{"id":19015,"date":"2011-01-16T23:14:58","date_gmt":"2011-01-16T15:14:58","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=19015"},"modified":"2021-10-06T16:29:03","modified_gmt":"2021-10-06T08:29:03","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%883%ef%bc%89%e5%be%ae%e7%a9%8d%e5%88%86%e6%98%af%e3%80%8c%e4%bb%a5","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%883%ef%bc%89%e5%be%ae%e7%a9%8d%e5%88%86%e6%98%af%e3%80%8c%e4%bb%a5\/","title":{"rendered":"\u5fae\u7a4d\u5206\u521d\u968e\uff0d\u6b77\u53f2\u767c\u5c55\u7684\u773c\u5149\uff083\uff09\u5fae\u7a4d\u5206\u662f\u300c\u4ee5\u6709\u6daf\u9010\u7121\u6daf\u300d\u7684\u5b78\u554f\uff08First Course in Calculus\uff0dA Historical Approach 3.From finite processes to infinite processes\uff09"},"content":{"rendered":"

\u5fae\u7a4d\u5206\u521d\u968e\uff0d\u6b77\u53f2\u767c\u5c55\u7684\u773c\u5149\uff083\uff09\u5fae\u7a4d\u5206\u662f\u300c\u4ee5\u6709\u6daf\u9010\u7121\u6daf\u300d\u7684\u5b78\u554f\uff08First Course in Calculus\uff0dA Historical Approach 3.From finite processes to infinite processes\uff09
\n<\/span><\/strong>\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

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\u4ec0\u9ebc\u53eb\u505a\u5207\u7dda\uff1f\u4ec0\u9ebc\u53eb\u505a\u9762\u7a4d\uff1f<\/strong><\/p>\n

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\"\"<\/a><\/p>\n

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\u8003\u616e $$x$$ \u7684\u8b8a\u5316\u91cf $$\\Delta{x}$$\uff0c\u65bc\u662f\u5272\u7dda\u7684\u659c\u7387\u70ba $$\\displaystyle\\frac{\\Delta{F(x)}}{\\Delta{x}}=\\frac{F(x+\\Delta{x}-F(x))}{\\Delta{x}}$$\uff0c<\/p>\n

\u73fe\u5728\u8b93 $$\\Delta{x}$$ \u8d8a\u4f86\u8d8a\u5c0f\uff0c\u4e43\u81f3\u8da8\u8fd1\u65bc $$0$$\uff0c\u4ea6\u5373\u53d6\u6975\u9650\uff1a$$\\displaystyle \\lim_{\\Delta x\\to 0}\\frac{F(x+\\Delta x)-F(x)}{\\Delta x}$$<\/p>\n

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    \n
  1. \u5fae\u5206\u8207\u7a4d\u5206\u7684\u4e92\u9006\u6027\uff1b<\/strong><\/li>\n
  2. \u5fae\u7a4d\u5206\u5b78\u6839\u672c\u5b9a\u7406\u3002<\/strong><\/li>\n<\/ol>\n

    \u9023\u7d50\uff1a\u5fae\u7a4d\u5206\u521d\u968e\uff0d\u6b77\u53f2\u767c\u5c55\u7684\u773c\u5149\uff08\uff14\uff09\u963f\u57fa\u7c73\u5fb7\u6c42\u62cb\u7269\u7dda\u5f13\u5f62\u9818\u57df\u7684\u9762\u7a4d<\/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\uff0c2009\u3002<\/li>\n
    2. \u8521\u8070\u660e\uff1a\u6578\u5b78\u7684\u767c\u73fe\u8da3\u8ac7\uff0c\u7b2c\u4e8c\u7248\uff0c\u7b2c19\u7ae0\u3002\u4e09\u6c11\u66f8\u5c40\uff0c\u53f0\u5317\uff0c2010\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":"

      \u672c\u7bc7\u900f\u904e\u6975\u9650\u7684\u6982\u5ff5\uff0c\u5206\u5225\u89e3\u8aaa\u5207\u7dda\u659c\u7387\u8207\u66f2\u7dda\u4e0b\u9762\u7a4d\u7684\u6c42\u6cd5\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":[756,755,747],"class_list":["post-19015","post","type-post","status-publish","format-standard","hentry","category-math08","category-mathematics00","tag-756","tag-755","tag-747","loop-entry","cat-233","cat-111","no-thumbnail"],"views":4838,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/19015","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=19015"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/19015\/revisions"}],"predecessor-version":[{"id":88936,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/19015\/revisions\/88936"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=19015"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=19015"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=19015"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}