calculus.ipynb

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   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: latexify-py in c:\\users\\bundl\\anaconda3\\envs\\aidemy\\lib\\site-packages (0.2.0)\n",
      "Requirement already satisfied: dill>=0.3.2 in c:\\users\\bundl\\anaconda3\\envs\\aidemy\\lib\\site-packages (from latexify-py) (0.3.6)\n"
     ]
    }
   ],
   "source": [
    "!pip install latexify-py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sym\n",
    "x = sym.Symbol('x')\n",
    "f = sym.Function('f')\n",
    "f= x + 2\n",
    "sym.diff(f)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3 x^{2} + 1$"
      ],
      "text/plain": [
       "3*x**2 + 1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h = x**3 + x + 1\n",
    "h.diff(x,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import latexify"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$ \\displaystyle \\mathrm{F}(x) = x^{{3}} + x + {1} $$"
      ],
      "text/plain": [
       "<latexify.frontend.LatexifiedFunction at 0x2511f05f1c0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@latexify.function\n",
    "def F(x):\n",
    "    return x**3 + x + 1\n",
    "F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\mathrm{F}(x) = x^{{3}} + x + {1}\n"
     ]
    }
   ],
   "source": [
    "print(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e^{x}$"
      ],
      "text/plain": [
       "exp(x)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = sym.exp(x)\n",
    "sym.diff(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f{\\left(x \\right)} = C_{1} e^{- \\frac{5 x}{2}}$"
      ],
      "text/plain": [
       "Eq(f(x), C1*exp(-5*x/2))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = sym.Function('f')\n",
    "eq = sym.Eq(2 * f(x).diff(x,1) + 5 * f(x),0 )\n",
    "eq\n",
    "sym.dsolve(eq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x^{2} - 12 x = -8$"
      ],
      "text/plain": [
       "Eq(x**2 - 12*x, -8)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq = sym.Eq(x**2-12*x, -8)\n",
    "eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[6 - 2*sqrt(7), 2*sqrt(7) + 6]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym.solve(eq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{x: 3, y: 4}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = sym.Symbol('y')\n",
    "\n",
    "eq1 = 3 * x + 5 * y - 29\n",
    "eq2 = x + y - 7\n",
    "\n",
    "sym.solve([eq1, eq2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Eq(f(x), C3*exp(2*x) - (C1 + C2)*exp(-x)),\n",
       " Eq(g(x), C1*exp(-x) + C3*exp(2*x)),\n",
       " Eq(h(x), C2*exp(-x) + C3*exp(2*x))]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sym.Symbol('x')\n",
    "f = sym.Function('f')\n",
    "g = sym.Function('g')\n",
    "h = sym.Function('h')\n",
    "eq1 = sym.Eq(f(x).diff(x,1),g(x)+h(x) )\n",
    "eq2 = sym.Eq(g(x).diff(x,1),h(x)+f(x) )\n",
    "eq3 = sym.Eq(h(x).diff(x,1),f(x)+g(x))\n",
    "sym.dsolve([eq1, eq2, eq3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 x$"
      ],
      "text/plain": [
       "2*x"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = sym.Symbol('x')\n",
    "y = sym.Symbol('y')\n",
    "\n",
    "u = x**2 - y**2\n",
    "\n",
    "u.diff(x,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{5}{3}$"
      ],
      "text/plain": [
       "5/3"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "\n",
    "x,y = symbols('x y')\n",
    "#y = Symbol('y')\n",
    "\n",
    "f = x**2 + y**2 + 1\n",
    "\n",
    "integrate(f,(x, 0, 1),(y,0,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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