2.math.analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Computer science center\n",
    "## Математика для разработчиков\n",
    "Семинар 2. Математический анализ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Предел последовательности"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def odds():\n",
    "    i = 1\n",
    "    while True:\n",
    "        yield i\n",
    "        i += 2\n",
    "gen_odd = odds()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3, 5, 7, 9, 11, 13, 15, 17, 19]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[next(gen_odd) for i in range(10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def sqrt2():\n",
    "    a = 1\n",
    "    while True:\n",
    "        a = 0.5 * (a + 2 / a)\n",
    "        yield a\n",
    "gen_sqrt2 = sqrt2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.5\n",
      "1.4166666666666665\n",
      "1.4142156862745097\n",
      "1.4142135623746899\n",
      "1.414213562373095\n"
     ]
    }
   ],
   "source": [
    "for i in range(5):\n",
    "    print(next(gen_sqrt2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eps =  2.220446049250313e-16\n"
     ]
    }
   ],
   "source": [
    "print(\"eps = \", 2**0.5 - next(gen_sqrt2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def some_seq():\n",
    "    n = 1\n",
    "    while True:\n",
    "        yield n**3/(n**2 + 5) - 2*n**2/(2*n - 1)\n",
    "        n += 1\n",
    "gen_seq = some_seq()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "for i in range(10000):\n",
    "    tmp = next(gen_seq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.500524948729435,\n",
       " -0.5005248962461337,\n",
       " -0.5005248437719274,\n",
       " -0.500524791308635,\n",
       " -0.5005247388544376]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[next(gen_seq) for i in range(5)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Число e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def e():\n",
    "    n = 1\n",
    "    while True:\n",
    "        yield (1 + 1/n)**n\n",
    "        n += 1\n",
    "gen_e = e()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "for i in range(10**7):\n",
    "    tmp = next(gen_e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.718281694349334,\n",
       " 2.718281694566533,\n",
       " 2.718281694783677,\n",
       " 2.718281695000767,\n",
       " 2.718281695217802]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[next(gen_e) for i in range(5)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def e_faster():\n",
    "    s, n, fact = 1, 0, 1\n",
    "    while True:\n",
    "        yield s\n",
    "        n += 1\n",
    "        fact *= n\n",
    "        s += 1 / fact\n",
    "gen_e_faster = e_faster()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "for i in range(10):\n",
    "    tmp = next(gen_e_faster)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2.7182818011463845,\n",
       " 2.718281826198493,\n",
       " 2.7182818282861687,\n",
       " 2.7182818284467594,\n",
       " 2.71828182845823]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[next(gen_e_faster) for i in range(5)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Графики"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "xs = np.linspace(-5, 5, 100)\n",
    "ys = [x*x*x - 10 for x in xs]\n",
    "\n",
    "def map_abs(xs):\n",
    "    return list(map(abs, xs)) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2aab2f4f4518>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2aab2f4f40f0>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2aaabe109cc0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2aab31798d68>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2aab31798ac8>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2aab317de4e0>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2aab317de358>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2aab31806da0>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# x^3-10\n",
    "plt.subplot (2, 2, 1)\n",
    "plt.plot(xs, ys)\n",
    "\n",
    "# |x|^3-10\n",
    "plt.subplot (2, 2, 2)\n",
    "plt.plot(xs, [abs(x*x*x) - 10 for x in xs])\n",
    "\n",
    "# |x^3-10|\n",
    "plt.subplot (2, 2, 3)\n",
    "plt.plot(xs, map_abs(ys))\n",
    "\n",
    "# ||x|^3-10|\n",
    "plt.subplot (2, 2, 4)\n",
    "plt.plot(xs, map_abs([abs(x*x*x) - 10 for x in xs]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Производная"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Определим _приближенную_ производную функции $f(x)$ как\n",
    "$$\n",
    "g(x, \\delta) = \\frac{f(x + \\delta) - f(x)}{\\delta}\n",
    "$$\n",
    "\n",
    "Производная функции $𝑒^𝑥$ при $x=0$ равна 1. \n",
    "\n",
    "**Задача 2.1.** Вычислите приближённую производную по формуле выше для $\\delta = 10^{−2𝑛}$ и $𝑛 = 1, \\dots , 7$. Результаты должны сначала улучшаться, потом ухудшиться. Объясните, почему так происходит."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def g(f, x, dx):\n",
    "    return (f(x + dx) - f(x)) / dx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 0,  g = 1.718281828459045\n",
      "n = 1,  g = 1.005016708416795\n",
      "n = 2,  g = 1.000050001667141\n",
      "n = 3,  g = 1.0000004999621837\n",
      "n = 4,  g = 0.999999993922529\n",
      "n = 5,  g = 1.000000082740371\n",
      "n = 6,  g = 1.000088900582341\n",
      "n = 7,  g = 0.9992007221626409\n",
      "n = 8,  g = 0.0\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "for n in range(9):\n",
    "    print(f\"n = {n}, \", f\"g = {g(math.exp, 0, 10**(-2*n))}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Интеграл"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The result is (6.500000000000002, 7.216449660063519e-15).\n"
     ]
    }
   ],
   "source": [
    "from scipy.integrate import quad\n",
    "\n",
    "def integrand(x):\n",
    "    return abs(x - 3)\n",
    "\n",
    "result = quad(integrand, 1.0, 6.0)\n",
    "print(f\"The result is {result}.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Фрактал Мандельброта"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def in_mandelbrot_set(c):\n",
    "    z = complex(0,0)\n",
    "    for i in range(100):\n",
    "        z = z*z + c\n",
    "        if abs(z) > 2:\n",
    "            return False\n",
    "    return True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "in_mandelbrot_set(complex(0,0))\n",
    "in_mandelbrot_set(complex(2,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def gen_mask(N):\n",
    "    x = np.linspace(-2, 2, N)\n",
    "    y = np.linspace(-2, 2, N)\n",
    "    mask = np.zeros((N, N))\n",
    "    for i in range(N):\n",
    "        for j in range(N):\n",
    "            mask[i, j] = int(in_mandelbrot_set(complex(x[i], y[j])))\n",
    "    return mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x2aab38fcb438>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(gen_mask(1000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Задача 2.2.**\n",
    "\n",
    "Напишите функцию iteration_number, возвращающую логарифм числа итераций, после которого модуль становится больше 2. Нарисуйте результат через imshow.\n",
    "\n",
    "Попробуйте задать попбольше точек и отобразить только часть всего изображения фрактала Мандельброта."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Числа Бернулли"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B( 0) =    1/1\n",
      "B( 1) =    1/2\n",
      "B( 2) =    1/6\n",
      "B( 4) =   -1/30\n",
      "B( 6) =    1/42\n",
      "B( 8) =   -1/30\n",
      "B(10) =    5/66\n",
      "B(12) = -691/2730\n",
      "B(14) =    7/6\n"
     ]
    }
   ],
   "source": [
    "from fractions import Fraction as Fr\n",
    "\n",
    "def bernoulli():\n",
    "    A, m = [], 0\n",
    "    while True:\n",
    "        A.append(Fr(1, m+1))\n",
    "        for j in range(m, 0, -1):\n",
    "            A[j-1] = j*(A[j-1] - A[j])\n",
    "        yield A[0] # (which is Bm)\n",
    "        m += 1\n",
    " \n",
    "bn = [ix for ix in zip(range(16), bernoulli())]\n",
    "bn = [(i, b) for i, b in bn if b]\n",
    "width = max(len(str(b.numerator)) for i,b in bn)\n",
    "for i, b in bn:\n",
    "    print('B(%2i) = %*i/%i' % (i, width, b.numerator, b.denominator))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Сравните с формулой (8) [отсюда](http://www.fourmilab.ch/babbage/sketch.html).\n",
    "\n",
    "Спасибо за внимание, всё на сегодня."
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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