{"id":14,"date":"2016-03-28T23:29:12","date_gmt":"2016-03-28T15:29:12","guid":{"rendered":"http:\/\/www.91tfboys.com\/?p=14"},"modified":"2017-01-03T21:28:04","modified_gmt":"2017-01-03T13:28:04","slug":"thoughts-on-advanced-mathematics-1","status":"publish","type":"post","link":"https:\/\/www.91tfboys.com\/?p=14","title":{"rendered":"Thoughts on Advanced Mathematics (1)"},"content":{"rendered":"<p>\u5b66\u5f97\u8d8a\u591a\uff0c\u4fbf\u66f4\u80fd\u7406\u89e3\u66f4\u6df1\u5c42\u7684\u542b\u4e49\u3002\u539f\u6765\u4e8b\u5148\u770b\u4f3c\u72ec\u7acb\u7684\u6570\u5b66\u516c\u5f0f\u95f4\u90fd\u5b58\u5728\u7740\u5173\u8054\u3002<\/p>\n<p>\u4eca\u5929\u4e5f\u662f\u5076\u5c14\u53d1\u73b0\u7684\uff0c\u5bfc\u6570\u7684\u5b9a\u4e49\u7adf\u7136\u4e5f\u53ef\u4ee5\u770b\u505a\u662f\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406\u7684\u7279\u6b8a\u60c5\u51b5\uff0c\u6216\u8005\u8bf4\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406\u662f\u5bfc\u6570\u5b9a\u4e49\u7684\u6269\u5c55\u3002<!--more--><\/p>\n<p>\u7531\u5bfc\u6570\u7684\u5b9a\u4e49\u53ef\u77e5\uff0c<em>f&#8217;<\/em>(<em>x<\/em>)=lim\u252c(<em>x<\/em>\u2192<em>\u0394x<\/em>)\u2061[(<em>f<\/em>(<em>x<\/em>+<em>\u0394x<\/em>)-<em>f<\/em>(<em>x<\/em>))\/<em>\u0394x<\/em>]\uff0c\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406\u7684\u516c\u5f0f\u53ef\u4ee5\u5199\u6210<em>f<\/em>(<em>a<\/em>)-<em>f<\/em>(<em>b<\/em>)= <em>f&#8217;<\/em>(<em>\u03be<\/em>)(<em>a-b<\/em>)\u7684\u5f62\u5f0f\u3002\u5f53\u6211\u4eec\u628a\u533a\u95f4\u53d6\u4e3a[<em>x<\/em>, <em>x+<em>\u0394x<\/em><\/em>]\u65f6\uff0c\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406\u4e5f\u5c31\u53d8\u6210\u4e86<em>f<\/em>(<em>x<\/em>+<em>\u0394x<\/em>)-<em>f<\/em>(<em>x<\/em>) = <em>\u0394x<\/em>\u00b7<em>f&#8217;<\/em>(<em>x<\/em><sub>0<\/sub>)\uff0c\u5176\u4e2d<em>x<\/em><sub>0<\/sub>\u220a(<em>x<\/em>, <em>x+<em>\u0394x<\/em><\/em>)\u3002\u4f46\u5728\u5bfc\u6570\u5b9a\u4e49\u91cc\uff0c<em>x<\/em>\u662f\u8d8b\u8fd1\u4e8e<em>\u0394x<\/em>\u7684\uff0c\u6216\u8005\u8bf4<em>\u0394x<\/em>\u662f\u8d8b\u8fd1\u4e8e0\u7684\uff0c\u6b64\u65f6<em>x<\/em><sub>0<\/sub>\u53ef\u4ee5\u770b\u505a\u4e0e<em>x<\/em>\u6216<em>x<\/em>+<em>\u0394x<\/em>\u76f8\u7b49\uff0c\u6216<em>x<\/em><sub>0<\/sub>=<em>x<\/em><sup>+<\/sup>\uff0c<em>x<\/em><sub>0<\/sub>=(<em>x<\/em>+<em>\u0394x<\/em>)<sup>&#8211;<\/sup>\u3002\u5f53\u7136<em>x<\/em><sub>0<\/sub>\u8fd8\u662f\u5728<em>x<\/em>\u548c<em>x<\/em>+<em>\u0394x<\/em>\u4e4b\u95f4\u7684\u3002\u5982\u679c\u6211\u4eec\u6269\u5927\u8fd9\u4e2a\u533a\u95f4\u8303\u56f4\uff0c\u4ee4<em>x<\/em>=<em>a<\/em>\uff0c<em>x<\/em>+<em>\u0394x<\/em>=<em>b<\/em>\uff0c\u8fd9\u65f6\u8fd9\u4e2a\u516c\u5f0f\u5c31\u6210\u4e86\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406\u7684\u5f62\u5f0f\u4e86\u3002<\/p>\n<p>\u8fd8\u6709\u79ef\u5206\u4e2d\u503c\u5b9a\u7406\u548c\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406\uff0c\u8fd9\u4e8c\u8005\u4e5f\u662f\u51e0\u4e4e\u76f8\u540c\u7684\u3002\u7531\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406\u53ef\u77e5\uff0c<em>f<\/em>(<em>x<\/em>)\u5728[<em>a<\/em>,<em>b<\/em>]\u4e0a\u662f\u53ef\u5bfc\u7684\uff0c\u4e14\u95ed\u533a\u95f4\u8fde\u7eed\uff0c\u6709\u754c\uff0c\u56e0\u6b64<em>f&#8217;<\/em>(<em>x<\/em>)\u5b58\u5728\uff0c\u4e14<em>f<\/em>(<em>x<\/em>)\u7684\u5b9a\u79ef\u5206\u5b58\u5728\u3002\u5982\u679c\u6211\u4eec\u628a<em>f<\/em>(<em>a<\/em>)-<em>f<\/em>(<em>b<\/em>)\u5199\u6210<em>\u222ba<\/em>^<em>b<\/em>[<em>f&#8217;<\/em>(<em>x<\/em>)]\u7684\u5f62\u5f0f\uff0c\u5219\u53ef\u4ee5\u8ba4\u4e3a\u8fd9\u4e24\u4e2a\u5b9a\u7406\u662f\u76f8\u7b49\u7684\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u6628\u5929\u8fd8\u542c\u4e86\u4e00\u4e2a\u89c2\u70b9\uff0c\u5373\u4ece\u67ef\u897f\u4e2d\u503c\u5b9a\u7406\u5230\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406\u518d\u5230\u7f57\u5c14\u5b9a\u7406\uff0c\u8fd9\u662f\u4e00\u5c42\u5c42\u7684\u7279\u6b8a\u5316\u3002\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406\u662f\u67ef\u897f\u4e2d\u503c\u5b9a\u7406\u4e2d\u5f53<em>g<\/em>(<em>x<\/em>)=<em>x<\/em>\u7684\u60c5\u51b5\uff0c\u7f57\u5c14\u5b9a\u7406\u662f\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406\u4e2d<em>f<\/em>(<em>a<\/em>)=<em>f<\/em>(<em>b<\/em>)\u7684\u60c5\u51b5\u3002\u73b0\u5728\u60f3\u60f3\u786e\u5b9e\u662f\u8fd9\u6837\u7684\u3002\u5b66\u4e60\u65f6\u6211\u4eec\u662f\u4ece\u6700\u7279\u6b8a\u7684\u60c5\u51b5\u2014\u2014\u7f57\u5c14\u5b9a\u7406\u5f00\u59cb\u7684\uff0c\u968f\u540e\u968f\u7740\u6df1\u5165\uff0c\u6211\u4eec\u53ef\u4ee5\u6e10\u6e10\u4e86\u89e3\u7279\u6b8a\u60c5\u51b5\u4e86\uff0c\u4e8e\u662f\u63a5\u89e6\u4e86\u62c9\u683c\u6717\u65e5\u4e2d\u503c\u5b9a\u7406\u548c\u67ef\u897f\u4e2d\u503c\u5b9a\u7406\u3002\u8fd8\u6709\u5bfc\u6570\u5fae\u5206\u4e0e\u79ef\u5206\u4e00\u6837\uff0c\u90fd\u662f\u8fd9\u79cd\u5173\u7cfb\u3002\u540c\u65f6\u6570\u5b66\u8fd8\u6709\u4e00\u4e2a\u8fde\u8d2f\u6027\uff0c\u53ef\u80fd\u524d\u9762\u4e00\u4e2a\u4e0d\u8d77\u773c\u7684\u77e5\u8bc6\uff0c\u6216\u8005\u81ea\u5df1\u603b\u7ed3\u7684\u4e00\u6761\u5c0f\u89c4\u5f8b\uff0c\u5728\u540e\u9762\u5c31\u80fd\u8ba9\u4f60\u604d\u7136\u5927\u609f\u3002\u603b\u7ed3\u4e0e\u7ec3\u4e60\uff0c\u8fd8\u6709\u8054\u7cfb\uff0c\u8fd9\u5927\u6982\u662f\u5b66\u4e60\u6570\u5b66\u7684\u5fc5\u5907\u5427\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5b66\u5f97\u8d8a\u591a\uff0c\u4fbf\u66f4\u80fd\u7406\u89e3\u66f4\u6df1\u5c42\u7684\u542b\u4e49\u3002\u539f\u6765\u4e8b\u5148\u770b\u4f3c\u72ec\u7acb\u7684\u6570\u5b66\u516c\u5f0f\u95f4\u90fd\u5b58\u5728\u7740\u5173\u8054\u3002 \u4eca\u5929\u4e5f\u662f\u5076\u5c14\u53d1\u73b0\u7684\uff0c\u5bfc\u6570\u7684\u5b9a\u4e49\u7adf [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":246,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-14","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathing"],"_links":{"self":[{"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/posts\/14","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14"}],"version-history":[{"count":1,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/posts\/14\/revisions"}],"predecessor-version":[{"id":15,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/posts\/14\/revisions\/15"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=\/wp\/v2\/media\/246"}],"wp:attachment":[{"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.91tfboys.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}