/blockquote>\n\n\n\n<hr 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