{"id":29870,"date":"2021-09-22T17:39:49","date_gmt":"2021-09-22T17:39:49","guid":{"rendered":"https:\/\/www.enago.com\/academy\/tw\/?p=29870"},"modified":"2023-11-09T09:47:19","modified_gmt":"2023-11-09T09:47:19","slug":"using-mathematica","status":"publish","type":"post","link":"https:\/\/www.enago.com\/academy\/tw\/using-mathematica\/","title":{"rendered":"Mathematica\u2014\u2014\u80fd\u8207MATLAB\u5ab2\u7f8e\u7684\u5f37\u5927\u8a08\u7b97\u5de5\u5177"},"content":{"rendered":"

\u63d0\u5230\u8a08\u7b97\uff0c\u5927\u5bb6\u99ac\u4e0a\u806f\u60f3\u5230\u7684\u53ef\u80fd\u662f\u4f7f\u7528\u8a08\u7b97\u5668\u548cExcel\u8868\u683c\u3002\u5be6\u969b\u4e0a\uff0c\u5c0d\u65bc\u66f4\u52a0\u8907\u96dc\u7684\u5de5\u7a0b\u8a08\u7b97\u3001\u7a0b\u5f0f\u8a2d\u8a08\u548c\u4f5c\u5716\u9700\u6c42\uff0c\u76ee\u524d\u6700\u6d41\u884c\u7684\u5169\u5927\u8edf\u9ad4\u662fMATLAB\u548cMathematica\u3002\u5b83\u5011\u5747\u5728\u5927\u5b78\u6559\u5b78\u3001\u5b78\u8853\u754c\u548c\u5de5\u696d\u754c\u767c\u63ee\u8457\u91cd\u8981\u4f5c\u7528\u3002MATLAB\u66f4\u52a0\u9069\u5408\u5de5\u7a0b\u61c9\u7528\uff0cMathematica\u66f4\u52a0\u9069\u5408\u6578\u5b78\u5206\u6790\u3002<\/p>\n

Mathematica\u662f\u7531\u7f8e\u570b\u7684\u6c83\u723e\u592b\u52d2\u59c6\uff08Wolfram\uff09\u7814\u7a76\u516c\u53f8\u958b\u767c\u7684\u8a08\u7b97\u8edf\u9ad4\uff0c\u65bc1988\u5e74\u554f\u4e16\uff0c\u5728\u6578\u503c\u8a08\u7b97\u3001\u7b26\u865f\u904b\u7b97\u3001\u6578\u5b78\u7e6a\u5716\u548c\u52d5\u756b\u986f\u793a\u7b49\u65b9\u9762\u5177\u6709\u5f37\u5927\u80fd\u529b\u3002Mathematica\u4f5c\u70ba\u4e00\u7a2e\u4e92\u52d5\u5f0f\u8a08\u7b97\u5de5\u5177\uff0c\u80fd\u5920\u667a\u6167\u5316\u7406\u89e3\u7528\u6236\u8f38\u5165\u7684\u82f1\u6587\u8a08\u7b97\u547d\u4ee4\uff0c\u4f7f\u7528\u65b9\u4fbf\u3002\u5b83\u4f5c\u70ba\u4e00\u7a2e\u7a0b\u5f0f\u8a9e\u8a00\uff0c\u8a9e\u6cd5\u898f\u5247\u7c21\u55ae\uff0c\u8a9e\u53e5\u7cbe\u7149\uff0c\u80fd\u5920\u4f7f\u7528\u8f03\u5c11\u8a9e\u53e5\u5b8c\u6210\u8907\u96dc\u8a08\u7b97\u548c\u516c\u5f0f\u63a8\u5c0e\u7b49\u4efb\u52d9\u3002\u4f7f\u7528\u8005\u53ef\u4ee5\u9078\u64c7\u55ae\u547d\u4ee4\u5c0d\u8a71\u65b9\u5f0f\u6216\u6279\u6b21\u7a0b\u5f0f\u65b9\u5f0f\u9032\u884c\u8a08\u7b97\u3002<\/p>\n

Mathematica\u5167\u7f6e\u5927\u91cf\u51fd\u6578\uff0c\u4f8b\u5982Abs[x]\u8868\u793ax\u7684\u7d55\u5c0d\u503c\uff0cRandom[]\u8868\u793a\u7522\u751f[0, 1]\u5340\u9593\u4e0a\u7684\u4e82\u6578\uff0cFactor[expr]\u8868\u793a\u5c0dexpr\u9032\u884c\u56e0\u5f0f\u5206\u89e3\uff0cPlot[f[x], {x, xmin, xmax}]\u8868\u793a\u5bf9\u51fd\u6570f\u4f5c\u5716\u3002\u5b83\u53ef\u4ee5\u6c42\u89e3\u65b9\u7a0b\u3001\u65b9\u7a0b\u7d44\u548c\u4e0d\u7b49\u5f0f\uff0c\u4f8b\u5982\u4f7f\u7528Solve[x2<\/sup>-2x+1==0, x] \u547d\u4ee4\u6c42\u89e3\u65b9\u7a0b\u4e2d\u7684\u672a\u77e5\u6578x\u3002\u5b83\u53ef\u4ee5\u6c42\u5c0e\u6578\uff0c\u4f8b\u5982\u4f7f\u7528D[f, x1, x2, x3] \u547d\u4ee4\u80fd\u5920\u6c42f\u95dc\u65bcx1\u3001x2\u3001x3\u7684\u504f\u5c0e\u6578\u3002\u5b83\u53ef\u4ee5\u6c42\u7a4d\u5206\uff0c\u4f8b\u5982\u4f7f\u7528Integrate[f, {x, a, b}]\u547d\u4ee4\u80fd\u5920\u6c42\u51fd\u6578f\u76f8\u5c0d\u65bcx\u5728x=a\u5230x=b\u7684\u7bc4\u570d\u5167\u7684\u7a4d\u5206\u503c\u3002\u5b83\u9084\u53ef\u4ee5\u6c42\u89e3\u5e38\u5fae\u5206\u65b9\u7a0b\u548c\u504f\u5fae\u5206\u65b9\u7a0b\uff0c\u4f8b\u5982\u4f7f\u7528DSolve[{x\u2019\u2019[t]-3x\u2019[t]+8y\u2019[t]+4y[t]==0, x\u2019[t]-2y\u2019[t]+7x[t]==3 Exp[t]}, {x[t], y[t]}, t]\u7684\u547d\u4ee4\u80fd\u5920\u6c42\u89e3\u5f15\u6578\u70bat\u7684\u5e38\u5fae\u5206\u65b9\u7a0b\u7d44\u3002\u5f9e\u4ee5\u4e0a\u5e7e\u500b\u4f8b\u5b50\u53ef\u4ee5\u770b\u51fa\uff0cMathematica\u7684\u8a08\u7b97\u65b9\u5f0f\u662f\u4f7f\u7528\u5927\u91cf\u5167\u7f6e\u51fd\u6578\u547d\u4ee4\uff0c\u975e\u5e38\u4fbf\u65bc\u8a08\u7b97\u548c\u516c\u5f0f\u63a8\u5c0e\uff0c\u514d\u53bb\u4e86\u4f7f\u7528\u8005\u67e5\u627e\u6f14\u7b97\u6cd5\u4e26\u4f7f\u7528FORTRAN\u6216C\u8a9e\u8a00\u81ea\u5df1\u7a0b\u5f0f\u8a2d\u8a08\u7684\u9ebb\u7169\u3002<\/p>\n

Mathematica\u8207MATLAB\u5728\u5f88\u591a\u8a08\u7b97\u3001\u7e6a\u5716\u548c\u7a0b\u5f0f\u8a2d\u8a08\u7684\u529f\u80fd\u4e0a\u985e\u4f3c\u3002\u5b83\u5011\u4e4b\u9593\u7684\u5340\u5225\u53ef\u4ee5\u6b78\u7d0d\u70ba\u4ee5\u4e0b\u5e7e\u9ede\uff0c\u5404\u6709\u512a\u52a3\u3002<\/p>\n

    \n
  1. MATLAB\u5728\u8edf\u9ad4\u8a9e\u8a00\u898f\u5247\u3001\u7a0b\u5f0f\u8a2d\u8a08\u4fbf\u5229\u6027\u548c\u7a0b\u5f0f\u8abf\u8a66\u65b9\u9762\u6bd4Mathematica\u66f4\u52a0\u65b9\u4fbf\u6613\u7528\u3002<\/li>\n
  2. MATLAB\u5305\u62ec\u5404\u7a2e\u5de5\u5177\u5305\uff0c\u4f8b\u5982\u4fe1\u865f\u8655\u7406\u5de5\u5177\u5305\u3001\u512a\u5316\u5de5\u5177\u5305\u3001\u795e\u7d93\u7db2\u8def\u5de5\u5177\u5305\u3001\u63a7\u5236\u7cfb\u7d71\u5de5\u5177\u5305\u3001\u6a23\u689d\u5de5\u5177\u5305\u3001\u7b26\u865f\u6578\u5b78\u5de5\u5177\u5305\u3001\u5f71\u50cf\u8655\u7406\u5de5\u5177\u5305\u3001\u7d71\u8a08\u5de5\u5177\u5305\u7b49\u3002<\/li>\n
  3. \u7531\u65bcMathematica\u63d0\u4f9b\u4e00\u7a2e\u7a31\u70ba\u201cNotebook\u201d\u7684\u4f7f\u7528\u8005\u4ecb\u9762\uff0c\u683c\u5f0f\u9748\u6d3b\u53cb\u597d\uff0c\u56e0\u6b64\u7528\u6236\u80fd\u5920\u5f88\u5bb9\u6613\u5730\u5c07\u8a08\u7b97\u7d50\u679c\u76f4\u63a5\u5b58\u6210\u5f59\u5831\u6f14\u8b1b\u7a3f\u683c\u5f0f\u7684\u6a94\uff0c\u5728\u9019\u65b9\u9762\u6bd4MATLAB\u66f4\u52a0\u65b9\u4fbf\u3002<\/li>\n<\/ol>\n

    \u95dc\u65bcMathematica\u7684\u4f7f\u7528\u65b9\u6cd5\uff0c\u672c\u6587\u5f9e\u7db2\u4e0a\u7cbe\u9078\u51fa\u4e00\u500b\u8a73\u7d30\u7684\u8996\u983b\u6307\u5357<\/a>\u548c\u4e00\u500b\u8b1b\u5ea7\u793a\u4f8b<\/a>\uff0c\u5efa\u8b70\u8b80\u8005\u89c0\u770b\u3002\u638c\u63e1Mathematica\u7684\u95dc\u9375\u662f\u719f\u6089\u5176\u8a9e\u6cd5\u898f\u5247\u3002\u4ee5\u4e0b\u7e3d\u7d50\u5b83\u768420<\/strong>\u689d\u91cd\u8981\u8a9e\u6cd5\u898f\u5247<\/strong>\u3002<\/p>\n

      \n
    1. \u542f\u52a8\u8f6f\u4ef6\u5f8c\uff0c\u51fa\u73b0Notebook\u7a97\u53e3\u3002\u8f93\u5165\u7528In[ ]\u8868\u793a\uff0c\u8f93\u51fa\u7528Out[ ]\u8868\u793a\uff0c\u6309\u201cShift+Enter\u201d\u9375\u904b\u884c\u8a08\u7b97\u3002<\/li>\n
    2. \u7528\u6236\u5728Notebook\u754c\u9762\u4e0b\uff0c\u4f7f\u7528\u201c?\u201d\u6216\u201c??\u201d\u53ef\u67e5\u8be2\u51fd\u6570\u7684\u5b9a\u4e49\u548c\u7528\u6cd5\uff0c\u83b7\u53d6\u5e2e\u52a9\u4fe1\u606f\u3002\u5982\u679c\u4f7f\u7528\u4e24\u4e2a\u95ee\u53f7\u201c??\u201d\uff0c\u5219\u5e2e\u52a9\u4fe1\u606f\u4f1a\u66f4\u8be6\u7ec6\u3002\u4f8b\u5982\uff0c\u201c?Plot*\u201d\u7ed9\u51fa\u6240\u6709\u4ee5\u201cPlot\u201d\u5f00\u5934\u7684\u547d\u4ee4\u3002<\/li>\n
    3. \u5b8c\u6210\u8ba1\u7b97\u540e\uff0c\u70b9\u51fbFile->Exit\u83dc\u5355\u9000\u51fa\u3002\u5982\u679c\u6587\u4ef6\u672a\u5b58\u76d8\uff0c\u7cfb\u7edf\u5c06\u63d0\u793a\u7528\u6237\u5b58\u76d8\uff0c\u6587\u4ef6\u540d\u4ee5\u201c.nb\u201d\u4f5c\u4e3a\u540e\u7f00\uff0c\u79f0\u4e3aNotebook\u6587\u4ef6\u3002\u9700\u8981\u518d\u6b21\u4f7f\u7528\u5b58\u76d8\u7684\u6587\u4ef6\u65f6\uff0c\u53ef\u4ee5\u70b9\u51fb\u6253\u5f00\u3002<\/li>\n
    4. Mathematica \u4e25\u683c\u533a\u5206\u5927\u5c0f\u5199\u3002\u5167\u7f6e\u51fd\u6570\u7684\u9996\u5b57\u6bcd\u9808\u5927\u5beb\u3002\u7576\u51fd\u6570\u540d\u7531\u51e0\u4e2a\u5355\u8bcd\u6784\u6210\u65f6\uff0c\u6bcf\u4e2a\u5355\u8bcd\u7684\u9996\u5199\u5b57\u6bcd\u5fc5\u987b\u5927\u5199\uff0c\u4f8b\u5982\uff1a\u6c42\u5c40\u90e8\u6781\u5c0f\u503c\u51fd\u6570FindMinimum[f[x], {x, x0]\u3002<\/li>\n
    5. \u7528\u6236\u81ea\u5b9a\u4e49\u53d8\u91cf\u987b\u4ee5\u5c0f\u5199\u5b57\u6bcd\u5f00\u5934\uff0c\u540e\u8ddf\u6570\u5b57\u548c\u5b57\u6bcd\u7684\u7ec4\u5408\uff0c\u957f\u5ea6\u4e0d\u9650\u3002<\/li>\n
    6. \u7279\u6b8a\u5b57\u5143\uff1a<\/li>\n<\/ol>\n

      Pi \u8868\u793a\u5713\u5468\u7387\u3002<\/p>\n

      E\u8868\u793a\u81ea\u7136\u5e38\u6578\u3002<\/p>\n

      Degree\u8868\u793a\u89d2\u5ea6\u8f49\u63db\u70ba\u5f27\u5ea6\u7684\u5e38\u6578\uff0c\u7b49\u65bcPi\/180\u3002<\/p>\n

      I\u8868\u793a\u865b\u6578\u55ae\u4f4d\uff0c\u5176\u503c\u70ba-1\u7684\u5e73\u65b9\u6839\u3002<\/p>\n

        \n
      1. \u53d8\u91cf\u8d4b\u503c\u89c4\u5219\uff1a<\/li>\n<\/ol>\n

        x=a\u8868\u793a\u5c07\u8b8a\u6578x\u7684\u503c\u8a2d\u70baa\u3002<\/p>\n

        x=y=b\u8868\u793a\u5c07\u8b8a\u6578x\u548cy\u7684\u503c\u5747\u8a2d\u70bab\u3002<\/p>\n

        x=.\u6216Clear[x]\u8868\u793a\u6e05\u9664\u8b8a\u6578x\u7684\u503c\u3002<\/p>\n

        Remove[f]\u8868\u793a\u5c07f\u5f9e\u7cfb\u7d71\u4e2d\u6e05\u9664\u3002<\/p>\n

          \n
        1. \u8b8a\u6578\u95dc\u4fc2\u898f\u5247\uff1a<\/li>\n<\/ol>\n

          \u7576xy\u4e2d\u9593\u6c92\u6709\u7a7a\u683c\u6642\uff0c\u8996\u70ba\u8b8a\u6578xy\u3002<\/p>\n

          \u7576x y\u4e2d\u9593\u6709\u4e00\u500b\u7a7a\u683c\u6642\uff0c\u8996\u70bax\u4e58y\u3002<\/p>\n

          3x\u8868\u793a3\u4e58x\u3002<\/p>\n

          x3\u8868\u793a\u8b8a\u6578x3\u3002<\/p>\n

            \n
          1. \u51fd\u6570\u540d\u548c\u81ea\u53d8\u91cf\u53c2\u6570\u4e4b\u95f4\u7528\u5206\u9694\u7b26[ ]\u8868\u793a\uff0c\u800c\u4e0d\u662f\u7528\u6570\u5b66\u4e66\u4e0a\u5e38\u7528\u7684\u5706\u62ec\u53f7\u201c( )\u201d\u8868\u793a\u3002<\/li>\n
          2. \u8b8a\u6578\u7684\u6e05\u55ae\u503c\u548c\u7bc4\u570d\u7528\u5927\u62ec\u5f27{ }\u8868\u793a\u3002<\/li>\n
          3. \u95dc\u65bc\u6578\u5b78\u8868\u8fbe\u5f0f\u7684\u8f93\u5165\uff0cMathematica\u5141\u8bb8\u7528\u6237\u4f7f\u7528\u4ee5\u4e0b\u4e24\u79cd\u683c\u5f0f\u3002\u5f62\u5982x\/(1+7x)+y\/(x-2)\u7684\u79f0\u4e3a\u4e00\u7ef4\u683c\u5f0f\u3002\u5f62\u5982\u4e0b\u5f0f\u7684\u4f7f\u7528\u5de5\u5177\u680f\u8f93\u5165\u7684\u683c\u5f0f\u79f0\u4e3a\u4e8c\u7ef4\u683c\u5f0f\uff1a\u3002<\/li>\n
          4. \u51fd\u6578\u7684\u5c55\u958b\u8207\u5206\u89e3\uff1a<\/li>\n<\/ol>\n

            Expand[expr]\u8868\u793a\u5c07expr\u5c55\u958b\u3002<\/p>\n

            Factor[expr]\u8868\u793a\u5c0dexpr\u505a\u56e0\u5f0f\u5206\u89e3\u3002<\/p>\n

            Simplify[expr]\u8868\u793a\u5c07expr\u5316\u7c21\u6210\u7cbe\u7c21\u7684\u5f0f\u5b50\u3002<\/p>\n

            FullSimplify[expr]\u8868\u793aMathematica\u6703\u5617\u8a66\u66f4\u591a\u7684\u5316\u7c21\u516c\u5f0f\uff0c\u5c07expr\u5316\u70ba\u66f4\u7cbe\u7c21\u7684\u5f0f\u5b50\u3002<\/p>\n

              \n
            1. \u5e38\u7528\u6578\u5b78\u51fd\u6578\uff1a<\/li>\n<\/ol>\n

              Sin[x], Cos[x], Tan[x], Cot[x], Sec[x], Csc[x]\u8868\u793a\u4e09\u89d2\u51fd\u6578\uff0c\u5176\u5f15\u6578\u7684\u55ae\u4f4d\u70ba\u5f27\u5ea6\u3002<\/p>\n

              Sinh[x], Cosh[x], Tanh[x]\u8868\u793a\u96d9\u66f2\u51fd\u6578\u3002<\/p>\n

              ArcSin[x], ArcCos[x], ArcTan[x]\u8868\u793a\u53cd\u4e09\u89d2\u51fd\u6578\u3002<\/p>\n

              Sqrt[x]\u8868\u793a\u6839\u865f\u3002<\/p>\n

              Exp[x]\u8868\u793a\u6307\u6578\u3002<\/p>\n

              Log[x]\u8868\u793a\u81ea\u7136\u5c0d\u6578\u3002Log[a, x]\u8868\u793a\u4ee5a\u70ba\u5e95\u7684\u5c0d\u6578\u3002<\/p>\n

              Abs[x]\u8868\u793a\u7d55\u5c0d\u503c\u3002<\/p>\n

              Round[x]\u8868\u793a\u6700\u63a5\u8fd1x\u7684\u6574\u6578\u3002<\/p>\n

              Floor[x]\u8868\u793a\u5c0f\u65bc\u6216\u7b49\u65bcx\u7684\u6700\u5927\u6574\u6578\u3002<\/p>\n

              Ceiling[x]\u8868\u793a\u5927\u65bc\u6216\u7b49\u65bcx\u7684\u6700\u5c0f\u6574\u6578\u3002<\/p>\n

              Max[a, b, c, …]\u548cMin[a, b, c, \u2026]\u5206\u5225\u8868\u793aa\u3001b\u3001c\u3001\u2026\u7684\u6975\u5927\u503c\u548c\u6975\u5c0f\u503c\u3002<\/p>\n

                \n
              1. \u95dc\u4fc2\u904b\u7b97\u5b50\uff1a<\/li>\n<\/ol>\n

                a==b\u8868\u793a\u7b49\u65bc\u3002<\/p>\n

                a!=b\u8868\u793a\u4e0d\u7b49\u65bc\u3002<\/p>\n

                a>b\u8868\u793a\u5927\u65bc\u3002<\/p>\n

                a>=b\u8868\u793a\u5927\u65bc\u7b49\u65bc\u3002<\/p>\n

                a<b\u8868\u793a\u5c0f\u65bc\u3002<\/p>\n

                a<=b\u8868\u793a\u5c0f\u65bc\u7b49\u65bc\u3002<\/p>\n

                  \n
                1. \u57fa\u672c\u904b\u7b97\u6cd5\u5247\uff1a<\/li>\n<\/ol>\n

                  a^b\u8868\u793a\u51aa\u6b21\u65b9\u3002<\/p>\n

                  a+b+c\u8868\u793a\u52a0\u6cd5\u3002<\/p>\n

                  2+6I\u8868\u793a\u8907\u6578\u5f62\u5f0f\u3002<\/p>\n

                  Conjugate[a+bI]\u8868\u793a\u5171\u8edb\u8907\u6578\u3002<\/p>\n

                  Re[z]\u548cIm[z]\u5206\u5225\u8868\u793a\u8907\u6578z\u7684\u5be6\u6578\u548c\u865b\u6578\u90e8\u5206\u3002Abs[z]\u8868\u793a\u8907\u6578z\u7684\u5927\u5c0f\u6216\u6a21\u6578\uff08Modulus\uff09\u3002Arg[z]\u8868\u793a\u8907\u6578z\u7684\u5e45\u89d2\uff08Argument\uff09\u3002<\/p>\n

                    \n
                  1. \u6c42\u548c\u8207\u6c42\u7a4d\u6cd5\u5247\uff1a<\/li>\n<\/ol>\n

                    Sum[f, {i, imin, imax}]\u8868\u793a\u6c42\u548c\u3002<\/p>\n

                    Sum[f, {i, imin, imax, di}]\u8868\u793a\u6c42\u6578\u5217\u4e4b\u548c\uff0c\u5f15\u6578i\u4ee5di\u905e\u589e\u3002<\/p>\n

                    Product[f, {i, imin, imax}]\u8868\u793a\u6c42\u7a4d\u3002<\/p>\n

                    Product[f, {i, imin, imax, di}]\u8868\u793a\u6c42\u6578\u5217\u4e4b\u7a4d\uff0c\u5f15\u6578i\u4ee5di\u905e\u589e\u3002<\/p>\n

                      \n
                    1. \u5fae\u5206\u6cd5\u5247\uff1a<\/li>\n<\/ol>\n

                      D[f, x]\u8868\u793a\u5c07\u51fd\u6578f\u76f8\u5c0d\u65bcx\u9032\u884c\u5fae\u5206\u3002<\/p>\n

                      D[f, x1, x2, \u2026]\u8868\u793a\u5c07\u51fd\u6578f\u76f8\u5c0d\u65bcx1\u3001x2\u3001\u2026\u9032\u884c\u5fae\u5206\u3002<\/p>\n

                      D[f, {x, n}]\u8868\u793a\u5c07\u51fd\u6578f\u76f8\u5c0d\u65bcx\u9032\u884cn\u6b21\u5fae\u5206\u3002<\/p>\n

                      D[f, x, NonConstants->{y, z, \u2026}]\u8868\u793a\u5c0d\u51fd\u6578f\u76f8\u5c0d\u65bcx\u9032\u884c\u5fae\u5206\uff0c\u4e26\u5c07y\u3001z\u3001\u2026\u8996\u70bax\u7684\u51fd\u6578\u3002<\/p>\n

                        \n
                      1. \u7a4d\u5206\u6cd5\u5247\uff1a<\/li>\n<\/ol>\n

                        Integrate[f, x]\u8868\u793a\u5c07\u51fd\u6578f\u76f8\u5c0d\u65bcx\u9032\u884c\u4e0d\u5b9a\u7a4d\u5206\u3002<\/p>\n

                        Integrate[f, {x, xmin, xmax}]\u8868\u793a\u5c07\u51fd\u6578f\u76f8\u5c0d\u65bcx\u9032\u884c\u5b9a\u7a4d\u5206\u3002<\/p>\n

                        Integrate[f, {x, xmin, xmax}, {y, ymin, ymax}]\u8868\u793a\u5c07\u51fd\u6578f\u76f8\u5c0d\u65bcx\u548cy\u9032\u884c\u5b9a\u7a4d\u5206\u3002<\/p>\n

                          \n
                        1. \u65b9\u7a0b\u5f0f\u6c42\u89e3\u6cd5\u5247\uff1a<\/li>\n<\/ol>\n

                          Solve[lhs==rhs, x]\u8868\u793a\u6c42\u89e3\u65b9\u7a0b\u5f0flhs==rhs\uff0cx\u662f\u5f15\u6578\u3002<\/p>\n

                          Nsolve[lhs==rhs, x]\u8868\u793a\u6c42\u65b9\u7a0b\u5f0flhs==rhs\u7684\u6578\u503c\u89e3\u3002<\/p>\n

                          Solve[{lhs1==rhs1, lhs2==rhs2, \u2026}, {x, y, \u2026}]\u8868\u793a\u6c42\u89e3\u65b9\u7a0b\u7d44\uff0c x\u548cy\u7b49\u662f\u5f15\u6578\u3002<\/p>\n

                          NSolve[{lhs1==rhs1, lhs2==rhs2, \u2026}, {x, y, \u2026}]\u8868\u793a\u6c42\u89e3\u65b9\u7a0b\u7d44\u7684\u6578\u503c\u89e3\u3002<\/p>\n

                          FindRoot[lhs==rhs, {x, x0}]\u8868\u793a\u7531\u521d\u59cb\u9edex0\u6c42\u65b9\u7a0blhs==rhs\u7684\u6839\u3002<\/p>\n

                            \n
                          1. \u4f5c\u56fe\u51fd\u6578\u4e3b\u8981\u5305\u62ecPlot\u3001Plot3D\u3001ParametricPlot\u3001ParametricPlot3D\u3001PolarPlot\u3001ContourPlot\u3001ContourPlot3D\u3001RevolutionPlot3D\u3001SphericalPlot3D\u3001DensityPlot\u3001DensityPlot3D\u3001RegionPlot\u3001RegionPlot3D\u3001ListPlot\u3001ListPlot3D\u3001ListContourPlot\u3001ListContourPlot3D\u3001ListContourPlot3D\u3001ListPointPlot3D\u3001ListDensityPlot\u3001ListDensityPlot3D\u3002\u7d71\u8a08\u5716\u4f5c\u5716\u51fd\u6578\u4e3b\u8981\u5305\u62ecHistogram\u3001Histogram3D\u3001DensityHistogram\u3001SmoothHistogram3D\u7b49\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

                            \u63d0\u5230\u8a08\u7b97\uff0c\u5927\u5bb6\u99ac\u4e0a\u806f\u60f3\u5230\u7684\u53ef\u80fd\u662f\u4f7f\u7528\u8a08\u7b97\u5668\u548cExcel\u8868\u683c\u3002\u5be6\u969b\u4e0a\uff0c\u5c0d\u65bc\u66f4\u52a0\u8907\u96dc\u7684\u5de5\u7a0b\u8a08\u7b97\u3001\u7a0b\u5f0f\u8a2d\u8a08\u548c\u4f5c\u5716\u9700\u6c42\uff0c\u76ee\u524d\u6700\u6d41\u884c\u7684\u5169\u5927\u8edf\u9ad4\u662fMATLAB\u548cMathematica\u3002\u5b83\u5011\u5747\u5728\u5927\u5b78\u6559\u5b78\u3001\u5b78\u8853\u754c\u548c\u5de5\u696d\u754c\u767c\u63ee\u8457\u91cd\u8981\u4f5c\u7528\u3002MATLAB\u66f4\u52a0\u9069\u5408\u5de5\u7a0b\u61c9\u7528\uff0cMathematica\u66f4\u52a0\u9069\u5408\u6578\u5b78\u5206\u6790\u3002 Mathematica\u662f\u7531\u7f8e\u570b\u7684\u6c83\u723e\u592b\u52d2\u59c6\uff08Wolfram\uff09\u7814\u7a76\u516c\u53f8\u958b\u767c\u7684\u8a08\u7b97\u8edf\u9ad4\uff0c\u65bc1988\u5e74\u554f\u4e16\uff0c\u5728\u6578\u503c\u8a08\u7b97\u3001\u7b26\u865f\u904b\u7b97\u3001\u6578\u5b78\u7e6a\u5716\u548c\u52d5\u756b\u986f\u793a\u7b49\u65b9\u9762\u5177\u6709\u5f37\u5927\u80fd\u529b\u3002Mathematica\u4f5c\u70ba\u4e00\u7a2e\u4e92\u52d5\u5f0f\u8a08\u7b97\u5de5\u5177\uff0c\u80fd\u5920\u667a\u6167\u5316\u7406\u89e3\u7528\u6236\u8f38\u5165\u7684\u82f1\u6587\u8a08\u7b97\u547d\u4ee4\uff0c\u4f7f\u7528\u65b9\u4fbf\u3002\u5b83\u4f5c\u70ba\u4e00\u7a2e\u7a0b\u5f0f\u8a9e\u8a00\uff0c\u8a9e\u6cd5\u898f\u5247\u7c21\u55ae\uff0c\u8a9e\u53e5\u7cbe\u7149\uff0c\u80fd\u5920\u4f7f\u7528\u8f03\u5c11\u8a9e\u53e5\u5b8c\u6210\u8907\u96dc\u8a08\u7b97\u548c\u516c\u5f0f\u63a8\u5c0e\u7b49\u4efb\u52d9\u3002\u4f7f\u7528\u8005\u53ef\u4ee5\u9078\u64c7\u55ae\u547d\u4ee4\u5c0d\u8a71\u65b9\u5f0f\u6216\u6279\u6b21\u7a0b\u5f0f\u65b9\u5f0f\u9032\u884c\u8a08\u7b97\u3002 Mathematica\u5167\u7f6e\u5927\u91cf\u51fd\u6578\uff0c\u4f8b\u5982Abs[x]\u8868\u793ax\u7684\u7d55\u5c0d\u503c\uff0cRandom[]\u8868\u793a\u7522\u751f[0, 1]\u5340\u9593\u4e0a\u7684\u4e82\u6578\uff0cFactor[expr]\u8868\u793a\u5c0dexpr\u9032\u884c\u56e0\u5f0f\u5206\u89e3\uff0cPlot[f[x], {x, xmin, xmax}]\u8868\u793a\u5bf9\u51fd\u6570f\u4f5c\u5716\u3002\u5b83\u53ef\u4ee5\u6c42\u89e3\u65b9\u7a0b\u3001\u65b9\u7a0b\u7d44\u548c\u4e0d\u7b49\u5f0f\uff0c\u4f8b\u5982\u4f7f\u7528Solve[x2-2x+1==0, x] \u547d\u4ee4\u6c42\u89e3\u65b9\u7a0b\u4e2d\u7684\u672a\u77e5\u6578x\u3002\u5b83\u53ef\u4ee5\u6c42\u5c0e\u6578\uff0c\u4f8b\u5982\u4f7f\u7528D[f, x1, x2, x3] \u547d\u4ee4\u80fd\u5920\u6c42f\u95dc\u65bcx1\u3001x2\u3001x3\u7684\u504f\u5c0e\u6578\u3002\u5b83\u53ef\u4ee5\u6c42\u7a4d\u5206\uff0c\u4f8b\u5982\u4f7f\u7528Integrate[f, {x, a, […]<\/p>\n","protected":false},"author":8210,"featured_media":29871,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1059,1058],"tags":[1175],"ppma_author":[1241],"class_list":["post-29870","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-phds-postdocs","category-career-corner","tag-digital-tools-for-researchers"],"better_featured_image":{"id":29871,"alt_text":"Mathematica","caption":"","description":"\u63d0\u5230\u8a08\u7b97\uff0c\u5927\u5bb6\u99ac\u4e0a\u806f\u60f3\u5230\u7684\u53ef\u80fd\u662f\u4f7f\u7528\u8a08\u7b97\u5668\u548cExcel\u8868\u683c\u3002\u5be6\u969b\u4e0a\uff0c\u5c0d\u65bc\u66f4\u52a0\u8907\u96dc\u7684\u5de5\u7a0b\u8a08\u7b97\u3001\u7a0b\u5f0f\u8a2d\u8a08\u548c\u4f5c\u5716\u9700\u6c42\uff0c\u76ee\u524d\u6700\u6d41\u884c\u7684\u5169\u5927\u8edf\u9ad4\u662fMATLAB\u548cMathematica\u3002\u5b83\u5011\u5747\u5728\u5927\u5b78\u6559\u5b78\u3001\u5b78\u8853\u754c\u548c\u5de5\u696d\u754c\u767c\u63ee\u8457\u91cd\u8981\u4f5c\u7528\u3002","media_type":"image","media_details":{"width":750,"height":430,"file":"2021\/09\/pexels-nothing-ahead-3729557.jpg","filesize":59287,"sizes":{},"image_meta":{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0","keywords":[]}},"post":29870,"source_url":"https:\/\/www.enago.com\/academy\/tw\/wp-content\/uploads\/sites\/16\/2021\/09\/pexels-nothing-ahead-3729557.jpg"},"yoast_head":"\nMathematica\u2014\u2014\u80fd\u8207MATLAB\u5ab2\u7f8e\u7684\u5f37\u5927\u8a08\u7b97\u5de5\u5177 - Enago\u82f1\u8ad6\u95a3 \u90e8\u843d\u683c\uff1a\u8ad6\u6587\u64b0\u5beb\u8207\u79d1\u5b78\u7814\u7a76\u767c\u8868\u652f\u63f4<\/title>\n<meta name=\"description\" content=\"\u63d0\u5230\u8a08\u7b97\uff0c\u5927\u5bb6\u99ac\u4e0a\u806f\u60f3\u5230\u7684\u53ef\u80fd\u662f\u4f7f\u7528\u8a08\u7b97\u5668\u548cExcel\u8868\u683c\u3002\u5be6\u969b\u4e0a\uff0c\u5c0d\u65bc\u66f4\u52a0\u8907\u96dc\u7684\u5de5\u7a0b\u8a08\u7b97\u3001\u7a0b\u5f0f\u8a2d\u8a08\u548c\u4f5c\u5716\u9700\u6c42\uff0c\u76ee\u524d\u6700\u6d41\u884c\u7684\u5169\u5927\u8edf\u9ad4\u662fMATLAB\u548cMathematica\u3002\u5b83\u5011\u5747\u5728\u5927\u5b78\u6559\u5b78\u3001\u5b78\u8853\u754c\u548c\u5de5\u696d\u754c\u767c\u63ee\u8457\u91cd\u8981\u4f5c\u7528\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" 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