{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": "true" }, "source": [ "# Table of Contents\n", "

1  微分(Diff)-I
1.1  単純な微分(diff)
1.2  偏微分(PartialDiff)
1.3  例題:関数の微分と増減表
1.3.1  解答例
1.4  例題:接線(Tangent)
1.4.1  解答例
2  極限(limit)
3  微分(Diff)-II
3.1  級数展開(series)
3.2  全微分(D)
3.3  複合関数の微分
3.4  課題
3.5  解答例
3.5.1  幾つかの関数の微分
3.5.2  高階微分
3.5.3  0以外での級数展開と表示
3.5.4  2次元関数の級数展開と3dplot
4  きれいな微分表示
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "
\n", "微分(differential)\n", "
\n", "
\n", "
\n", "file:/~/python/doing_math_with_python/differential.ipynb\n", "
\n", "cc by Shigeto R. Nishitani 2017 \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 微分(Diff)-I" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 単純な微分(diff) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "単純な一変数関数の一次微分は,以下の通り." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 2 x - 3$" ], "text/plain": [ "2*x - 3" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import *\n", "x,y = symbols('x y')\n", "\n", "diff(x**2-3*x+2,x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "高次の微分は,微分変数を必要なだけ並べる." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - \\sin{\\left(x \\right)}$" ], "text/plain": [ "-sin(x)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(sin(x),x,x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "さらに高階微分は次のように.これはxについての3次微分を表わす." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 24 x$" ], "text/plain": [ "24*x" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(x**4,x,3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 偏微分(PartialDiff) \n", "複数の変数を持つ多変数の関数では,微分する変数を明示すれば偏微分が求められる." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 1 x + y\n", "─── - ─────\n", "x⋅y 2 \n", " x ⋅y\n" ] } ], "source": [ "eq1=(x+y)/(x*y)\n", "pprint(diff(eq1,x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 例題:関数の微分と増減表 \n", "\n", "次の関数とその1次導関数を同時にプロットし概形を確認し,さらに増減表を求めよ.\n", "\n", "\n", "$$\n", "\\frac {x}{{x}^{2}-2x+4}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 解答例 " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x \n", "────────────\n", " 2 \n", "x - 2⋅x + 4\n", " x⋅(2 - 2⋅x) 1 \n", "─────────────── + ────────────\n", " 2 2 \n", "⎛ 2 ⎞ x - 2⋅x + 4\n", "⎝x - 2⋅x + 4⎠ \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sympy import *\n", "from sympy.plotting import plot\n", "x = symbols('x')\n", "\n", "f0 = x/(x**2 -2*x + 4)\n", "pprint(f0)\n", "pprint(diff(f0,x))\n", "\n", "df0 = diff(f0,x)\n", "\n", "p = plot(f0,df0, show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 例題:接線(Tangent) \n", "次の関数の$ x=3$での接線を求め,2つの関数を同時にプロットせよ.\n", "\n", "$$\n", "y={x}^{3}-2\\,{x}^{2}-35\\,x\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 解答例 \n", "与関数をf0と定義." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle x^{3} - 2 x^{2} - 35 x$" ], "text/plain": [ "x**3 - 2*x**2 - 35*x" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import *\n", "from sympy.plotting import plot\n", "x = symbols('x')\n", "\n", "f0 = x**3 -2*x**2 - 35*x\n", "f0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "微分関数をdfと定義" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2 \n", "3⋅x - 4⋅x - 35\n" ] } ], "source": [ "pprint(diff(f0,x))\n", "df0 = diff(f0,x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "接点(x0,f0(x0))で傾きdf(x0)の直線をf1と定義." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-20⋅x - 36\n" ] } ], "source": [ "x0 = 3\n", "a = df0.subs({x:x0})\n", "f1 = a*(x-x0)+f0.subs({x:x0})\n", "pprint(f1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2つの関数を同時にプロット." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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alAK6d5cdm60cYCdPyu4tf/4pg72UFNl2LCVFpjIyM+VxPXpIGLVoIb85JiTIIDA3VwKtuFjKBmTrsh07pBOqcWPZCebaD19foH79GpVudQwrqo6jR+V7vXt34N13gY4dta5IEwwruio3V0Zge/eWXQtWEmB+fpV3ZA4KksYOM86elZDZvVs+EhIkrDp3losY69SRtYFLwsTXVzaHa9pUPm65BahbV566eXMZcQEy2iookGUbL1yQkdfx4zJ4TE6W8Dt2TB5Tol8/uR6lRw9ZLy0wUP7evr128/0MK7LU8ePAHXfIj+fmzU655p+lGFZ0AyUBdu0UoskkSZOfDwQHo7iXEb/XD8b3J4OxaocPmjSRaz8ACajevWXWsVcvoEMHmXl0d6+dkk0mGaWVBNexYxKYv/5atpUZICOxBx4AmjUD/vIXoH9/+bstMKzIEqmpMqLKzpYllZxkE8WbxbCiarp0Cdi3D4X7f8eplT/B87dEtDj7O9xhAgAcaNgH9fTN4dY7GC2HBeOWO65OIdpB21JurqxB/OuvMgt6+rRcAXDlitzfubME15Ah8qdeXzt1MKyoKunpElRZWcDGjfILn4tjWJHllJJzRJ99BqxcKb/x9ewJ/KXnJTzQcR9C3BNR72wa8MMPcoLKJAGGVq1k6vD228s2tmzTxi4CLC9Ppil37JCPXbvktkuXgC5dgNBQ+bjzThmNWQPDim4kI0O+3zIypOuvb1+tK7ILDCuq2rlzwPLlwMKFcrK3fn25BnnCBHkj9zB32filSzKEKWngSEyUVqbt2+X+li3LlpAq+bCDADOZZAuzjRuBDRtk59XLl2Xa8sEH5eT2vffKye6bLZVhRddz+rQEVWoqEBcnI3wCwLCiG0lJAd55B/joI3nDDg8HwsIkqBo2vIlPWD7ASj4OHpT76tSRocu1XYh6vaYBVlAgo62NG+XcV1yc3N6uHXDPPfIxcKA0hFiKYUXmZGQAo0fLj8jatdJYQaUYVlTZ7t3Am28CX30lI4q//x146ikZTVjdpUtyAqlk9FUSYCaTbGaZn195BKZhgGVkAGvWAKtXy8jr8mU519Wzp7zRDB8u3Yw3wrCia/3+u/wieOutwNtvyy9AVAHDisocOAA895w0IWRnA48+CsyYcd0O9dpz+bL8ennwoEwbJiSUBRggP9VKVQwxDQIsPx/48Ufgm2+AmBg5GV63rpQ3erSMusyd52JYUXnbtgEjR8qF72vWyLczVcKwIhktzJol030NG8pCmZMny5q6dqMkwBITpQd90yYJsOJiub9FC+D++ysu5mujAFu3bh1mzHgSly71Qvv2T+L48WCcPCkzm+Hh0l04cmTZ1CnDikpER8s6fx06SF8St/q4LoaVK7t0CXjrLWDePLnAdvp0Wd7IVtcb1djlyzKFWDJ9mJEhc3PlAyw4WBZU8/OTv7dta9UAKy4uRqdOnbBhwwbo9Xr07t0bn3/+BS5e7Io1a6QxJTVVRlx33y3hNWeOEXv2MKxcmVLAG28AzzwjTbIxMS65hFJ1MKxcVWws8Mkn8kPyt78BkZGAwaB1VVaQl1e5iaOkxQ+QAAsKqngOrF27mw6wnTt34qWXXkLc1c6LyMhIAMBzzz0HQJ56507gyy+l3f/0aaBhQyNGjUrA+PGSo2a7KclpFRXJ9PrixbLFxyefVK9Bx0XVPKyGDRumzpw5Y5VqsrKy0KJFC6t8LltypLqvXJHf9LOzZVHYRo3OQ69vonVZN8Xi424ySYhdvizDycuX5d+AHIQrV6Qfv3596Y6oX9/iJa2zs7ORk5OD9u3bAwDOnj2LS5cuoV27dpVqPXPmDIqL66Ow8CLc3LqjuFiCqvwyU/bOkb7Xy7OXuouKgBMnZLmwFi0su/DcXmqvLmvWnZiYGKeUGlblA5VSN/qwmuDgYGt+OptxhLpNJqWWLVOqaVOlPD2Veu01pQoLHaP266lR7ZcvK7Vrl1IffKDUlClKBQYq5e6ulMzQKNW8udz+/PNKff21UseOyUG8xsqVK9XUqVNL/718+XL1f//3fzd86vr166u8PPm0998vXw9A/v7SS0r9+efNv6za5qjfL/ZQ9+bNSnl7K+XlpdSKFZb/P3uo/WZYue6qcghKKe4U7OjOnAFeeglYtEjWwFuyRBaScGn16gF9+sjHI4/IbXl5Fc+BJSfLSaeiIrm/WTNp4mjeXKYPjUbo27RBampq6adNS0uDjwUr1NetK5/q/vtlYd6vv5ZruF5+Wb5W/fvLRddjxjjQOUQyq7hYmpZefRXo1EmuoXLhBWlrFcPKgW3fLif1MzOB998HIiJqbxFZh1c+wErk51cMsJwc2aL1aoD1bdYM/7l8Gdn//Cca3H47ti1fjjdXrarW0zZpAkydKh+pqbJl+aefSsPL449LY8aECdIK7+VlxddLtS49HRg/Hti6Vbr+3nsPaNBA66qcWBVDL6v58MMPrfnpbMYe6y4uVmruXJnZ8vNTas8e84+zx9otpVnteXlK/fKLUu+/r9TUqep8hw4quU6dsinEZs2UGjxYqWefVerbb5VKSakwhdiuXbsqn8Jkkq/Zk08q1bq1fNoBA5R6+GGltm6Vr68WHPX7RYu616yR2eRbbpEp+JvFY66UsnAakN2ADubMGfkt7ocfZBuMJUvs7JopZ5SfL1dTl1+J48ABWYV0+3bpoLjafWhcuRIJGzfKNisWdCEWFcllZXFxwIcfSn9I+/byG/uECZzStTe5udKW/sorsnfaypWyygnVCFvXnc3OnXKeIzNT1vWbNk3ztWFdV36+BFZCQlmIHTgAY1EREgBg8ODKK3FUEWC5uXLZwWefyYrcJpN04k+YIG3QNdzQmWpAKWDVKuDJJ2VD0EcekcBiW7pVMKycyeefA3PmyN8//dTlN2uzT/n5MPbqhYTHHwcOH5b1mn77rayJo2lT+cINGCC/jgcHy7IGZgLs1Cm5fuuzz2STyQsXgL/+VdZyHD1a1pkj2/j9d+Cxx2QE3LNnWTMTWY1lv3JXMU9YLStXrlRdu3ZVOp1O7d69u8J9c+bMUX5+fqpTp05q3bp1Zv//2bNnVWhoqDIYDCo0NFSdO3euuiXU2JgxY1RgYKAKDAxU7du3V4GBgWYf1759e9W9e3cVGBhYq+2nJpO0ogNK3XmnUmfOXP+xs2bNUj4+PqX1r1mzxuzj1q5dqzp16qT8/PxUZGRkLVVuuaeeekp17txZBQQEqFGjRqns7Gyzj7PVMbfE9Y5hSV0mk0k99thjyr9DBzXWz08df+45pR56SKlevZRq3LjsHNittyo1aJD0ta9cqdSRI5Xa6A8dUurFF5Xq2FH+S506St17r7RI5+ZaXvOJEyfUnXfeqbp06aK6du2q5s+fX+kxW7ZsUY0aNSr9Hnr55Zdv6vjUhqq+/iXH3M/PTwUEBKjExMQaPd/Fi0rNnKmUh4d8yd57T6mioup/nkOHDpUez8DAQNWwYUP1zjvvVHiMvRz3f/zjH6pFixaqW7dupbdZ+r5cg/cVi85ZWTWsDh48qA4dOqQGDBhQIaySkpJUjx49VH5+vjp69Kjq0KGDKjLzVX/66adLX2RkZKSaOXNmdUuwqieffPK63zTt27dXWVlZtfr8hYXy/gYo9fe/K5Wff+PHz5o1S73xxhs3fExRUZHq0KGDOnLkiCooKFA9evRQSUlJVqy6+uLi4tSVK1eUUkrNnDnzul93WxxzS9zoGJa8ia5Zs0YNGzZMmUwmtXPnThUSElL2CfLzldq9W64De/hhCbDbb68cYM88UyHATCalEhKkMaNNG3nooEFKPfCAUl9+WXVwnTx5svQNPCcnR3Xs2LHS137Lli3q7rvvtt7BsqKqvv43PObVYDLJ8Sw5xv/4h1KnT99s1RUVFRWpVq1aqWPHjlW43V6O+9atW1ViYmKFsLLkfbmG7ysWhZWbNcdy/v7+6GzmbGNsbCzCw8Ph5eUFX19fGAwGxMfHm33cpEmTAACTJk1CTEyMNcurFqUUVq5ciXHjxmny/BcvykaAS5YA//mPTAdZo7U5Pj4eBoMBHTp0gKenJ8LDwxEbG1vzT1wDQ4YMgcfVdYn69u2LtLQ0TeupiiXHMDY2FhMnToROp0Pfvn1x/vx5ZGRkyJ1eXnIu65FHgKgoYM8eOUm1ezfwwQeyRlZ2tuwnMWaMrH0YGgrd4FAEr3wGb/VZiRNbjuDHLQq9e0vr9NixsmrC6NGygOrFi5Xr9vb2RtDV+eOGDRvC398f6enptX24bOaGx9wCJpOcM+zfX85NtWwJ/PwzsHSp/N0aNm3aBD8/v9JVUezNHXfcgabXLGRoyfuyLd5XrBpW15Oeno62bduW/luv15v9ITl9+jS8vb0ByA9WZmamLcoz66effkKrVq3QsWNHs/frdDoMGTIEwcHBiIqKsupznzwpm7Nt3CjvZa+9ZnkjxXvvvYcePXpgypQpyM7OrnS/pV8LrSxduhRhYWFm76vNY14dlhzDah/nunUrBlhioiROQoK0CfboIVcYz58PjB0Lt04GDLivKSLTJyJj4jM48OJKzBx9BD/vUBg3Tt5c/+//ZG26rKzKT3fs2DHs3bsXfcpfd3bVzp07ERgYiLCwMCQlJVXz6NSeqr7+N/u9XVQkvwwGBACjRskaj2++Kb879OtnzVcAREdHX/cXYHs97pa8L9vifaXaFwWHhobi1KlTlW6fPXs2Ro4cafb/KDNNHDoN29gseQ1ffPHFDUdVO3bsgI+PDzIzMzF48GB06dIFd1hh+8+jR2UhzGPHgO+/l/2TLK192rRpeOGFF6DT6fDCCy/g3//+N5YuXVrhcVp9LSw55rNnz4aHhwfGjx9v9nPU1jGvLkuOoVWOs5dXWSdhicJC6UIsaaHPzYXbu/PRrbAQ3QDMatIEF4KCkKAzYuvm3nh1US9MQQf0/4sOI0YAI0YAbdrkYvTo0Zg/fz4aXXPdQ1BQEI4fP44GDRrghx9+wKhRo5CcnFy9umtJVV//6h7zvDy5BvyNN+TnrXt3aWQaM6Z2FiAuLCzEd999V7ogcnn2fNwtYYv3lWp/STZu3FjtJ9Hr9RYtW9OqVStkZGTA29sbGRkZaGmtsfc1qnoNRUVF+Oabb5CYmHjdx5TU37JlS9x3332Ij4+v8RvnkSOyi2huruyGYTRWv/YSDz/8MO65555Kt1v6tbC2qupetmwZVq9ejU2bNl33m7w2jvnNsOQY1tpx9vSUjsKgIODhh+W2pUtLA0yXmIgmiYkI3T8fgwID8Sp2I69uE/y2Pwg/7gjGrGeCcaypQr0u/4OnZxBycyuuulA+vIYPH47p06fjzJkzaN68ec1rr6Gqvv6WHvP9+4Fly4CkJLm+rW9f4N13ZTURt1qca1q7di2CgoLQqlWrSvfZ83G35H3ZJu8rVZzUuinXNlgcOHCgQoOFr6+v2QaLp556qsKJvKeffvpmS6iRtWvXqjvuuOO69+fm5qqcnJzSv/fr10+tXbu2Rs95+LCc0G3WTKm9e2/uc5w8ebL072+//bYaO3ZspcdcuXJF+fr6qqNHj5aeCD1w4MBNVm0da9euVf7+/iozM/O6j6mNY36zbnQMSxosVq9eXeFkf+/evW1bZEGBfCNFRSn1yCNKGY3KVLKqLqCy0Vh9jEnqTben1Mv+X6iP/5Osdu00qRMnMpTpajfiL7/8otq2bVv6by1Z8vW/0TE/fVqpd95RqmfPso7KyZOV2rLF7BrGtWLs2LFq6dKlZu/LyLCf456SklKhwcKS9+Uavq/Yvhvwm2++UW3atFGenp6qZcuWasiQIaX3vfbaa6pDhw6qU6dO6ocffii9ferUqaXBdubMGXXXXXcpg8Gg7rrrLnX27NnqlmAVkyZNUosXL65wW3p6ugoLC1NKKXXkyBHVo0cP1aNHD9W1a1f12muv1ej5/vhDKR8fWb7l119v/vNMmDBBde/eXQUEBKh77723NLzK166UdE117NhRdejQoca1W4Ofn5/S6/WlbbuPPPKIUqp2j3lNmTuGixcvLl1uyWQyqenTp6sOHTqo7t27V7qUQwvbN29WPQH1Ups26sumLdQ3t/ipQrc6FQJss+5O9UKdR1RE48lqmN9YtXnjdq3LVkpd/+u/ePHi0p/Va4/5t9/uV4sWKRURIe3ngFJGo1ILFypl66bSS5cuqaZNm6rz58+X3la+9oULF6quXbuqHj16qD59+qgdO3bYtsCrwsPDVevWrZWHh4dq06aNWrJkyXXfl634vsLllhzBoUPAXXfJSd7Nm2XenByXw21rX1gIJCXhwuZEnIlLhMeviTh/0R2BebsAABfdGuHwLUHI7hAMjz7BaHWPER2H+sHD0ya9WdVy8SKwZYtM7cXFybQ6IFPrvXsDEycC3bppWyOZxRUs7N2xY7JkUlKSbC3AHyTH53BhZU5hIS78nISUrxJhSkhEvYOJ8L24H54oQB7qowge+LNREM60D8aVgGDU+2sw9Hca4OvnZum+ljV27pxsGr1vX9lH/frArl2y0eXAgcDQocCQIUDHjlyWzM4xrOxZVpYsn5OZCWzbJm2z5PicIqzMMBVcwfG1STj9QyJMvySgRWoi2mbvR10UAAD2IhAXcCv+bBIMBAUjpWkw3DoZ0MrbDd7eQKtWslVYo0YSJrfcUrnjzmSSgd7ly9Kln50ty06lpcn2KiV/njsn4VTC21uWQRo8WP7s35/brTgYhpW9ys2Vqb/ffpNrqf7yF60rImtx1rAy68oVXPg5CWfXJ+Ji0nE03R2HVqd+hadJAuwCGmEH+uN3dMWxpsGIO2dEq/4G7PzFDe3ayZR33bqyyvyxY9JKfvasjI46d5bQKmkwc3OThXzbtpXuvdatJZgCAyUIyaExrOxRYaGsTLFpE/Dtt/J3ch4uFVbmXLkCHDwIJMoUYkFqJrw2rIZbQT4AoLBuQ5xuE4RTPsE40z4Yp9oEw71LR5w77wY3N5muU0pGYQ0ayMXNer2EU21c+0R2gWFlb0wm4MEHZbfYjz4CpkzRuiKyNpcPK3PKBVjpx759QEEB0KaN7NDcq1fZBdDBwbJHfG1e9ET2hGFlT5QC/v1v2YcqMhJ49lmtK6LawLCy0JUr0lmUmChrIyYmSsdEvozA0KABMHKkDK0YYM6OYWVPFi2SpVz69JH1Sdmd5JwYVjVw5YpsHlUy+rp4UbbiLR9gvXrJ0i79+8tJLwaYM2BY2YvNm6WFdvhwICaGP1vOjGFlZUVFZQFWsiPzr79KZ8WuXWUBFhxctiszA8zu7d69G1OnTkV8fDzq1avXAEA8gLFKqQPX+z8Mq1p25AgQEiIniHfulNZdcl4MKxsoH2Dlz4Hl5cn9d9wh8+7XngNzd9e0bKrov//9L/Lz8/HWW2+9DyBNKVV5hd9yGFa1KCdHthjIyJDtBvz8tK6IahvDSiNFRbIcTGKi9MHHxVUMsAEDgOLiigHWuTMDTEOFhYXo3bs39u/fHw+gv1Kq+EaPZzNoLTGZgAkTgD/+kJ8bBhVRLfLwkHNYJeuVzZplPsCiosoCrHFjuVirZ08GmAbOnTuH3NxcAGgIoC6ASzd6PEdWteSFF2TTxIULZRM8cg0cWdm58gF26JAsH7Nvn1yBDMjSGnffLctiMMBq1YgRIxAeHo7x48f/F4C3UuqG75QMq1oQGws8/zwwaBCwYAE7/1wJw8oBFReXBVhiInDhArBqVcUAKxl99esna6N16cIAq4Hly5cjJiYG33zzDXQ6nQeAnwE8p5TafL3/w7CyspQU2RfPzw/YsYNrlLkahpWTuDbASq4Hq19f1oSqX78swEq6EBlgN4ut67ZWUADcfjtw+LB8X3fooHVFZGsMKydWVCQnocsH2N69ZSOwgQPlTaBk+tBoZIBZhmFlazNmyDmqb74B7rtP62pICwwrF1NcXBZgf/wB/PhjxQCrXx+4/37g1lvLQqxLFy50WBHDypa++gp44AHgiSdkSSVyTQwrqhBgJZ2IGzaUBVi9ejKFOGwY0K5d2QjMdQOMYWUrx48Djz4qe/Bs3QqbbUBHlnv66afx/fffw9PTE35+fvj444/RpEkTAEBkZCQ++ugjuLu7491338XQoUMBAImJiZg8eTLy8vIwfPhwLFiwALoqumUYVmTWtQGWmCirbGzbJveXBFhoqJw/CA4G/P1dJcAYVrZgMknXX8lF9DxPZZ/Wr1+Pu+66Cx4eHnjmmWcAAK+//joOHjyIcePGIT4+HidPnkRoaCgOHz4Md3d3hISEYMGCBejbty+GDx+OGTNmICws7IbPw7AiixUXywnu8gFWt66MwoCyACvfheicAWZRWDndq7a1+fNlmnrpUgaVPRsyZEjp3/v27YuvvvoKABAbG4vw8HB4eXnB19cXBoMB8fHxuO2225CTk4N+/foBACZOnIiYmJgqw4rIYu7uEj7+/rKCACABlpxctg5iYiLwySfSSn/6tARYYGDFlTi6dnXGAKvE+V9hLTpwAHjuOdnJYPJkrashSy1duhRjx44FAKSnp6Nv376l9+n1eqSnp6NOnTrQ6/WVbjcnKioKUVFRAICsrKxarJycnru7nL/q0qVigJW0GJcE2LJlspVDly5yHsIFAsy5Xo0NFRbK91KTJrKCCy/81V5oaChOnTpV6fbZs2dj5MiRpX/38PDA+PHjAQDmpsF1Ot11bzcnIiICERERAGQakMiqyo/Arn7fwmSSADtwAPj554oBBgBt2wI+PhUDzN/foU+oM6xu0ksvyU4FsbGyPxxpb+PGjTe8f9myZVi9ejU2bdpUGjx6vR6pqamlj0lLS4OPjw/0ej3S0tIq3U5kF9zcykZgf/ub3GYyyRTinj0yjZiQACxfDrz/vtwfEiK/VV87AqtTR7vXUR1KqRt9kBnbtyvl5qbU1KlaV0KWWrt2rfL391eZmZkVbj9w4IDq0aOHys/PV0ePHlW+vr6qqKhIKaWU0WhUO3fuVCaTSQ0bNkytWbOmyucJDg6ulfqJbkpxsVKHDin1+edKzZyp1B13KNWwoVKyiYpSffooFRKi1LRpSi1ZotS+fUoVFtq6yqpyCEopdgNW18WL0qCjlIysGjbUuiKyhMFgQEFBAZo1awZAmiw++OADADI1uHTpUnh4eGD+/PmlTRQJCQmlrethYWFYuHAhW9fJ8ZWMwBITZX24DRtkNHbxotzfp0/l/cC6davNERhb12vDCy8As2fL9VS33651NWRvGFbkkEwm4M8/ywJs/fqKAda8edn1X8HBwNChQLkGpBpiWFnb1q3AnXcCL78MvPii1tWQPWJYkdMoCbC9e2X32JLFfHNypJW+5FxZzTGsrCk/X6b/CgulAad+fa0rInvEsCKnVhJgrVsDjRpZ67PyomBrioyU1VLWrWNQEZGLcnMDOnXS5qk1eVYH8/vvElbjx8tULRER2RbDqgomExARIV1/b7+tdTVERK6J04BVWLIE2L4d+PhjXvxLRKQVjqxuICMDmDlTNgCdNEnraoiIXBfD6gZmzpQuwA8+4Np/RERaYlhdx6ZNcmH3nDmaNb8QEdFVDCszioqAxx+XFvXp07WuhoiI2GBhxgcfAElJwDffyMadRESkLY6srnH2rCylNGgQMGqU1tUQERHAsKrkhRdk6asFC9hUQURkLxhW5fz6K/Dhh3Keqls3rashIqISDKurlAKeeAK49VbZBZiIiOwHGyyu+vpr4McfZQfopk21roaIiMrjyApAXp5cANyjh6wDSERE9oVhBWDhQsDTE5g/H3B317oaIiK6lsuH1blzsv2HwSBrABIRkf1x+bCKjAQuXJA/iYjIPrl0WJ04IVOAkyYBAQFaV0NERNfj0mE1a5b8+fLL2tZBREQ35rJh9dtvwLJlwGOPAe3aaV0NERHdiMuG1fPPA40bA889p3UlRERUFZe8KHjbNmD1auD113kBMBGRI3C5kZVSwOzZwD33yBQgERHZP5cLqw0bgPXrgeHDgXr1tK6GiIgs4VJhpZTsVdW2LTBlitbVEBGRpVwqrNatA375BfjvfwEvL62rIS28+eab0Ol0OHPmTOltkZGRMBgM6Ny5M+Li4kpvT0xMREBAAAwGA2bMmAGllBYlExFcKKxKRlXt2wOTJ2tdDWkhNTUVGzZsQLty1yocPHgQ0dHRSEpKwrp16zB9+nQUFxcDAKZNm4aoqCgkJycjOTkZ69at06p0IpfnMmG1ejWQkCA7AXt6al0NaeFf//oX5s2bB125LaBjY2MRHh4OLy8v+Pr6wmAwID4+HhkZGcjJyUG/fv2g0+kwceJExMTEaFc8kYtzibBSSlar6NABmDhR62pIC9999x3atGmDwMDACrenp6ejbdu2pf/W6/VIT09Heno69Hp9pdvNiYqKgtFohNFoRFZWVu28ACIX5xLXWcXGAnv3Ah9/DNSpo3U1VFtCQ0Nx6tSpSrfPnj0bc+bMwfr16yvdZ+48lE6nu+7t5kRERCDi6kZoRqOxumUTkQWcPqyUAhYvli1AJkzQuhqqTRs3bjR7+2+//YaUlJTSUVVaWhqCgoIQHx8PvV6P1NTU0sempaXBx8cHer0eaWlplW4nIm04/TTgmjVybdWrrwIeTh/NZE5AQAAyMzNx7NgxHDt2DHq9Hnv27EHr1q0xYsQIREdHo6CgACkpKUhOTkZISAi8vb3RsGFD7Nq1C0opLF++HCNHjtT6pRC5LKd++1YKmDNHFqodPVrrasgedevWDWPGjEHXrl3h4eGBRYsWwf3qdtGLFy/G5MmTkZeXh7CwMISFhWlcLZHr0lVx7YhDX1iydStw553Ae+8B//yn1tWQKzAajUhISNC6DCJHYv5k8DWcehowMhJo2ZKrVRAROTqnDas9e4C4OOBf/+IagEREjs5pwyoyEmjUCJg2TetKiIioppwyrP74A/j6azlP1bix1tUQEVFNOWVYzZsnC9U+8YTWlRARkTU4XVilpgLLlwMPPSTNFURE5PicLqzeekv+fOopbesgIiLrcaqwOnsWOHBAFqtt317raoiIyFqcagWLqChg0yZg/36tKyEiImtympFVYSGwcCEweDAQEKB1NUREZE1OM7JauRLIyACWLtW6EiIisjanGFkpBbzzDuDvDwwdqnU1RERkbU4xsvrpJ1le6cMPgevsj0dERA7MKUZWb78NNGsGPPig1pUQEVFtcPiw+vNP4LvvZA1ALlhLROScHD6s3n1XdgCePl3rSoiIqLY4dFidPy/df+PGAd7eWldDRES1xaHD6n//Ay5dkj2riIjIeTlsWBUVAevXAwMHAj17al0NERHVJodtXf/+e2DjRiAmRutKiIiotjnsyOr994G2bYG779a6EiIiqm0OGVZ//CGjqkcekU5AIiJybg4ZVosXA3XqyAaLRETk/BwurC5dAj75BPjb34BWrbSuhoiIbMHhwmrFCuDCBeCf/9S6EiIishWHCiulpLGiRw+gf3+tqyEiIltxqPaEXbuAffuADz7g6upERK7EoUZWixYBjRoB48drXQkREdmSw4RVZiawahUwaRLQoIHW1ZAjWrhwITp37oxu3bph5syZpbdHRkbCYDCgc+fOiIuLK709MTERAQEBMBgMmDFjBpRSWpRNRHCgacClS4HCQq6uTjdny5YtiI2Nxf79++Hl5YXMzEwAwMGDBxEdHY2kpCScPHkSoaGhOHz4MNzd3TFt2jRERUWhb9++GD58ONatW4ewsDCNXwmRa3KIkZXJJKOqKVOALl20roYc0eLFi/Hss8/Cy8sLANCyZUsAQGxsLMLDw+Hl5QVfX18YDAbEx8cjIyMDOTk56NevH3Q6HSZOnIgYru1FpBmHCKtNm2Tb+tBQrSshR3X48GH89NNP6NOnDwYMGIDdu3cDANLT09G2bdvSx+n1eqSnpyM9PR16vb7S7eZERUXBaDTCaDQiKyurdl8IkYtyiGnAJUuApk2B++7TuhKyZ6GhoTh16lSl22fPno2ioiJkZ2dj165d2L17N8aMGYOjR4+aPQ+l0+mue7s5ERERiIiIAAAYjcYavgoiMsfuwyorC/j2WzlXVbeu1tWQPdu4ceN171u8eDHuv/9+6HQ6hISEwM3NDWfOnIFer0dqamrp49LS0uDj4wO9Xo+0tLRKtxORNux+GvDTT4ErV7gOINXMqFGjsHnzZgAyJVhYWIjmzZtjxIgRiI6ORkFBAVJSUpCcnIyQkBB4e3ujYcOG2LVrF5RSWL58OUaOHKnxqyByXXY9slJKpgD79gW6d9e6GnJkU6ZMwZQpU9C9e3d4enpi2bJl0Ol06NatG8aMGYOuXbvCw8MDixYtgru7OwAZjU2ePBl5eXkICwtjJyCRhnRVXDui6YUlO3YAf/2rBNbUqVpWQmQZo9GIhIQErcsgciQWrUdk19OAS5bIBcBjx2pdCRERacluw+rCBWDlSmDcOK5YQUTk6uw2rL74Arh8mY0VRERkx2G1ZIlsBdK7t9aVEBGR1uyyG3D/fqB+fTlXxa1AiIjILsPqk09k76pvv9W6EiIisgd2Nw145Qrw+efAvfcCzZppXQ0REdkDuwuruDjZu2riRK0rISIie2F3YbV8OdC8OcDFAoiIqIRdhVV2NhAbC/z974Cnp9bVEBGRvbCrsPryS9kNmFOARERUnl2F1bJlQLduQFCQ1pUQEZE9sZuwOnxY2tUnTeK1VUREVJHdhNXy5YCbGzB+vNaVEBGRvbGLsDKZZJPFwYMBbsZKRETXsouw+vFH4MQJmQIkIiK6ll2E1fLlQKNGwKhRWldCRET2SPOwys0FYmKABx4A6tXTuhoiIrJHmofVd9/JBcCTJ2tdCRER2SvNw2rFCsDLC+jfX+tKiIjIXmkaVmfPysK148ZJ2zoREZE5mkbEV18BRUWyFiAREdH1aBpWK1YA/v5AYKCWVRARkb3TLKxSU4Ft22QKkMsrERHRjWgWVl9+KX+OG6dVBURE5Cg0C6sVK4CQEMBg0KoCIiJyFJqE1aFDwN69bKwgIiLLaBJWX3whrepjxmjx7ERE5GhsHlZKyRTgwIGAt7etn51c1b59+9C3b1/07NkTRqMR8fHxpfdFRkbCYDCgc+fOiIuLK709MTERAQEBMBgMmDFjBpRSWpRORNAgrPbuBY4e5RQg2dbMmTMxa9Ys7Nu3D6+88gpmzpwJADh48CCio6ORlJSEdevWYfr06SguLgYATJs2DVFRUUhOTkZycjLWrVun5Usgcmk2D6sVK4DWrbnCOtmWTqdDTk4OAODChQvwubpxWmxsLMLDw+Hl5QVfX18YDAbEx8cjIyMDOTk56NevH3Q6HSZOnIiYmBgNXwGRa/Ow5ZMpBaxaBfTqBTRtastnJlc3f/58DB06FE899RRMJhN+/vlnAEB6ejr69u1b+ji9Xo/09HTUqVMHer2+0u3mREVFISoqCgCQlZVVi6+CyHXZNKzi42WTxVdfteWzkqsIDQ3FqVOnKt0+e/ZsbNq0Ce+88w5Gjx6NlStXYurUqdi4caPZ81A6ne66t5sTERGBiIgIAIDRaKzhqyAic2waVitXynYgI0bY8lnJVWzcuPG6902cOBELFiwAADzwwAN46KGHAMiIKTU1tfRxaWlp8PHxgV6vR1paWqXbiUgbNjtnZTLJFODQoUCTJrZ6ViLh4+ODrVu3AgA2b96Mjh07AgBGjBiB6OhoFBQUICUlBcnJyQgJCYG3tzcaNmyIXbt2QSmF5cuXY+TIkVq+BCKXZrOR1S+/yHqAc+bY6hmJyvzvf//D448/jqKiItStW7f0HFO3bt0wZswYdO3aFR4eHli0aBHc3d0BAIsXL8bkyZORl5eHsLAwhIWFafkSiFyaroprR6x2YcmTTwKLFgGZmUDjxtb6rET2xWg0IiEhQesyiByJRUuZ22QasGQKcNgwBhUREVWfTcJq1y4gLY3LKxER0c2xSVitXAl4eQH33muLZyMiImdjk7C65RZg/HigUSNbPBsRETkbm3QDzp5ti2chIiJnpdnmi0RERJZiWBERkd1jWBERkd1jWBERkd1jWBERkd1jWBERkd1jWBERkd1jWBERkd1jWBERkd1jWBERkd1jWBERkd2ravNFIqoGnU63Tik1TOs6iJwNw4qIiOwepwGJiMjuMayIiMjuMayIiMjuMayIiMjuMayIiMju/T9h8Mf0mWOBnQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "p = plot(f0,f1, show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 極限(limit)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "微分の原理を理解する時に不可欠な極限(limit)について記す." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", "oo\n", "0\n", "1\n" ] } ], "source": [ "from sympy import *\n", "x = symbols('x')\n", "print(limit(x, x, 0))\n", "print(limit(x, x, oo))\n", "print(limit(1/x, x, oo))\n", "print(limit(x/sin(x), x, 0))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4\n" ] }, { "data": { "text/latex": [ "$\\displaystyle 2 x$" ], "text/plain": [ "2*x" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d = symbols('d')\n", "f = x**2\n", "df = diff(f,x)\n", "print(df.subs({x:2}))\n", "\n", "limit((f.subs({x:x+d})-f.subs({x:x}))/d,d,0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 微分(Diff)-II" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 級数展開(series) \n", "Taylor級数は以下のようにして,中心点(x=a),次数(4次)を指定する." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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yvKeeSFnSKQqnzepRlnRKQhF6nWyusxbFDTTNAqf7cLqz7m04X8ifC9C3PfyzCDpfiyatv/VFlc0pqPLZ0zkXfZdmnreiDJWXJdCsHM+gWTuSsiSqWT6EWhUaSVb31BMpUzpF4bRZLcqUTkkoQq8vAp+j0JPuhNN9MN1d9zacL+RPH+BQFP5Xi/O1cLLwt11Qr10z9o899iSGodnxOo0Nsw2AK5rPUDfmCDTw5+OE52kGLqT4eGobWd1TT6SZ8qRTFE6b1aKZ8qRTEorQ6/oJz9lonO6DaaZ7696G84X8WYAK0E2YGaAMztfCaSa9v91I+Pd0ehJvYJlOvQw9Lw6Hw+FwOBwOh8MRSdB3XhwOh8PhcDgcDoejVLjKi8PhcDgcDofD4egWuMqLw+FwOBwOh8Ph6Bb8H+BPMqmwjnvbAAAAAElFTkSuQmCC\n", "text/latex": [ "$\\displaystyle \\sin{\\left(a \\right)} + \\left(- a + x\\right) \\cos{\\left(a \\right)} - \\frac{\\left(- a + x\\right)^{2} \\sin{\\left(a \\right)}}{2} - \\frac{\\left(- a + x\\right)^{3} \\cos{\\left(a \\right)}}{6} + O\\left(\\left(- a + x\\right)^{4}; x\\rightarrow a\\right)$" ], "text/plain": [ " 2 3 \n", " (-a + x) ⋅sin(a) (-a + x) ⋅cos(a) ⎛ 4 \n", "sin(a) + (-a + x)⋅cos(a) - ──────────────── - ──────────────── + O⎝(-a + x) ; \n", " 2 6 \n", "\n", " \n", " ⎞\n", "x → a⎠\n", " " ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import *\n", "from sympy.plotting import plot\n", "init_printing()\n", "\n", "x,a = symbols('x a')\n", "\n", "sin(x).series(x,a,4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Oはどれくらいのエラーがあるかの表示ですが,関数として取り込むにはOのところが邪魔です.これはremoveO(まんまやん!)で取り除けます." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 3 2 \n", " (-a + x) ⋅cos(a) (-a + x) ⋅sin(a) \n", "- ──────────────── - ──────────────── + (-a + x)⋅cos(a) + sin(a)\n", " 6 2 \n", " 3 \n", " (x - π) \n", "-x + ──────── + π\n", " 6 \n" ] } ], "source": [ "fs = series(sin(x),x,a,4)\n", "\n", "f0 = fs.removeO()\n", "pprint(f0)\n", "f1 = f0.subs({a:pi})\n", "pprint(f1)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y = symbols('y')\n", "p = plot(sin(x),f1, (x,0,2*pi), ylim=[-1,1], show=False)\n", "p[0].line_color = 'b'\n", "p[1].line_color = 'r'\n", "p.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 全微分(D) \n", "sympyでは全微分(total derivatives)は用意されてないようです.\n", "\n", "下のMapleコマンドDを参照して,考えてください.\n", "```maple\n", "> f:=unapply(x^4*exp(-y^2),(x,y));\n", "> D(f(x,y));\n", "> (D@@2)(f(x,y));\n", "```\n", "$$\n", "f\\, := \\,( {x,y} )\\mapsto {x}^{4}\\exp(-{y}^{2}) \\notag \\\\\n", "4\\, {D} \\left( x \\right) {x}^{3}\\exp(-{y}^{2})+{x}^{4} {D} \\left( \\exp(-{y}^{2}) \\right) \\notag \\\\\n", "4\\, \\left( D^{ \\left( 2 \\right) } \\right) \\left( x \\right) {x}^{3}\\exp(-{y}^{2})+12\\, \\left( {D} \\left( x \\right) \\right) ^{2}{x}^{2}\\exp(-{y}^{2})+8\\, {D} \\left( x \\right) {x}^{3} {D} \\left( \\exp(-{y}^{2}) \\right) +{x}^{4} \\left( D^{ \\left( 2 \\right) } \\right) \\left( \\exp(-{y}^{2}) \\right) \\notag\n", "$$\n", "\n", "ここで,D(x)などはxの全微分を表わす.これは,x,yを変数としているので\n", "```maple\n", "> diff(x,x);\n", "> diff(exp(-y^2),y);\n", "```\n", "$$\n", "1 \\notag \\\\\n", "-2\\,y\\exp(-{y}^{2}) \\notag\n", "$$\n", "であるがMapleには分からない.そこで全微分の最終形を得るには,あらかじめD(x)などの結果を求めておき,subsで明示的に代入する必要がある.\n", "```maple\n", "> dd:=D(f(x,y)):\n", "> eqs:={D(x)=diff(x,x),D(exp(-y^2))=diff(exp(-y^2),y)};\n", "> subs(eqs,dd);\n", "```\n", "$$\n", "{\\it eqs}\\, := \\, \\left\\{ {D} \\left( x \\right) =1, {D} \\left( \\exp(-{y}^{2}) \\right) =-2\\,y\\exp(-{y}^{2}) \\right\\} \\notag \\\\\n", "4\\,{x}^{3}\\exp(-{y}^{2})-2\\,{x}^{4}y\\exp(-{y}^{2}) \\notag\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 複合関数の微分 \n", "```maple\n", "> diff(f(x)*g(x),x);\n", "> diff(f(g(x)),x);\n", "```\n", "$$\n", "\\left( {\\frac {d}{dx}}f \\left( x \\right) \\right) g \\left( x \\right) +f \\left( x \\right) {\\frac {d}{dx}}g \\left( x \\right) \\notag \\\\\n", "\\mbox {D} \\left( f \\right) \\left( g \\left( x \\right) \\right) {\\frac {d}{dx}}g \\left( x \\right) \\notag\n", "$$\n", "\n", "```maple\n", "> f:=x->exp(x);\n", "> g:=x->cos(x);\n", "> diff(f(x)*g(x),x);\n", "> diff(f(g(x)),x);\n", "```\n", "$$\n", "f\\, := \\,x\\mapsto \\exp(x) \\notag \\\\\n", "g\\, := \\,x\\mapsto \\cos \\left( x \\right) \\notag \\\\\n", "\\exp(x)\\cos \\left( x \\right) -\\exp(x)\\sin \\left( x \\right) \\notag \\\\\n", "-\\sin \\left( x \\right) \\exp(\\cos x ) \\notag\n", "$$" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x x \n", "- ℯ ⋅sin(x) + ℯ ⋅cos(x)\n", " cos(x) \n", "-ℯ ⋅sin(x)\n" ] } ], "source": [ "f = exp(x)\n", "g = cos(x)\n", "\n", "pprint(diff(f*g, x))\n", "pprint(diff(f.subs({x:g}), x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 課題 \n", "1. 次の関数を微分せよ.\n", " 1. $ {x} \\log x$, \n", " 1. $ \\frac{1}{ \\left( 1+x \\right) ^{3}}$, \n", " 1. $ \\sqrt{4\\,x+3}$, \n", " 1. $ \\frac{1}{ a^2+ \\left( x-x_0 \\right)^2 }$\n", "1. 次の関数の1次から5次導関数を求めよ.\n", " 1. $\\sin^2 x$, \n", " 1. ${e}^{x}$\n", "1. 以下の関数をx0まわりで3次までテイラー展開し,得られた関数ともとの関数をプロットせよ.さらに5次まで展開した場合はどう変化するか.\n", " 1. $ y=\\sin x, x_0=0 $, \n", " 1. $ y=\\cos x, x_0=\\frac{\\pi}{2}$\n", "1. (発展課題)$f \\left( x,y \\right) ={e}^{x}{\\it log} \\left( 1+y \\right) $を$ x=0,\\,y=0$のまわりで3次まで展開せよ." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 解答例" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 幾つかの関数の微分\n", "```maple\n", "> diff(x*log(x),x);\n", "> diff(1/(1 + x)^3,x);\n", "> diff(sqrt(4*x + 3),x);\n", ">diff(1/(a^2+(x-x0)^2),x);\n", "```\n", "$$\n", "\\ln \\left( x \\right) +1 \\notag \\\\\n", "-3\\, \\left( 1+x \\right) ^{-4} \\notag \\\\\n", "2\\, \\left( \\sqrt{4\\,x+3} \\right) ^{-1} \\notag \\\\\n", "-{\\frac {2\\,x-2\\,{\\it x0}}{ \\left( {a}^{2}+ \\left( x-{\\it x0} \\right) ^{2} \\right) ^{2}}} \\notag\n", "$$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log(x) + 1\n", " -3 \n", "────────\n", " 4\n", "(x + 1) \n", "2/sqrt(4*x + 3)\n", " -2⋅x + 2⋅x₀ \n", "─────────────────\n", " 2\n", "⎛ 2 2⎞ \n", "⎝a + (x - x₀) ⎠ \n" ] } ], "source": [ "from sympy import *\n", "x,a,x0 = symbols('x a x0')\n", "\n", "pprint(diff(x*log(x),x))\n", "pprint(diff(1/(1+x)**3,x))\n", "print(diff(sqrt(4*x+3),x))\n", "pprint(diff(1/(a**2+(x-x0)**2),x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 高階微分\n", "```maple\n", "> diff(sin(x)^2,x);\n", "> diff(sin(x)^2,x$2);\n", "```\n", "\n", "$$\n", "2\\,\\sin \\left( x \\right) \\cos \\left( x \\right) \\notag \\\\\n", "2\\, \\left( \\cos \\left( x \\right) \\right) ^{2}-2\\, \\left( \\sin \\left( x \\right) \\right) ^{2}\\notag\n", "$$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", " 2 \n", "sin (x)\n", "1\n", "2⋅sin(x)⋅cos(x)\n", "2\n", " ⎛ 2 2 ⎞\n", "2⋅⎝- sin (x) + cos (x)⎠\n", "3\n", "-8⋅sin(x)⋅cos(x)\n", "4\n", " ⎛ 2 2 ⎞\n", "8⋅⎝sin (x) - cos (x)⎠\n" ] } ], "source": [ "from sympy import *\n", "x = symbols('x')\n", "for i in range(0,5):\n", " print(i)\n", " pprint(diff(sin(x)**2,x,i))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", " x\n", "ℯ \n", "1\n", " x\n", "ℯ \n", "2\n", " x\n", "ℯ \n", "3\n", " x\n", "ℯ \n", "4\n", " x\n", "ℯ \n" ] } ], "source": [ "from sympy import *\n", "x = symbols('x')\n", "for i in range(0,5):\n", " print(i)\n", " pprint(diff(exp(x),x,i))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 0以外での級数展開と表示\n", "テキストを参照して." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2次元関数の級数展開と3dplot" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle y^{2} \\left(- \\frac{x^{2}}{4} - \\frac{x}{2} - \\frac{1}{2}\\right) + y \\left(\\frac{x^{2}}{2} + x + 1\\right)$" ], "text/plain": [ " ⎛ 2 ⎞ ⎛ 2 ⎞\n", " 2 ⎜ x x 1⎟ ⎜x ⎟\n", "y ⋅⎜- ── - ─ - ─⎟ + y⋅⎜── + x + 1⎟\n", " ⎝ 4 2 2⎠ ⎝2 ⎠" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import *\n", "\n", "x,y = symbols('x y')\n", "f = exp(x)*log(1+y)\n", "fx = f.series(x,0,3).removeO()\n", "fxy = fx.series(y,0,3).removeO()\n", "\n", "fxy" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sympy.plotting import plot3d\n", "\n", "p = plot3d(f, fxy, (x, -0.5, 2), (y, -0.5, 2), show = False)\n", "p[0].surface_color = 'r'\n", "p[1].surface_color = 'b'\n", "p.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# きれいな微分表示 \n", "\n", "以下のようにすると表示がきれい." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2\n", " 4 -y \n", "x ⋅ℯ \n" ] }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{\\partial}{\\partial x} x^{4} e^{- y^{2}}$" ], "text/plain": [ " ⎛ 2⎞\n", "∂ ⎜ 4 -y ⎟\n", "──⎝x ⋅ℯ ⎠\n", "∂x " ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = x**4*exp(-y**2)\n", "pprint(f)\n", "\n", "df = Derivative(f,x)\n", "#df.doit()\n", "df" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "colors": { "hover_highlight": "#DAA520", "navigate_num": "#000000", "navigate_text": "#333333", "running_highlight": "#FF0000", "selected_highlight": "#FFD700", "sidebar_border": "#EEEEEE", "wrapper_background": "#FFFFFF" }, "moveMenuLeft": true, "nav_menu": { "height": "260px", "width": "253px" }, "navigate_menu": true, "number_sections": true, "sideBar": true, "threshold": 4, "toc_cell": true, "toc_section_display": "block", "toc_window_display": false, "widenNotebook": false } }, "nbformat": 4, "nbformat_minor": 2 }