{"id":18959,"date":"2011-01-18T16:57:28","date_gmt":"2011-01-18T08:57:28","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=18959"},"modified":"2021-10-06T16:29:02","modified_gmt":"2021-10-06T08:29:02","slug":"%e5%be%ae%e7%a9%8d%e5%88%86%e5%88%9d%e9%9a%8e%ef%bc%8d%e6%ad%b7%e5%8f%b2%e7%99%bc%e5%b1%95%e7%9a%84%e7%9c%bc%e5%85%89%ef%bc%881%ef%bc%89%e5%89%8d%e8%a8%80%ef%bc%88first-course-in-calculus","status":"publish","type":"post","link":"http:\/\/localhost\/%e5%be%ae%e7%a9%8d%e5%88%86%e5%88%9d%e9%9a%8e%ef%bc%8d%e6%ad%b7%e5%8f%b2%e7%99%bc%e5%b1%95%e7%9a%84%e7%9c%bc%e5%85%89%ef%bc%881%ef%bc%89%e5%89%8d%e8%a8%80%ef%bc%88first-course-in-calculus\/","title":{"rendered":"\u5fae\u7a4d\u5206\u521d\u968e\uff0d\u6b77\u53f2\u767c\u5c55\u7684\u773c\u5149\uff081\uff09\u524d\u8a00\uff08First Course in Calculus\uff0dA Historical Approach 1. Introduction"},"content":{"rendered":"

\u5fae\u7a4d\u5206\u521d\u968e\uff0d\u6b77\u53f2\u767c\u5c55\u7684\u773c\u5149\uff081\uff09\u524d\u8a00\uff08First Course in Calculus\uff0dA Historical Approach 1. Introduction\uff09<\/span><\/strong>
\n\u570b\u7acb\u81fa\u7063\u5927\u5b78\u6578\u5b78\u7cfb\u8521\u8070\u660e\u526f\u6559\u6388\/\u570b\u7acb\u81fa\u7063\u5927\u5b78\u6578\u5b78\u7cfb\u8521\u8070\u660e\u526f\u6559\u6388\u8cac\u4efb\u7de8\u8f2f<\/span><\/strong><\/p>\n

\u6578\u3001\u51fd\u6578\u3001\u7a7a\u9593<\/strong>\u662f\u6578\u5b78\u7814\u7a76\u7684\u4e3b\u8981\u5c0d\u8c61\uff0c\u5206\u5225\u767c\u5c55\u51fa\u4ee3\u6578\u5b78\u3001\u5206\u6790\u5b78<\/strong>\u8207\u5e7e\u4f55\u5b78<\/strong>\u3002\u51fd\u6578<\/strong>\uff08function\uff09\u662f\u5fae\u7a4d\u5206\u7684\u4e3b\u89d2\u3002\u6211\u5011\u8981\u5c0d\u51fd\u6578\u505a\u5fae\u5206\u4e26\u4e14\u505a\u7a4d\u5206\uff0c\u7136\u5019\u4f5c\u5404\u7a2e\u7684\u61c9\u7528\uff0c\u5305\u62ec\u61c9\u7528\u5230\u6578\u5b78\u672c\u8eab\u4ee5\u53ca\u5927\u81ea\u7136\u7684\u8b8a\u5316\u8207\u904b\u52d5\u73fe\u8c61\u3002<\/p>\n

\u51fd\u6578\u7684\u91cd\u8981\u6027\u662f\uff0c\u5b83\u5011\u4ee3\u8868\u8457\u81ea\u7136\u5f8b<\/strong>\uff08laws of nature\uff09\u6216\u662f\u66f4\u5ee3\u6cdb\u7684\u6578\u5b78\u5f8b<\/strong>\uff08laws of mathematics\uff09\uff0c\u53cd\u61c9\u8457\u6578\u5b78\u3001\u81ea\u7136\u6216\u4eba\u6587\u73fe\u8c61\u7684\u91cf\u8207\u91cf\u4e4b\u9593\u7684\u95dc\u4fc2\uff0c\u8868\u73fe\u70ba\u5404\u7a2e\u6a21\u578b<\/strong>\uff08models\uff09\u3002\u51fd\u6578\u6709\u7121\u7aae\u591a\uff0c\u5176\u4e2d\u53ea\u6709\u5c11\u6578\u6709\u540d\u5b57\u3001\u6709\u516c\u5f0f\uff0c\u5927\u591a\u6578\u662f\u5c6c\u65bc\u6c92\u6709\u540d\u5b57\u3001\u6c92\u6709\u516c\u5f0f\u7684\u7121\u540d\u82f1\u96c4\u3002<\/p>\n

\u5728\u6709\u540d\u5b57\u3001\u6709\u516c\u5f0f\u7684\u51fd\u6578\u4e2d\uff0c\u6211\u5011\u6700\u719f\u6089\u7684\u662f\uff1a\u591a\u9805\u51fd\u6578\u3001\u4e09\u89d2\u51fd\u6578\u3001\u6307\u6578\u51fd\u6578\u3001\u5c0d\u6578\u51fd\u6578\u3001\u96d9\u66f2\u4e09\u89d2\u51fd\u6578\u3001\u6709\u7406\u51fd\u6578\u3001\u7121\u7406\u51fd\u6578<\/strong>\u3001\uff0e\uff0e\uff0e\u7b49\u3002\u9019\u4e9b\u51fd\u6578\u4e5f\u662f\u5fae\u7a4d\u5206\u8981\u7814\u7a76\u7684\u9996\u8981\u5c0d\u8c61\u3002<\/p>\n

\u5fae\u7a4d\u5206\u662f\u9ad8\u4e2d\u57fa\u790e\u6578\u5b78\u7684\u7e3d\u9a57\u6536\uff0c\u5728\u9019\u500b\u57fa\u790e\u4e0a\u4f5c\u66f4\u4e0a\u4e00\u5c64\u6a13\u7684\u767c\u5c55\u3002\u5c0d\u65bc\u4e00\u500b\u51fd\u6578 $$y=f(x)$$\uff0c\u5fae\u7a4d\u5206\u8981\u7814\u7a76\uff1a\u56e0\u70ba\u7368\u7acb\u8b8a\u6578 $$x$$ \u7684\u7121\u7aae\u5c0f\u8b8a\u5316\u91cf $$dx$$\uff0c\u5f9e\u800c\u5c0e\u81f4\u61c9\u8b8a\u6578 $$y$$ \u7684\u7121\u7aae\u5c0f\u8b8a\u5316\u91cf $$dy$$\uff0c\u7136\u5f8c\u63a2\u6c42\u5b83\u5011\u7684\u8b8a\u5316\u7387 $$dy\/dx$$\uff0c\u53eb\u505a\u5fae\u5206\uff0c\u4ee5\u53ca\u7121\u7aae\u591a\u500b\u7121\u7aae\u5c0f\u7684\u9762\u7a4d\u00a0$$f(x)dx$$\u00a0<\/strong>\u4e4b\u9023\u7e8c\u6c42\u548c\u00a0$${\\int}_a^b{f(x)}dx$$<\/strong>\uff0c\u53eb\u505a\u7a4d\u5206<\/strong>\u3002<\/p>\n

\u9019\u4e9b\u90fd\u6d89\u53ca\u7121\u7aae\u6b65\u9a5f<\/strong>\uff08infinite processes\uff09\uff0c\u5f9e\u800c\u7522\u751f\uff1a\u7121\u7aae\u5c0f\u91cf\u3001\u7121\u7aae\u5927\u3001\u7121\u7aae\u591a\u3001\u7121\u9650\u5730\u9760\u8fd1\u3001\u9023\u7e8c\u6027\u3001\u6975\u9650<\/strong>\u3001\uff0e\uff0e\uff0e\u7b49\u6df1\u5967\u800c\u53c8\u96e3\u7e8f\u7684\u6982\u5ff5\u3002\u5fae\u7a4d\u5206\u662f\u9053\u9053\u5730\u5730\u76f4\u63a5\u9762\u5c0d\u4e86\u300c\u7121\u7aae<\/strong>\u300d\uff0c\u5145\u6eff\u8457\u7f8e\u5999\u3001\u56f0\u60d1\u8207\u8ff7\u4eba\uff0c\u6709\u6642\u53c8\u4e0d\u514d\u53c8\u6703\u51fa\u73fe\u77db\u76fe\u3002<\/p>\n

\u9023\u7d50<\/b>\uff1a\u5fae\u7a4d\u5206\u521d\u968e\uff0d\u6b77\u53f2\u767c\u5c55\u7684\u773c\u5149\uff082\uff09\u4fc3\u52d5\u5fae\u7a4d\u5206\u8a95\u751f\u7684\u56db\u985e\u554f\u984c<\/a><\/p>\n

\u53c3\u8003\u6587\u737b\uff1a<\/strong><\/p>\n

    \n
  1. \u8521\u8070\u660e\uff1a\u5fae\u7a4d\u5206\u7684\u6b77\u53f2\u6b65\u9053\u3002\u4e09\u6c11\u66f8\u5c40\uff0c\u53f0\u5317\uff0c$$2009$$\u3002<\/li>\n
  2. \u8521\u8070\u660e\uff1a\u6578\u5b78\u7684\u767c\u73fe\u8da3\u8ac7\uff0c\u7b2c\u4e8c\u7248\uff0c\u7b2c$$19$$\u7ae0\u3002\u4e09\u6c11\u66f8\u5c40\uff0c\u53f0\u5317\uff0c$$2010$$\u3002<\/li>\n
  3. Edward\uff1a\u5fae\u7a4d\u5206\u767c\u5c55\u53f2\uff0c\u51e1\u7570\u51fa\u7248\u793e\uff0c\u6797\u8070\u6e90\u8b6f\u3002<\/li>\n
  4. Simons\uff1aCalculus Gems, Brief Lives and Memorable Mathematics.McGraw-Hill, Inc.$$1992$$.<\/li>\n
  5. Dunham\uff1aThe Calculus Gallery, Masterpieces from Newton to Lebesgue.Princeton University Press,$$2005$$.<\/li>\n
  6. Toeplitz\uff1aThe Calculus,A Genetic Approach.The University of Chicago Press.$$1963$$<\/li>\n<\/ol>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u9019\u662f\u95dc\u65bc\u5fae\u7a4d\u5206\u4e00\u7cfb\u5217\u6587\u7ae0\u7684\u7b2c\u4e00\u7bc7\uff0c\u5fae\u7a4d\u5206\u662f\u9ad8\u4e2d\u57fa\u790e\u6578\u5b78\u7684\u7e3d\u7d50\uff0c\u66f4\u662f\u9032\u5165\u73fe\u4ee3\u6578\u5b78\u4e4b\u9580\u3002\u672c\u6587\u6dfa\u8ac7\u51fd\u6578\u7684\u91cd\u8981\u6027\uff0c\u4e26\u85c9\u7531\u5b83\u5728\u5fae\u7a4d\u5206\u7576\u4e2d\u6240\u626e\u6f14\u7684\u89d2\u8272\uff0c\u7c21\u55ae\u4ecb\u7d39\u4f55\u8b02\u5fae\u5206\u8207\u7a4d\u5206\u3002\u6578\u3001\u51fd\u6578\u3001\u7a7a\u9593\u662f\u6578\u5b78\u7814\u7a76\u7684\u4e3b\u8981\u5c0d\u8c61\uff0c\u5206\u5225\u767c\u5c55\u51fa\u4ee3\u6578\u5b78\u3001\u5206\u6790\u5b78\u8207\u5e7e\u4f55\u5b78\u3002\u51fd\u6578\uff08function\uff09\u662f\u5fae\u7a4d\u5206\u7684\u4e3b\u89d2\u3002\u6211\u5011\u8981\u5c0d\u51fd\u6578\u505a\u5fae\u5206\u4e26\u4e14\u505a\u7a4d\u5206\uff0c\u7136\u5019\u4f5c\u5404\u7a2e\u7684\u61c9\u7528\uff0c\u5305\u62ec\u61c9\u7528\u5230\u6578\u5b78\u672c\u8eab\u4ee5\u53ca\u5927\u81ea\u7136\u7684\u8b8a\u5316\u8207\u904b\u52d5\u73fe\u8c61\u3002
    \n\u51fd\u6578\u7684\u91cd\u8981\u6027\u662f\uff0c\u5b83\u5011\u4ee3\u8868\u8457\u81ea\u7136\u5f8b\uff08laws of nature\uff09\u6216\u662f\u66f4\u5ee3\u6cdb\u7684\u6578\u5b78\u5f8b\uff08laws of mathematics\uff09\uff0c\u53cd\u61c9\u8457\u6578\u5b78\u3001\u81ea\u7136\u6216\u4eba\u6587\u73fe\u8c61\u7684\u91cf\u8207\u91cf\u4e4b\u9593\u7684\u95dc\u4fc2\uff0c\u8868\u73fe\u70ba\u5404\u7a2e\u6a21\u578b\uff08models\uff09\u3002\u51fd\u6578\u6709\u7121\u7aae\u591a\uff0c\u5176\u4e2d\u53ea\u6709\u5c11\u6578\u6709\u540d\u5b57\u3001\u6709\u516c\u5f0f\uff0c\u5927\u591a\u6578\u662f\u5c6c\u65bc\u6c92\u6709\u540d\u5b57\u3001\u6c92\u6709\u516c\u5f0f\u7684\u7121\u540d\u82f1\u96c4\u3002
    \n\u5728\u6709\u540d\u5b57\u3001\u6709\u516c\u5f0f\u7684\u51fd\u6578\u4e2d\uff0c\u6211\u5011\u6700\u719f\u6089\u7684\u662f\uff1a\u591a\u9805\u51fd\u6578\u3001\u4e09\u89d2\u51fd\u6578\u3001\u6307\u6578\u51fd\u6578\u3001\u5c0d\u6578\u51fd\u6578\u3001\u96d9\u66f2\u4e09\u89d2\u51fd\u6578\u3001\u6709\u7406\u51fd\u6578\u3001\u7121\u7406\u51fd\u6578\u3001\uff0e\uff0e\uff0e\u7b49\u3002\u9019\u4e9b\u51fd\u6578\u4e5f\u662f\u5fae\u7a4d\u5206\u8981\u7814\u7a76\u7684\u9996\u8981\u5c0d\u8c61\u3002<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[233,111],"tags":[466,745,747,746],"class_list":["post-18959","post","type-post","status-publish","format-standard","hentry","category-math08","category-mathematics00","tag-466","tag-745","tag-747","tag-746","loop-entry","cat-233","cat-111","no-thumbnail"],"views":4575,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/18959","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=18959"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/18959\/revisions"}],"predecessor-version":[{"id":88931,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/18959\/revisions\/88931"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=18959"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=18959"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=18959"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}