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class=\"wp-block-paragraph\">\u56e0\u4e3a\u300a\u5fae\u79ef\u5206\u300b\u662f\u5b66\u4e60\u300a\u6982\u7387\u7edf\u8ba1\u300b\u548c\u300a\u7ebf\u6027\u4ee3\u6570\u300b\u7684\u5fc5\u5907\u6761\u4ef6\uff0c\u56e0\u6b64\u76f4\u63a5\u5bfc\u81f4\u6574\u4f53\u8003\u7814\u6570\u5b66\u6210\u7ee9\u975e\u5e38\u5dee\uff0c\u800c\u5b9e\u9645\u4e0a\u76ee\u524d\u8003\u7814\u7684\u6570\u5b66\u9898\u76ee\u90fd\u662f\u975e\u5e38\u57fa\u7840\u7684\uff0c\u662f\u6559\u6750\u4e0a\u4f8b\u9898\u7684\u52a0\u5f3a\u7248\uff0c\u5408\u7406\u7684\u5b66\u4e60\u5b89\u6392\u4e0b\uff0c\u5e94\u8be5\u80fd\u8003\u5230120\u5206\u5de6\u53f3\u3002\u4f46\u56e0\u4e3a\u6559\u6750\u7684\u5de8\u5927\u8bf1\u5bfc\u6027\uff0c\u8ba9\u5b66\u751f\u4ea7\u751f\u4e86\u4e25\u91cd\u7684\u6050\u60e7\u5fc3\u7406\u548c\u4e0d\u6ee1\u60c5\u7eea\uff0c\u8fd9\u53c8\u53cd\u4f5c\u7528\u4e86\u5bf9\u6570\u5b66\u7684\u5bb3\u6015\u548c\u53cd\u611f\uff0c\u771f\u662f\u4e00\u4ef6\u5f88\u60b2\u54c0\u7684\u4e8b\u60c5\u3002<\/p>\n\n\n\n<h2 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class=\"wp-block-paragraph\">\u53ef\u4ee5\u8bf4\u4e00\u5207\u77e5\u8bc6\u90fd\u662f\uff1a\u201c\u70b9\u5230\u4e3a\u6b62\uff0c\u6cdb\u800c\u4e0d\u7cbe\u201d\u3002\u5168\u4e66\u8bed\u8a00\u90fd\u8fc7\u4e8e\u673a\u68b0\u6570\u5b57\u5316\uff0c\u5f53\u7136\u5185\u5bb9\u90fd\u662f\u6b63\u786e\u7684\uff0c\u4e5f\u6ca1\u6709\u660e\u663e\u9519\u8bef\uff0c\u4f46\u6b63\u662f\u8fd9\u79cd\u201d\u4e2d\u5eb8\u7cbe\u795e\u201c\uff0c\u5c11\u4e86\u4e00\u4efd\u7075\u6c14\uff0c\u5c11\u4e86\u4e00\u4efd\u8ba9\u5b66\u751f\u52a0\u6df1\u7406\u89e3\u7684\u8f85\u52a9\u6750\u6599\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8981\u590d\u5236\u516c\u5f0f\u8c01\u4e0d\u4f1a\uff0c\u6211\u53ef\u4ee5\u7528\u51e0\u9875A4\u7eb8\u628a\u6240\u6709\u516c\u5f0f\u90fd\u5199\u51fa\u6765\uff0c\u96be\u9053\u8fd9\u6837\u5c31\u4ee3\u8868\u6574\u4e2a\u300a\u5fae\u79ef\u5206\u300b\u4e86\u5417\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f80\u5f80\u662f\u5728\u516c\u5f0f\u4e4b\u5916\u7684\u5730\u65b9\uff0c\u5728\u4e66\u672c\u7559\u767d\u7684\u8fb9\u7f18\uff0c\u5728\u6700\u7ec6\u8282\u7684\u5730\u65b9\uff0c\u6700\u96be\u7684\u5730\u65b9\uff0c\u6700\u62bd\u8c61\u7684\u5730\u65b9\uff0c\u6700\u9700\u8981descriptive statement \u7684\u5730\u65b9\u624d\u80fd\u770b\u51fa\u4e00\u4e2a\u4f5c\u8005\u7684\u529f\u529b\u662f\u5426\u6df1\u539a\uff0c\u5b66\u95ee\u662f\u5426\u5230\u5bb6\u3002\u201c\u4e3e\u91cd\u82e5\u8f7b\u201d\uff0c\u662f\u5bf9\u4e00\u4e2a\u5b66\u8005\u7684\u6700\u9ad8\u7684\u8d5e\u8a89\u548c\u8bc4\u4ef7\uff0c\u53ef\u60dc\u56fd\u5185\u6559\u6750\u548c\u6559\u6388\u4eec\u5728\u8fd9\u4e2a\u65b9\u9762\uff0c\u8fd8\u6709\u5f88\u957f\u7684\u8def\u8981\u8d70\u5462\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300a\u540c\u6d4e\u9ad8\u6570\u300b\u7528\u5f88\u51c6\u786e\u7684\u8bed\u8a00\u628a\u6781\u9650\u201cD-E\u201d\u5b9a\u4e49\u6446\u51fa\u6765\uff0c\u4f46\u662f\u6ca1\u6709\u8bf4\u660e\u8fd9\u4e2a\u5b9a\u4e49\u7684\u6765\u9f99\u53bb\u8109\uff0c\u56e0\u6b64\u5f88\u591a\u5b66\u751f\u90fd\u770b\u4e0d\u61c2\uff0c\u751a\u81f3\u76f8\u5f53\u4e00\u90e8\u5206\u5b66\u751f\u90fd\u65e0\u6cd5\u51c6\u786e\u53d1\u97f3 delta -epislon\uff0c\u66f4\u522b\u8bf4\u7406\u89e3\u5230\u201c\u4e3a\u4ec0\u4e48\u8981\u7528D-E\u6765\u4ee3\u8868\u6781\u9650\uff1f\u4e0d\u80fd\u7528\u5176\u4ed6\u7b26\u53f7\u5417\uff1f\u201d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u5b9e\u9645\u4e0a D-E \u5728\u53e4\u5e0c\u814a\u5b57\u6bcd\u4e2d\u4ec5\u4ec5\u8868\u793a\u5b57\u6bcd\u8868\u7684\u7b2c\u56db\u4e2a\u548c\u7b2c\u4e94\u4e2a\u5b57\u6bcd\uff0c\u6ca1\u6709\u4efb\u4f55\u7279\u6b8a\u7684\u542b\u4e49\uff0c\u4e3b\u8981\u662fABC \u90fd\u88ab\u6b27\u51e0\u91cc\u5f97\u9738\u5360\u5728\u51e0\u4f55\u5b66\u91cc\uff0c\u6ca1\u529e\u6cd5\u7528\u4e86\uff0c\u88ab\u8feb\u65e0\u5948\u91c7\u7528\u4e86 D-E\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u5728\u7f8e\u56fd\u6559\u6750\u4e2d\uff0c\u539f\u4f5c\u8005\u7528\u4e86\u4e00\u5927\u6bb5\u5f88\u7b80\u5355\u7684\u8bed\u8a00\u548c\u51e0\u5e45\u56fe\u7247\uff0c\u5c06\u6781\u9650\u8fdb\u884c\u4e86\u89e3\u91ca\u201cLimit is an active approachingprocess, it is not a still real-valued number nor variable, no matter how closeyou are, you will never reach that target \u201d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6781\u9650\u8fd9\u4e2a\u6982\u5ff5\u5728\u725b\u987f&#8212;\u83b1\u5e03\u5c3c\u8328\u7684\u65f6\u4ee3\u8fd8\u6ca1\u6709\u51fa\u73b0\uff0c\u56e0\u4e3a\u6781\u9650\u6d89\u53ca\u5230\u7684\u6570\u5b66\u539f\u7406\u5176\u5b9e\u5f88\u590d\u6742\uff0c\u4ec5\u4ec5\u662f\u201c\u8fde\u7eed\u6027\u201d\u548c\u201c\u5149\u6ed1\u6027\u201d\u8fd9\u4e24\u4e2a\u770b\u8d77\u6765\u5f88\u7b80\u5355\u7684\u540d\u8bcd\uff0c\u5c31\u8ba9\u6574\u6574\u4e00\u4e2a\u4e16\u7eaa\u7684\u6570\u5b66\u5bb6\u5e9f\u5bdd\u5fd8\u98df\uff0c\u591c\u4ee5\u7ee7\u65e5\uff0c\u624d\u5f97\u51fa\u7ed3\u8bba\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u81f3\u4e8e\u6211\u4eec\u4eca\u5929\u770b\u5230\u7684D-E\u5b9a\u4e49\uff0c\u66f4\u662f\u725b\u987f\u6b7b\u540e\u8fd1\u4e24\u767e\u5e74\u624d\u88ab\u5fb7\u56fd\u6570\u5b66\u5bb6\u5a01\u5c14\u65af\u7279\u62c9\u65af\u63d0\u51fa\uff0c\u56e0\u6b64\u7f8e\u7248\u6559\u6750\u666e\u904d\u90fd\u4e0d\u8981\u6c42\u201c\u8bc1\u660e\u201d\uff0c\u53ea\u8981\u6c42\u201c\u4e86\u89e3\u201d\u6781\u9650\u7684\u610f\u8bc6\u5f62\u6001\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300a\u540c\u6d4e\u9ad8\u6570\u300b\u5bf9\u4e8e\u4e00\u5143\u5fae\u79ef\u5206\u51e0\u4e4e\u5b8c\u5168\u6ca1\u6709\u5b9e\u4f8b\uff0c\u800c\u5bf9\u4e8e\u6781\u7aef\u91cd\u8981\u7684sinhx\uff0ccoshx\uff0c\u66f4\u662f\u53ea\u6709\u5be5\u5be5\u51e0\u9875\u7eb8\uff0c\u5e76\u4e14\u8fd8\u5e26\u4e86\u4e00\u4e2a\u661f\u53f7\uff0c\u7ed9\u4eba\u4e00\u79cd\u201c\u6b32\u7ec3\u6b64\u529f\uff0c\u5fc5\u5148\u81ea\u5bab\u201d\u7684\u6050\u60e7\uff0csinhx,coshx \u5c31\u662f\u7531 E^X \u8ddf\u5b83\u7684\u53cd\u51fd\u6570E^(-X)\u8fdb\u884c\u7ebf\u6027\u7ec4\u5408\u5f97\u5230\u7684\uff0c\u7b80\u5355\u5427\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f46\u662f\u540c\u6d4e\u76f4\u63a5\u5ffd\u7565\u4e86 y=e^x \u7684\u6559\u5b66\uff0c\u5b9e\u9645\u4e0a y=e^x \u662f\u5fae\u79ef\u5206\u4e2d\u6700\u7b80\u5355\uff0c\u4e5f\u662f\u6700\u91cd\u8981\u7684\u51fd\u6570\u65cf\u3002\u6b63\u56e0\u4e3a\u8fd9\u4e2a\u7279\u70b9\uff0c\u5bf9\u5b83\u4eec\u7684\u6c42\u5bfc\/\u6c42\u79ef\u5c31\u975e\u5e38\u7b80\u5355\uff0c\u7279\u522b\u662f\u540e\u671f\u5b66\u4e60\u65e0\u7a77\u7ea7\u6570\uff0c\u6cf0\u52d2\u5c55\u5f00\u5f0f\uff0c\u5411\u91cf\u5fae\u79ef\u5206\uff0c\u5f00\u666e\u52d2\u4e09\u5927\u5b9a\u7406\uff0c\u6982\u7387\u7684MGF\uff0c\u90fd\u65f6\u65f6\u523b\u523b\u4f53\u73b0\u51fa y=e^x \u7684\u5de8\u5927\u5a01\u529b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u66f4\u4e25\u91cd\u7684\u95ee\u9898\u662f\uff0c\u540c\u6d4e\u548c\u6d59\u5927\u7684\u7f16\u8005\uff0c\u90fd\u7528\u4e86\u53cd\u4eba\u7c7b\u7684\u601d\u7ef4\u65b9\u6cd5\u6765\u5f00\u5c55\u6559\u5b66\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bd4\u5982\u5bf9y=x^n\u7684\u6c42\u5bfc\u6559\u5b66\uff0c\u540c\u6d4e\u662f\u76f4\u63a5\u62ff\u5b9a\u4e49\u51fa\u6765\uff0c\u5148\u628a\u5b83\u8bc1\u660e\u4e86\uff0c\u518d\u4e3e\u4f8b\u544a\u8bc9\u5b66\u751f\u8fd9\u4e2a\u5b9a\u7406\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u3002\u53f0\u4e0b\u7684\u5b66\u751f\u4e00\u8138\u95ee\u597d\u2026\u2026<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u96be\u9053\u5927\u5bb6\u4e0d\u4f1a\u89c9\u5f97\u8fd9\u662f\u8ddf\u6b63\u5e38\u601d\u7ef4\u76f8\u53cd\u5417\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7f8e\u7248\u6559\u6750\u5c31\u662f\u5148\u5e26\u9886\u6211\u4eec\u5b66\u4f1ay=1\u7684\u6c42\u5bfc\uff0c\u7136\u540ey=x\u7684\u6c42\u5bfc\uff0c\u7136\u540ey=x^2\u7684\u6c42\u5bfc\uff0c\u7136\u540ey=x^3\u7684\u6c42\u5bfc\uff0c\u7136\u540e\u4f5c\u8005Stewart\u5faa\u5faa\u5584\u8bf1\u5730\u95ee\u540c\u5b66\u8bf4&#8221;nowdo you see any pattern among these process ? Can you GUESS what maybe thederivative of y=x^5 ? And what about y=x^n?&#8221;\u6700\u540e\u4ed6\u624d\u4f1a\u6446\u51fa\u4e25\u5bc6\u7684\u5b9a\u4e49\uff0c\u5e76\u8bc1\u660e\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b64\u65f6\uff0c\u5b66\u751f\u4e5f\u5728\u8fc7\u7a0b\u4e4b\u4e2d\u5b66\u4f1a\u4e86\u201c\u7531\u7279\u6b8a\u5230\u4e00\u822c\uff0c\u518d\u7531\u4e00\u822c\u5230\u7279\u6b8a\u201d\u8fd9\u6837\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u6570\u5b66\u601d\u7ef4\u3002\u76f8\u5bf9\u5e94\u7684\u6c42\u79ef\u4e5f\u4e00\u6837\uff0c\u5148\u8ba1\u7b97y=1\u7684\u79ef\u5206\uff0c\u7136\u540ey=x\u7684\u79ef\u5206\uff0c\u7136\u540ey=x^2\u7684\u79ef\u5206\uff0c\u7136\u540ey=x^3\u7684\u79ef\u5206\uff0c\u6700\u540e\u518d\u95ee\u5b66\u751f&#8221;now do you see any pattern among these process ?Can you GUESS what maybe the antiderivative of y=x^8, and what abouty=x^n?&#8221;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Stewart\u4ece\u6765\u4e0d\u4f1a\u76f4\u63a5\u7529\u51fa\u4e00\u5806\u6666\u6da9\u7684\u8bc1\u660e\uff0c\u800c\u662f\u5148\u4ece\u51e0\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\uff0c\u5f15\u5bfc\u5b66\u751f\u53bb GUESS \u8fd9\u6837\u7684\u7ed3\u8bba\u662f\u5426\u5177\u6709\u4e00\u822c\u6027\uff0c\u5e76\u4e14\u8bc1\u660e\u81ea\u5df1\u7684GUESS \u662f\u5bf9\u7684\u8fd8\u662f\u9519\u7684\u3002Stewart \u6240\u7528\u7684\u4f8b\u5b50\u90fd\u5f88\u7b80\u5355\uff0c\u5e76\u6ca1\u6709\u592a\u591a\u7684\u6280\u5de7\u548c\u5957\u8def\uff0c\u4f46\u662f\u8fd9\u6837\u7684\u6548\u679c\u5374\u975e\u5e38\u597d\uff0c\u7531\u6d45\u5165\u6df1\u7684\u5e2e\u52a9\u5b66\u751f&#8221;explore the unknown&#8221;\uff0c\u8fd9\u624d\u662f\u4e00\u540d\u4f18\u79c0\u7684\u8001\u5e08\u6240\u5e94\u6709\u7684\u6001\u5ea6\u548c\u6c34\u5e73\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u591a\u5e74\u540e\uff0c\u6216\u8bb8\u4f60\u4f1a\u5fd8\u8bb0\u591a\u5143\u79ef\u5206\u7684\u516c\u5f0f\uff0c\u4f60\u4e5f\u4f1a\u5fd8\u8bb0Laplace\uff0c Fourier\uff0cTaylor\u7684\u516c\u5f0f\uff0c\u4f46\u53ea\u8981\u4f60\u8fd8\u8bb0\u5f97\u63a8\u7406\u7684\u65b9\u6cd5\uff0c\u4f60\u5c31\u5f88\u5bb9\u6613\u5728\u51e0\u5206\u949f\u5185\u5b8c\u6210\u8fd9\u4e00\u4e2a\u8fc7\u7a0b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u674e\u5f00\u590d\u66fe\u7ecf\u8bf4\u5230\u201c\u5fd8\u6389\u4f60\u6240\u5b66\u7684\u4e00\u5207\u516c\u5f0f\u548c\u5b9a\u7406\uff0c\u5982\u679c\u4f60\u8fd8\u80fd\u5229\u7528\u81ea\u5df1\u7684\u7406\u89e3\u53bb\u63a8\u7406\u51fa\u6765\uff0c\u90a3\u5c31\u8bf4\u660e\u4f60\u7684\u5b66\u95ee\u5df2\u7ecf\u5230\u5bb6\u4e86\u3002\u201d \u5bf9\u8fd9\u53e5\u8bdd\uff0c\u672c\u4eba\u65e0\u6bd4\u8d5e\u540c\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7f8e\u7248\u6559\u6750\u540c\u65f6\u9644\u5e26\u4e86\u5927\u91cf\u7684\u4e00\u5143\u5fae\u79ef\u5206\u4e60\u9898\uff0c\u53ea\u5217\u4e3e\u7b80\u5355\u7684\u5165\u95e8\u4e60\u9898\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff081\uff09\u56fa\u5b9a\u7684\u9c7c\u5858\u91cc\u653e\u5165\u4e00\u5b9a\u6570\u91cf\u7684\u9c7c\u82d7\uff0c\u5728\u8db3\u591f\u8425\u517b\u4e0b\uff0c\u9c7c\u82d7\u4e0d\u4f1a\u65e0\u9650\u589e\u957f\uff0c\u800c\u662f\u6307\u6570\u589e\u957f\uff0c\u5229\u7528\u5fae\u79ef\u5206\u77e5\u8bc6\uff0c\u5c31\u53ef\u4ee5\u6c42\u7684\u76f8\u5e94\u7684\u589e\u957f\u6570\u91cf\u3002&nbsp; &nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff082\uff09\u535a\u5c14\u7279\u5728\u4e00\u6b21110\u7c73\u680f\u6bd4\u8d5b\u4e2d\uff0c\u603b\u7528\u65f612\u79d2\uff0c\u90a3\u4e48\u95ee\u4f60\uff0c\u4ed6\u57284.5\u79d2\u7684\u65f6\u5019\uff0c\u5177\u4f53\u7684\u77ac\u95f4\u901f\u5ea6\u662f\u591a\u5c11\uff1f\u540c\u6837\u524d\u63d0\u6761\u4ef6\u4e0b\uff0c\u535a\u5c14\u7279\u57288.5\u79d2\u7684\u65f6\u5019\uff0c\u5df2\u7ecf\u603b\u5171\u8dd1\u4e86\u591a\u5c11\u7c73\uff1f\u6700\u540e\u5c31\u4f1a\u95ee\uff0c\u6709\u4ec0\u4e48\u65b9\u5f0f\u628a\u4e0a\u9762\u4e24\u4e2a\u4e0d\u76f8\u5e72\u7684\u95ee\u9898\u8054\u7cfb\u8d77\u6765\uff1f&nbsp; &nbsp; &nbsp; &nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff083\uff09\u67d0\u964d\u8840\u538b\u7684\u836f\u7269\uff0c\u7ed9\u9ad8\u8840\u538b\u75c5\u4eba\u5403\u4e86\u540e\uff0c\u68c0\u6d4b\u5f97\u8840\u538b\u4e0b\u964d\u7684\u901f\u5ea6\u4e0e\u836f\u7269\u6d53\u5ea6\u6709\u76f4\u63a5\u5173\u7cfb\uff0c\u5229\u7528\u5fae\u79ef\u5206\u5c31\u53ef\u4ee5\u6c42\u5f97\uff0c\u5403\u591a\u5c11\u7684\u836f\u7269\uff0c\u624d\u662f\u6709\u6548\u7684\u5b89\u5168\u8303\u56f4\u3002&nbsp; &nbsp; &nbsp; &nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff084\uff09\u5316\u5b66\u53cd\u5e94\u4e2d\uff0c\u67d0\u5143\u7d20\u53cd\u5e94\u65f6\u95f4\u8ddf\u5143\u7d20\u6d53\u5ea6\u5448\u6b63\u6bd4\u5173\u7cfb\uff0c\u4f46\u662f\u660e\u663e\u4e0d\u662f\u666e\u901a\u7684\u7ebf\u6027\u5173\u7cfb\uff0c\u5229\u7528\u5fae\u79ef\u5206\uff0c\u5c31\u53ef\u4ee5\u6c42\u7684\u67d0\u65f6\u95f4\u7684\u6d53\u5ea6\uff0c\u6216\u8005\u5b8c\u5168\u53cd\u5e94\u6240\u9700\u7684\u65f6\u95f4\u3002&nbsp; &nbsp; &nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff085\uff09\u53d1\u5c04\u5730\u7403\u540c\u6b65\u536b\u661f\uff0c\u9700\u8981\u591a\u5c11\u505a\u529f\uff0c\u67d0\u77ac\u95f4\u9700\u8981\u591a\u5927\u7684\u901f\u5ea6\uff0c\u5982\u4f55\u786e\u5b9a\u901f\u5ea6\u8ddf\u505a\u529f\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u5728\u7b80\u6613\u6761\u4ef6\u4e0b\u5982\u4f55\u68c0\u9a8c\u76f8\u5bf9\u8bba\u7684\u6b63\u786e\u6027\u3002&nbsp; &nbsp; &nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff086\uff09\u6c34\u9762\u7684\u6ce2\u6d6a\u4ece\u4e2d\u5fc3\u70b9\u5411\u5916\u6269\u5f20\uff0c\u5448 sinhx \u7684\u8f68\u8ff9\uff1b\u800c\u60ac\u94fe\u7ebf\u7684\u53d7\u529b\u60c5\u51b5\uff0c\u5374\u662f\u5448coshx\u7684\u8f68\u8ff9\uff0c\u8bd5\u7528\u5fae\u79ef\u5206\u77e5\u8bc6\u8fdb\u884c\u7b80\u5355\u8bf4\u660e\u3002&nbsp; &nbsp; &nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff087\uff09\u6d41\u4f53\u901a\u8fc7\u67d0\u7ba1\u9053\u65f6\uff0c\u5176\u9760\u8fd1\u7ba1\u58c1\u7684\u6d41\u4f53\u901f\u5ea6\u4f1a\u56e0\u4e3a\u963b\u529b\u4e8c\u51cf\u6162\uff0c\u4e2d\u5fc3\u90e8\u5206\u7531\u4e8e\u963b\u529b\u8f83\u5c0f\u800c\u901f\u5ea6\u52a0\u5feb\uff0c\u8bd5\u7528\u5fae\u79ef\u5206\u77e5\u8bc6\u6765\u89e3\u91ca\u4e3a\u4ec0\u4e48\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53\u7136\u8fd8\u6709\u5927\u91cf\u7684\u53d8\u901f\u7684\u4f4d\u79fb\uff0c\u53d8\u529b\u505a\u5de5\uff0c\u7ecf\u6d4e\u5b66\u7684\u8fb9\u9645\u6548\u5e94\uff0c\u4ef7\u683c\u5f39\u6027\uff0c\u8d44\u4ea7\u5b9a\u4ef7\u6a21\u578b\uff08CAPM, WACC\uff09\uff0c\u65cb\u8f6c\u4f53\u7684\u4f53\u79ef\uff0c\u7b49\u7b49\u90fd\u662f\u300a\u540c\u6d4e\u9ad8\u6570\u300b\u6240\u7f3a\u5c11\u7684\u5b9e\u9645\u5e94\u7528\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b63\u662f\u56e0\u4e3a\u8fd9\u4e9b\u6829\u6829\u5982\u751f\u7684\u4f8b\u5b50\uff0c\u5b66\u751f\u624d\u80fd\u6df1\u523b\u7406\u89e3\u5230\u5fae\u79ef\u5206\u5bf9\u4e8e\u73b0\u4ee3\u751f\u6d3b\u7684\u5de8\u5927\u6539\u53d8\u548c\u610f\u4e49\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5426\u5219\uff0c\u5047\u5982\u4ec5\u4ec5\u662f\u628a\u7eaf\u7cb9\u7684\u6570\u5b57\u7ffb\u6765\u7ffb\u53bb\uff0c\u6c42\u5bfc\/\u6c42\u79ef\uff0c\u5b66\u751f\u90fd\u4f1a\u4e86\uff0c\u90a3\u7136\u540e\u5462\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u96be\u9053\u5b66\u4e86\u5fae\u79ef\u5206\u5c31\u662f\u6765\u505a\u4e00\u4e2a\u4eba\u5de5\u8ba1\u7b97\u5668\u5417\uff1f\u56fd\u5185\u6559\u6750\u603b\u662f\u76f4\u63a5\u53eb\u5b66\u751f\u5957\u7528\u67d0\u67d0\u516c\u5f0f\u89e3\u9898\u76ee\uff0c\u800c\u5ffd\u7565\u4e86\u516c\u5f0f\u4e4b\u5916\u7684\u903b\u8f91\u7406\u89e3\u548c\u63a8\u5230\u80fd\u529b\uff0c\u7f8e\u7248\u6559\u6750\u5c31\u57fa\u672c\u76f8\u53cd\uff0c\u5f88\u5f3a\u8c03\u5bf9\u57fa\u672c\u516c\u5f0f\u7684\u63a8\u5230\u548c\u5f52\u7eb3\u80fd\u529b\uff0c\u800c\u964d\u4f4e\u5bf9\u516c\u5f0f\u672c\u8eab\u7684\u4f9d\u8010\u6027\u3002\u8fd9\u662f\u4e24\u79cd\u622a\u7136\u4e0d\u540c\u6559\u80b2\u7406\u5ff5\u7684\u51b2\u7a81\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56fd\u5185\u6559\u6750\u5c31\u50cf\uff08\u6388\u4eba\u4e0e\u9c7c\uff09\uff0c\u7ed9\u4f60\u4e00\u5806\u516c\u5f0f\u548c\u5b9a\u7406\uff0c\u8ba9\u4f60\u7167\u7740\u7528\u3002\u7f8e\u7248\u6559\u6750\u5c31\u50cf\uff08\u6388\u4eba\u4e0e\u6e14\uff09\u7ed9\u4f60\u4e00\u79cd\u53d1\u73b0\u516c\u5f0f\u548c\u5b9a\u7406\u7684\u601d\u7ef4\uff0c\u8ba9\u4f60\u5b66\u4f1a\u81ea\u5df1\u5f52\u7eb3\u603b\u7ed3\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b83\u9996\u5148\u5c31\u4f1a\u544a\u8bc9\u6211\u4eec\uff1a\u300a\u5fae\u5206\u5b66\u300b\u7814\u7a76\u201cinstantaneous,incremental and related changes\u201d \u7684\u95ee\u9898\uff1b\u800c\u300a\u79ef\u5206\u5b66\u300b\u7814\u7a76\u201coutputfrom irregular input \u201d\u7684\u95ee\u9898\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300a\u5fae\u79ef\u5206\u300b\u7684\u672c\u8d28\u5c31\u662f\u7814\u7a76&#8221;activevariable&#8221;\u7684\u95ee\u9898\uff0c\u6559\u6750\u7279\u522b\u591a\u6b21\u5f3a\u8c03\u201cthesignificant difference between calculus and algebra and geometry is thatcalculus is dealing with ACTIVE\/MOVING variable and algebra\/geometry is workingon still variable\u201d.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5bf9\u540c\u6d4e\u300a\u7ebf\u6027\u4ee3\u6570\u300b\uff0c\u6d59\u5927\u300a\u6982\u7387\u7edf\u8ba1\u300b\u7684\u610f\u89c1<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u4e24\u5957\u6559\u6750\u4e5f\u662f\u88ab\u56fd\u4eba\u89c6\u4e3a\u7470\u5b9d\uff0c\u656c\u800c\u8fdc\u4e4b\uff0c\u4f46\u662f\u76f8\u5f53\u5927\u91cf\u7684\u5b66\u751f\u53cd\u6620\uff1a\u201c\u300a\u6982\u7387\u7edf\u8ba1\u300b\u7531\u4e8e\u6bd4\u8f83\u5177\u4f53\uff0c\u8fd8\u52c9\u5f3a\u770b\u5f97\u61c2\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f46\u662f\u300a\u73b0\u4ee3\u300b\u5b9e\u5728\u592a\u62bd\u8c61\uff0c\u6240\u4ee5\u5f88\u591a\u5b66\u751f\u53cd\u5e94\u65e0\u6cd5\u7406\u89e3\u201d\u3002\u56e0\u4e3a\u8fd9\u4e24\u5957\u6559\u6750\u4e5f\u5341\u5206\u62bd\u8c61\u548c\u7406\u8bba\u5316\uff0c\u7f3a\u5c11\u5f88\u91cd\u8981\u7684PREFACE\uff0c\u8ba9\u5b66\u751f\u5728\u5b66\u4e60\u4e4b\u524d\u80fd\u5bf9\u672c\u5b66\u79d1\u6709\u4e00\u4e2a FRAMEWORK \u4e0a\u7684\u628a\u63e1\u548c\u638c\u63a7\uff0c\u57fa\u672c\u4e0a\u770b\u5b8c\u4e86\u4e5f\u4e0d\u77e5\u6240\u4e91\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7f8e\u7248\u6559\u6750\u65e0\u8bba\u5982\u4f55\u90fd\u4f1a\u6709\u8fd9\u4e9b\u4e1c\u897f\uff0c\u5e76\u4e14\u5f00\u7bc7\u5c31\u544a\u8bc9\u4f60\u300a\u7ebf\u4ee3\u300b\u7814\u7a76\u7684\u5bf9\u8c61\u662f\u201cvector, especially COLUMN vector\u201d\uff0c\u5e76\u4e0d\u662f\u6240\u8c13\u7684\u201cmatrix\u201d\u6216\u8005\u201cdeterminant\u201d\u6216\u8005\u201ceigenvalue\u201d\uff0c\u5e76\u5728\u4e00\u5f00\u59cb\u5c31\u5bf9\u5411\u91cf\u8fdb\u884c\u4e86\u7ec6\u81f4\u7684\u6559\u5b66\uff0c\u4ece\u52a0\u6cd5\u3001\u51cf\u6cd5\uff0c\u4e8c\u7ef4\u56fe\u793a\uff0c\u4e09\u7ef4\u56fe\u793a\uff0c\u5230dotproduct\uff0c\u5230cross product\uff0c\u5230matrix\uff0c\u5230determinant\uff0c\u6700\u540e\u624d\u662f\u6c34\u5230\u6e20\u6210\u5730\u5f15\u5165matrix as linear transformation\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u975e\u7406\u5de5\u79d1\u7684\u5b66\u751f\uff0c\u5b66\u5230\u8fd9\u91cc\u5c31\u5dee\u4e0d\u591a\u4e86\uff0c\u540e\u9762vector space \u548c orthogonallity ,\u6bd4\u8f83\u62bd\u8c61\uff0c\u96be\u5ea6\u4e5f\u5927\uff0c\u53ef\u4ee5\u6709\u9009\u62e9\u5730\u653e\u5f03\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u81f3\u4e8e\u6700\u91cd\u8981\u7684rank , nuliity , dimension ,\u540c\u6d4e\u5e76\u6ca1\u6709\u8bf4\u6e05\u695a\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u662f\u4e00\u7ef4\u7684\uff0c\u90a3\u5c31\u662f\u4e24\u4e2a\u5411\u91cf\u5171\u7ebf\uff1b\u4e8c\u7ef4\u7684\uff0c\u90a3\u5c31\u662f\u4e24\u4e2a\u5411\u91cf\u5f62\u6210\u4e00\u4e2a\u56db\u8fb9\u5f62\uff1b\u4e09\u7ef4\u7684\uff0c\u90a3\u5c31\u662f\u4e09\u4e2a\u5411\u91cf\u5f62\u6210\u4e00\u4e2a\u4f53\u79ef\uff1b\u56db\u7ef4\u4ee5\u4e0a\u7684\uff0c\u7167\u6837\u662f\u4f53\u79ef\uff0c\u4f46\u662f\u4e00\u822c\u4e0d\u8ba8\u8bba\u3002\u800c\u6240\u6709\u7684\u201c\u884c\u5217\u5f0f\u201d\u3001\u201c\u77e9\u9635\u201d\u3001\u201c\u79e9\u201d\u3001\u201c\u901a\u89e3\u201d\u3001\u201c\u7279\u89e3\u201d\u3001\u201c\u7279\u5f81\u5411\u91cf\u201d\uff0c\u201c\u7279\u5f81\u503c\u201d\uff0c\u7b49\u7b49\u540d\u8bcd\uff0c\u90fd\u662frref \u540e\u56f4\u7ed5COLUMNvector \u5c55\u5f00\u7684\u8fd0\u7b97\u800c\u5df2\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4f46\u662f\u7531\u4e8e\u300a\u540c\u6d4e\u7ebf\u4ee3\u300b\u6839\u672c\u6ca1\u6709\u8fd9\u4e9b\u57fa\u7840\u77e5\u8bc6\u505a\u94fa\u57ab\uff0c\u5bfc\u81f4\u5b66\u751f\u57fa\u672c\u770b\u4e0d\u61c2\u6559\u6750\u7684\u5185\u5bb9\u3002\u5c31\u76f8\u5f53\u4e8e\uff1a\u8ba9\u5b66\u751f\u53bb\u5efa\u9020\u4e00\u680b\u6469\u5929\u5927\u697c\uff0c\u4f46\u662f\u4e0d\u8ba9\u4f60\u6253\u5730\u57fa\uff0c\u76f4\u63a5\u5c31\u5728\u5e73\u5730\u65bd\u5de5\u5efa\u9020\u7b2c\u4e00\u5c42\u3002\u5b9e\u9645\u4e0a\u975e\u7406\u5de5\u7c7b\u672c\u79d1\u9636\u6bb5\u7684\u300a\u7ebf\u6027\u4ee3\u6570\u300b\u662f\u975e\u5e38\u7b80\u5355\u7684\uff0c\u662f\u6700\u57fa\u7840\u7684\u52a0\u51cf\u4e58\u800c\u5df2\uff0c\u4f46\u662f\uff08\u5f88\u591a\uff09\u5b66\u751f\u5374\u8bf4\u4e0d\u6e05\u695a columnspace&nbsp; \u548c row space \u7684\u533a\u522b\uff0c\u8fd9\u5c31\u76f4\u63a5\u5bfc\u81f4\u540e\u671f\u5b66\u4e60\u6349\u895f\u89c1\u8098\uff0c\u4e3e\u6b65\u7ef4\u8270\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6d59\u5927\u7684\u300a\u6982\u7387\u7edf\u8ba1\u300b\u76f8\u5bf9\u6765\u8bf4\u6bd4\u540c\u6d4e\u4f18\u79c0\u592a\u591a\u4e86\uff0c\u4f46\u8fd8\u662f\u5b58\u5728\u975e\u5e38\u81f4\u547d\u7684\u7f3a\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9996\u5148\uff0c\u662f\u4f53\u7cfb\u592a\u6df7\u4e71\uff0c\u7adf\u7136\u5bf9\u4e8ediscrete\/continuous RV \u7684\u6700\u57fa\u7840\u672f\u8bed(pmf, pdf,cdf)\u90fd\u6b20\u7f3a\u5b8c\u6574\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u6b21\uff0c\u662f\u6559\u5b66\u592a\u6d45\u663e\uff0c\u6240\u6709\u7684\u5b9e\u4f8b\u90fd\u662f\u4e00\u7b14\u5e26\u8fc7\uff0c\u5bf9\u4e8e\u5927\u540d\u9f0e\u9f0e\u7684Poisson\uff08\uff09\uff0c\u548cExponential () \u751a\u81f3\u90fd\u6ca1\u6709\u8bf4\u660e\u767d\u4e4b\u95f4\u7684\u5fae\u5999\u5173\u7cfb\uff0c\u7b80\u76f4\u4e0d\u5982\u7ef4\u57fa\u767e\u79d1\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7f8e\u7248\u7684\u300a\u6982\u7387\u4e0e\u7edf\u8ba1\u300b\u5bf9\u4e00\u7ef4\u7684\u53d8\u91cf\u5206\u5e03\u8fdb\u884c\u4e86\u975e\u5e38\u7ec6\u81f4\u7684\u6559\u5b66\uff0c\u4e94\u79cddiscrete\/continuous RV \uff0c\u53ca\u5176\u76f8\u5173\u7684mean\uff0cvariance\uff0cmedian, skewness\u3002\u6bcf\u4e00\u79cd\u5206\u5e03\u90fd\u914d\u4e86\u81f3\u5c11\u4e94\u9053\u4f8b\u9898\uff0c\u6bcf\u5230\u4f8b\u9898\u90fd\u6709\u8be6\u7ec6\u7684\u89e3\u7b54\u601d\u8def\u548c\u5b8c\u6574\u7684mathmatical induction\uff0c\u51e0\u4e4e\u5360\u636e\u4e86\u4e00\u534a\u7684\u6559\u6750\u5185\u5bb9\uff0c\u5e76\u9644\u5e26\u6709\u975e\u5e38\u4e30\u5bcc\u7684\u8bfe\u540e\u7ec3\u4e60\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u800c\u5bf9\u4e8e\u66f4\u52a0\u590d\u6742\u7684\u4e8c\u7ef4\u53d8\u91cf\uff0c\u53ca\u5176mean\uff0ccor-variance\uff0cco-relation,\u6559\u6750\u53cd\u800c\u7528\u4e86\u8f83\u5c11\u7684\u7248\u9762\uff0c\u56e0\u4e3a\u4e8c\u7ef4\u4e0d\u8fc7\u662f\u4e24\u4e2a\u4e00\u7ef4\u53d8\u91cf\u56f4\u6210\u7684\u4e00\u4e2a\u9762\u79ef\u800c\u5df2\uff0c\u5176\u4ed6\u5e76\u65e0\u660e\u663e\u5dee\u5f02\uff0c\u53ea\u8981\u5148\u624e\u624e\u5b9e\u5b9e\u5b66\u597d\u4e00\u7ef4\u7684\uff0c\u4e8c\u7ef4\u7684\u95ee\u9898\u5c31\u53d8\u5f97\u5f88\u7b80\u5355\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7f8e\u7248\u6559\u6750\u7279\u522b\u8bf4\u660e\u4e86\u51e0\u4e2a\u95ee\u9898\u201cPoissondistribution looks very complicated at first, but it is actually the discreteversion of Exponential distribution, which is very easy to calculate. ButExponential distribution, together with its brother Erlang distribution, isalso a simplified version of Gamma distribution. But the most interestingfinding is that the Chi-squared distribution is a special case of Gammadistribution as well as a special case of Norma distribution, which means tosome extent, all the important distributions can be related to Normaldistribution ! \u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5176\u5b9e\u8d8a\u662f\u5b66\u5230\u540e\u9762\uff0c\u8d8a\u4f1a\u53d1\u73b0\u201c\u5411\u91cf\u201d\u7684\u91cd\u8981\u6027\uff0c\u5b83\u5373\u51fa\u73b0\u5728\u300a\u7ebf\u4ee3\u300b\uff0c\u4e5f\u51fa\u73b0\u5728\u300a\u6982\u7387\u300b\uff0c\u66f4\u51fa\u73b0\u5728\u300a\u9ad8\u7b49\u5fae\u79ef\u5206\u300b\u4e2d\uff0c\u53ef\u4ee5\u8bf4\u201c\u5411\u91cf\u201d\uff0c\u662f\u8fde\u63a5\u201c\u53ef\u611f\u77e5\u4e16\u754c\u201d\u4e0e\u201c\u4e0d\u53ef\u611f\u77e5\u4e16\u754c\u201d\u7684\u6865\u6881\uff0c\u662f\u6570\u5b66\u7684\u201c\u6838\u6b66\u5668\u201d\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u770b\u5b8c\u7f8e\u56fd\u6559\u6750\u53ea\u6709\u4e00\u4e2a\u611f\u53d7\uff1a\u771f\u6b63\u597d\u7684\u6559\u80b2\u662f\u5c06\u590d\u6742\u7684\u4e1c\u897f\u7b80\u5316\uff0c\u5f3a\u5316\u57fa\u7840\u6982\u5ff5\u548c\u5b9e\u9645\u5e94\u7528\uff0c\u5f31\u5316\u5177\u4f53\u8ba1\u7b97\u548c\u903b\u8f91\u8bc1\u660e\uff0c\u6700\u7ec8\u8ba9\u666e\u901a\u5b66\u751f\u4e5f\u53ef\u638c\u63e1\u76f8\u5bf9\u6df1\u5965\u7684\u7406\u8bba\u77e5\u8bc6\uff0c\u5e76\u8fc5\u901f\u8f6c\u5165\u5b9e\u9645\u5e94\u7528\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u56fd\u5185\u7684\u6559\u80b2\u6b63\u597d\u76f8\u53cd\uff1a\u5f3a\u5316\u5177\u4f53\u8ba1\u7b97\u548c\u903b\u8f91\u8bc1\u660e\uff0c\u5374\u5f31\u5316\u4e86\u57fa\u7840\u6982\u5ff5\u548c\u5b9e\u9645\u5e94\u7528\uff0c\u6700\u7ec8\u751f\u4ea7\u4e86\u8bb8\u591a\u89e3\u9898\u9ad8\u624b\uff0c\u4f46\u4ed6\u4eec\u5b8c\u5168\u4e0d\u61c2\u8fd9\u4e9b\u6570\u5b66\u201c\u6709\u4ec0\u4e48\u7528\uff1f\u201d\u3002<\/p>\n\n\n\n<h2 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