{"nbformat":4,"nbformat_minor":0,"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":"3.6.7"},"colab":{"name":"Functions.ipynb","provenance":[],"collapsed_sections":["Q5LuaTTCJd-H","rJEojfexJd-P","u0zlgAJ_Jd-T","ISRJTaddJd-U","6hYUXjaFJd-a","oRs74FKQJd-y","FsElN_9QJd-5","DDzKWeIEJd-6","VURaA57aJd_F","2ve00piQJd_K","8qd-Pgd2Jd_W","4hhUZmacJd_X","nWushvWwJd_Z","c3qquhmTJd_f","FWZVLil6Jd_p","Nx9zzWHWJd_r","SSboPhEoJd_s"],"toc_visible":true}},"cells":[{"cell_type":"markdown","metadata":{"id":"AE0UJdFzJd-E","colab_type":"text"},"source":["# Функция одной переменной"]},{"cell_type":"markdown","metadata":{"id":"Q5LuaTTCJd-H","colab_type":"text"},"source":["## Определение функции"]},{"cell_type":"markdown","metadata":{"id":"XV9IEXLaJ2gJ","colab_type":"text"},"source":["Пусть $X$ и $Y$ — два множества. \n","\n","**Функция**, заданная на $X$ со значениями в $Y$ – закон $F$, согласно которому каждому элементу $x \\in X$ поставлен в соответствие единственный элемент $y \\in Y$.\n","\n","Если, согласно функции $F$, элемент y $\\in$ Y соответствует элементу x $\\in$ X, то обозначается:
\n","
\n","$y = F(x)$.\n","\n","$y$ является **образом** элемента $x$ при функции $F$, $x$ является **прообразом** элемента $y$ при функции $F$."]},{"cell_type":"markdown","metadata":{"id":"4ujGp-a8Jd-K","colab_type":"text"},"source":["> *Пример #1*:
\n","
\n","Функция $F(x) = x + 2$, $x \\in \\mathbb{R}$
\n","$y=4$ есть образ $x=2$ при функции F (y = x + 2, 4 = 2 + 2)
\n","$x=198$ есть прообраз $x=200$ при функции F (y = x + 2, 200 = 198 + 2)"]},{"cell_type":"markdown","metadata":{"id":"ULMd1tXqJd-N","colab_type":"text"},"source":["При записи функции в виде $y = F(x)$ $x$ называется **переменной** или **аргументом функции F**, потому что вместо $x$ мы можем подставлять разные значения (изменять $x$) и получать разные значения $y$.\n","\n","Говоря простыми словами, функция показывает, как изменение величины $y$ зависит от изменения величины $x$.\n","Примером функции из реальной жизни может быть функция зависимости высоты дома от количества этажей в нем:\n","\n","$y = 2*x + 1$ \n","\n","$y$ — высота дома в метрах
\n","$x$ — количество этажей в доме
\n","2 метра высотой каждый этаж и 1 метр высотой фундамент. Поэтому высота дома в метрах — это количество этажей, умноженное на два плюс один метр фундамента."]},{"cell_type":"markdown","metadata":{"id":"rJEojfexJd-P","colab_type":"text"},"source":["## Область значений и область определения"]},{"cell_type":"markdown","metadata":{"id":"hGcUpu1mJ4kC","colab_type":"text"},"source":["Пусть дана функция $F$, заданная на множестве $X$ со значениями в множестве $Y$.\n","\n","$X$ называется **областью определения** функции $F$, $Y$ называется **областью значений** функции $F$."]},{"cell_type":"markdown","metadata":{"id":"zz0aN4WiJd-Q","colab_type":"text"},"source":["> *Пример #2*:
\n","
\n","Функция $F(x) = x + 2$
\n"," Область определения F — все действительные числа. Мы можем взять любое действительное число $x$, подставить в функцию F и получить результат.
\n","Область значения F — также все действительные числа. Мы можем взять любое действительное число $y$ и найти такое число $x$, что $y = F(x)$."]},{"cell_type":"markdown","metadata":{"id":"N4OEOh5HJd-S","colab_type":"text"},"source":["> *Пример #3*:
\n","
\n","Функция $F(x) = x^2$
\n","Область определения F — все действительные числа. Мы можем взять любое действительное число $x$ и подставить в функцию F.
\n","Область значения F — все числа, большие 0. Действительно, мы можем взять любое число $y > 0$ и найти такое число $x$, что $y = F(x)$ ($x$ в этом случае будет корнем из $y$). Но ни для какого числа $y < 0$ не существует такого $x$, что $y = F(x)$ — иначе $x$ должен быть корнем из $y$, а корней из отрицательных чисел не существует (забудем пока про комплексные числа)."]},{"cell_type":"markdown","metadata":{"id":"u0zlgAJ_Jd-T","colab_type":"text"},"source":["# Исследование функций"]},{"cell_type":"markdown","metadata":{"id":"ISRJTaddJd-U","colab_type":"text"},"source":["## Минимум и максимум функций"]},{"cell_type":"markdown","metadata":{"id":"tn0BDLoiJd-V","colab_type":"text"},"source":["Одна из самых распространенных задач, связанных с функциями — поиск их минимумов/максимумов. На самом деле, ровно эта задача решается всеми нейронными сетями в процессе обучения =) Сейчас мы поймем, что это значит.\n","\n","Давайте вернемся к множествам $X$ и $Y$ — области определения и области значений некоторой функции F. Задача **поиска минимума функции** — найти такое значение переменной $x_{min} \\in X$, что соответствующее ему значение $y_{min} = F(x_{min}) \\in Y$ будет минимально возможным. \n","\n","То есть, для любого другого $x \\in X$, $x \\ne x_{min}$ выполнено: $F(x) \\geq F(x_{min})$\n","\n","$y_{min}$ называется **минимумом функции F**, $x_{min}$ — **аргминимумом** (минимальным аргументом).\n","\n","Таких минимальных значений аргумента $x_{min} \\in X$ может быть несколько или даже бесконечно — тогда значения функции для всех этих значений одинаковые — $y_{min}$. А еще минимальных значений аргумента $x_{min} \\in X$ может вовсе не быть — в этом случае функция $F$ не имеет минимума.\n","\n","Давайте рассмотрим несколько примеров:"]},{"cell_type":"markdown","metadata":{"id":"pcBzVQe-Jd-X","colab_type":"text"},"source":[" > Пример #4
\n","
\n"," Функция $y = x + 1$
\n"," У этой функции нет минимума. Действительно -- допустим, что минимум есть, обозначим его $y_{min}$. Тогда соответствующий аргминимум $x_{min} = y_{min} - 1$. Тогда возьмем значение $x = x_{min}-1$ и подставим в функцию. \n"," Получим значение $y = x - 1 = (x_{min}-1)-1 = x_{min}-2 = y_{min}-1 < y_{min}$. Это противоречит тому, что $y_{min}$ -- минимальное значение."]},{"cell_type":"markdown","metadata":{"id":"zye5sPTnJd-Y","colab_type":"text"},"source":[" > Пример #5
\n","
\n"," Функция $y = x^2$
\n"," У этой функции минимум в точке 0. Действительно 0 в квадрате это 0. $y < 0$ мы получить не сможем, потому что квадрат любого числа -- неотрицательное число (мы рассматриваем $x \\in \\mathbb{R}$. Значит, меньшее значение функции, чем ноль, мы получить не можем, значит, минимум функции -- 0."]},{"cell_type":"markdown","metadata":{"id":"VrRePYGIJd-Z","colab_type":"text"},"source":["Аналогичным образом, как и минимум, мы можем определить максимум функции и задачу поиска максимума функции. "]},{"cell_type":"markdown","metadata":{"id":"6hYUXjaFJd-a","colab_type":"text"},"source":["## График функции "]},{"cell_type":"markdown","metadata":{"id":"_g7XZcViJp4S","colab_type":"text"},"source":["Рассмотренные нами функции можно графически изображать, часто это оказывается полезно.\n","\n","Для этого вводится понятие **декартовой плоскости** — это плоскость с двумя выделенными перпендикулярными$^*$ осями OX и OY.
\n","По оси OX мы можем откладывать значения переменной $x$, по оси OY — значения переменной $y$.
\n","Ось ОХ обычно горизонтальная, OY — векртикальная (см последующие примеры)\n","\n","$^*$ перпендикулярные оси (прямые) — прямые, угол между которыми 90 градусов.
"]},{"cell_type":"markdown","metadata":{"id":"NrmC1zURJd-b","colab_type":"text"},"source":[" > Пример #6
\n","
\n"," График функции $y = F(x) = 2x + 1$:"]},{"cell_type":"code","metadata":{"id":"6RTz3-n4Jd-e","colab_type":"code","colab":{}},"source":["def F(x):\n"," return 2*x + 1"],"execution_count":0,"outputs":[]},{"cell_type":"code","metadata":{"id":"p2o1K_J-Jd-i","colab_type":"code","outputId":"46ed3919-0db3-444e-ef25-ebc86e4138da","executionInfo":{"status":"ok","timestamp":1580415209877,"user_tz":-180,"elapsed":2109,"user":{"displayName":"Татьяна Андреевна Гайнцева","photoUrl":"https://lh3.googleusercontent.com/a-/AAuE7mDUSm2bidz9H6v18nagYGAfBWJwHqXRTr0biU4p=s64","userId":"17554479887788199937"}},"colab":{"base_uri":"https://localhost:8080/","height":279}},"source":["import numpy as np\n","import matplotlib.pyplot as plt\n","\n","def plot_function(f):\n"," x = range(-100, 100)\n"," y = list(map(f, x))\n","\n"," plt.plot(x, y)\n"," plt.ylabel(\"Y\")\n"," plt.xlabel(\"X\")\n"," \n","plot_function(F)"],"execution_count":0,"outputs":[{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAY0AAAEGCAYAAACZ0MnKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nVo00YFD+v3guDQfmmJkDz7j7JKCtu+cE29cDbUu6opmNBkYDJCYmxiKrSK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az0tbTN6EJ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\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"9rwsGzP7Jd-o","colab_type":"text"},"source":[" > Пример #7
\n","
\n"," График функции $y = F(x) = x^2$:"]},{"cell_type":"code","metadata":{"id":"HM2jPxGNJd-p","colab_type":"code","outputId":"f2e5e371-1d50-41dd-9d6a-d4837f3a4029","colab":{}},"source":["def F(x):\n"," return (x+25)**2\n","\n","plot_function(F)"],"execution_count":0,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"kZJssFMIJd-t","colab_type":"text"},"source":["Вы можете сами определить свою функцию $F$ и построить ее график, вызвав plot_function:"]},{"cell_type":"code","metadata":{"id":"KmKoW4wQJd-u","colab_type":"code","colab":{}},"source":["def F(x):\n"," return <тут ваш код>\n","\n","plot_function(F)"],"execution_count":0,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"3nLiCCkOJd-x","colab_type":"text"},"source":["По виду графиков функций часто становится понятно, как \"ведет\" себя функция в разных точках и какими свойствами обладает. Например, посмотрите на график функции $y = (x+25)^2$ (см пример #5). Из графика видно, что функция принимает минимальное значени в точке x = -25."]},{"cell_type":"markdown","metadata":{"id":"oRs74FKQJd-y","colab_type":"text"},"source":["## Локальный минимум"]},{"cell_type":"markdown","metadata":{"id":"GnE-m6tXJuP_","colab_type":"text"},"source":["Минимум, который мы рассмотрели выше называется **глобальным минимумом** функции. \"Глобальный\", потому что мы определяли его как \"наименьше значение, которое функция сможет принимать на ВСЕЙ области определения\".\n","\n","Также существует понятие локального минимума. Точка $x_{min}$ — **локальный минимум** функции $F$, если существует такая величина $\\Delta x > 0$, что значение функции $F$ в любой точке $x \\in [x_{min} - \\Delta x, x_{min} + \\Delta x]$ не меньше значения функции в точке $x_{min}$.\n","\n","Другими словами, если бы мы область определения нашей функции была отрезком $x \\in [x_{min} - \\Delta x, x_{min} + \\Delta x]$, то точка $x_{min}$ была бы глобальным минимумом функции $F$.\n","\n","Точки локальных минимумом и максимумов также называются **точками экстремума**."]},{"cell_type":"markdown","metadata":{"id":"lHNvD42AJd-z","colab_type":"text"},"source":["> Пример #8
\n","
\n","Давайте посмотрим на график функции $F(x) = x^4 + 5x^3 - 10x$ на интервале $x \\in[-5, 2]$:"]},{"cell_type":"code","metadata":{"id":"zHKAQBBMFgMn","colab_type":"code","outputId":"73b11afb-7dda-413b-a889-3b1b2b5ab401","executionInfo":{"status":"ok","timestamp":1580415216734,"user_tz":-180,"elapsed":1867,"user":{"displayName":"Татьяна Андреевна Гайнцева","photoUrl":"https://lh3.googleusercontent.com/a-/AAuE7mDUSm2bidz9H6v18nagYGAfBWJwHqXRTr0biU4p=s64","userId":"17554479887788199937"}},"colab":{"base_uri":"https://localhost:8080/","height":34}},"source":["F(-3.5518), F(-0.9439), F(0.7457)"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(-29.3714438337351, 6.027961573411785, -5.07448646946412)"]},"metadata":{"tags":[]},"execution_count":5}]},{"cell_type":"code","metadata":{"id":"fIQfA0n8Jd-1","colab_type":"code","outputId":"6ba22103-e9ad-464f-9c35-b1794af4eb11","executionInfo":{"status":"ok","timestamp":1580415216732,"user_tz":-180,"elapsed":2147,"user":{"displayName":"Татьяна Андреевна Гайнцева","photoUrl":"https://lh3.googleusercontent.com/a-/AAuE7mDUSm2bidz9H6v18nagYGAfBWJwHqXRTr0biU4p=s64","userId":"17554479887788199937"}},"colab":{"base_uri":"https://localhost:8080/","height":296}},"source":["def F(x):\n"," return x**4 + 5*x**3 - 10*x\n","\n","x = np.linspace(-5, 2, 100)\n","y = list(map(F, x))\n","\n","plt.plot(x, y)\n","plt.ylabel(\"Y\")\n","plt.xlabel(\"X\")\n","plt.scatter([-3.5518, -0.9439, 0.7457], [F(-3.5518), F(-0.9439), F(0.7457)])"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":[""]},"metadata":{"tags":[]},"execution_count":4},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAYcAAAEGCAYAAACO8lkDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRWRzm3MxIrJYRLLdf/Z1MuOxjLQRS8aYU/ThthIqahq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UVHdYGADqmlroFxXK9CGxnDk0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\nioMxxph2rDgYY4xp5/8DYRhCGTKkSKgAAAAASUVORK5CYII=\n","text/plain":["
"]},"metadata":{"tags":[]}}]},{"cell_type":"markdown","metadata":{"id":"ugLI1B0CJd-4","colab_type":"text"},"source":["> эта функция имеет на отрезке $[-5, 2]$ два локальных минимума — в точках $x \\sim -3.5518$ и $x \\sim 0.7457$. И также один локальный максимум — в точке $x \\sim -0.9439$"]},{"cell_type":"markdown","metadata":{"id":"FsElN_9QJd-5","colab_type":"text"},"source":["## Возрастание и убывание функции"]},{"cell_type":"markdown","metadata":{"id":"DDzKWeIEJd-6","colab_type":"text"},"source":["### возрастание и убывание на интервале"]},{"cell_type":"markdown","metadata":{"id":"1dHUpB_hJd-8","colab_type":"text"},"source":["Функция F **возрастает на интервале** $[a, b]$, если для любых двух точек интервала $x_1, x_2 \\in [a, b]$ если $x_2 > x_1$, то $F(x_1) > F(x_2)$. В этом случае функция F **(строго) монотонна** (монотонно возрастает) на интервале $[a, b]$.\n","\n","Также есть смежное понятие:
\n","Функция F **неубывает на интервале** $[a, b]$, если для любых двух точек интервала $x_1, x_2 \\in [a, b]$ если $x_2 > x_1$, то $F(x_1) \\geq F(x_2)$. То есть, здесь функция может принимать одинаковые значения в нескольких точках интервала. В этом случае функция F **нестрого монотонна** (нестрого монотонно возрастает) на интервале $[a, b]$.\n","\n","Аналогично определяются **убывающая на интервале** и **невозрастающая на интервале** функции.\n","\n"]},{"cell_type":"markdown","metadata":{"id":"G-DhHChGJd-9","colab_type":"text"},"source":["> Пример #9
\n","
\n","Давайте снова посмотрим на график функции из предыдущего примера:
$x^4 + 5x^3 - 10x$ на интервале $x \\in[-5, 2]$: "]},{"cell_type":"code","metadata":{"id":"Wwxjh14wJd--","colab_type":"code","outputId":"c128c87d-8419-46ec-ff96-e3b697458233","colab":{}},"source":["def F(x):\n"," return x**4 + 5*x**3 - 10*x\n","\n","x = np.linspace(-5, 2, 100)\n","y = list(map(F, x))\n","\n","plt.plot(x, y)\n","plt.ylabel(\"Y\")\n","plt.xlabel(\"X\")\n","plt.scatter([-3.5518, -0.9439, 0.7457], [F(-3.5518), F(-0.9439), F(0.7457)])"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":[""]},"metadata":{"tags":[]},"execution_count":54},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"9KjwQ_2RJd_A","colab_type":"text"},"source":["Эта функция убывает на отрезке $[-5, -3.5518]$, возрастает на $[-3.5518, -0.9439]$, снова убывает на $[-0.9439, 0.7457]$ и снова возрастает на $[0.7457, 2]$."]},{"cell_type":"markdown","metadata":{"id":"UH_GFIrzJd_B","colab_type":"text"},"source":["> Пример #10
\n","
\n","Посмотрим на график функции
\n","$F(x) = \\left\\{\\begin{array}{l}-x-1, x < -1\\\\x = 0, x \\in [-1, 1] \\\\ x - 1, x > 1\\end{array}\\right.$: "]},{"cell_type":"code","metadata":{"id":"-AfDnf3jJd_B","colab_type":"code","outputId":"593a4a62-600a-4d52-91dd-42e70d9ee08c","colab":{}},"source":["def F(x):\n"," if x < -1:\n"," return -x - 1\n"," elif x < 1:\n"," return 0\n"," else:\n"," return x - 1\n","\n","x = np.linspace(-2, 2, 100)\n","y = list(map(F, x))\n","\n","plt.plot(x, y)\n","plt.ylabel(\"Y\")\n","plt.xlabel(\"X\")"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["Text(0.5, 0, 'X')"]},"metadata":{"tags":[]},"execution_count":58},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"yC5wkUAiJd_E","colab_type":"text"},"source":["> Эта функция строго убывает на $[-2, -1]$, нестрого убывает на $[-2, 1]$"]},{"cell_type":"markdown","metadata":{"id":"VURaA57aJd_F","colab_type":"text"},"source":["### возрастание и убывание в точке"]},{"cell_type":"markdown","metadata":{"id":"zH7mHuqKJd_F","colab_type":"text"},"source":["кроме возрастания/убывания функции на определенном интервале также определяется возрастание и убывание функции в точке.\n","\n","Функция $F$ **убывает в точке** $x$, если существует такое число $\\delta x > 0$, что на интервале $[x - \\delta x, x + \\delta x]$ функция F убывает.\n","Аналогично функция $F$ **возрастает в точке** $x$, если существует такое число $\\delta x > 0$, что на интервале $[x - \\delta x, x + \\delta x]$ функция F возрастает.\n","\n","$\\delta x$ может быть сколь угодно маленьким. Давайте рассмотрим примеры:"]},{"cell_type":"markdown","metadata":{"id":"HLADohROJd_G","colab_type":"text"},"source":["> Пример #11
\n","
\n","Давайте снова посмотрим на график функции из предыдущих примеров:
\n","$x^4 + 5x^3 - 10x$ на интервале $x \\in[-5, 2]$: "]},{"cell_type":"code","metadata":{"id":"h8xSuvEsJd_H","colab_type":"code","outputId":"e9220ec2-34cb-45bd-ea82-39aa0c35c903","colab":{}},"source":["def F(x):\n"," return x**4 + 5*x**3 - 10*x\n","\n","x = np.linspace(-5, 2, 100)\n","y = list(map(F, x))\n","\n","plt.plot(x, y)\n","plt.ylabel(\"Y\")\n","plt.xlabel(\"X\")\n","plt.scatter([-3.5518, -0.9439, 0.7457], [F(-3.5518), F(-0.9439), F(0.7457)])\n","plt.scatter([-3, -0.8, 1.5], [F(-3), F(-0.8), F(1.5)])"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":[""]},"metadata":{"tags":[]},"execution_count":62},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"xChVX4GRJd_J","colab_type":"text"},"source":[" > Синим цветом отмечены точки минимума и максимума (экстремумы) функций.
\n","
\n","Посмотрим на желтые точки.
\n","
\n","Функция в первой желтой точке возрастает, во второй — убывает, в третьей опять возрастает.
\n","
\n","Вообще, данная функция будет убывать в любой точке интервала (-0.9439, 0.7457) (интервал между точкой максимума и точкой минимума). Потому что какую бы точку $x$ из этого интервала мы ни взяли, найдутся две точки $x_1$ и $x_2$ такие, что $-0.9439 < x_1 < x$ и $x > x_2 > 0.7457$. На отрезке $[x_1, x_2]$ функция будет убывать, а значит, функция убывает в точке $x$."]},{"cell_type":"markdown","metadata":{"id":"2ve00piQJd_K","colab_type":"text"},"source":["## Непрерывность функции"]},{"cell_type":"markdown","metadata":{"id":"oJLkchtGJd_L","colab_type":"text"},"source":["Пришло время познакомиться с понятием непрерывности функции.\n","\n","Функция F **непрерывна в точке** x, если:
\n","1. F определена в точке x\n","2. Для любого числа $\\delta > 0$ можно найти такое $\\Delta x > 0$, что для любой точки $x' \\in [x - \\Delta x, x + \\Delta x]$ выполняется: $|F(x') - F(x)| < \\delta$
\n","($|F|$ означает модуль $F$)\n","\n","Эта запись может показаться сложной, но на самом деле она не очень сложная. Просто прочитайте и вдумайтесь в нее несколько раз.
\n","Интуитивно это определение значит, что функция $F$ в точках, близких к $x$, имеет значение, близкое к $F(x)$.\n","\n","Давайте рассмотрим примеры, чтоб окончательно понять значение непрерывности:"]},{"cell_type":"markdown","metadata":{"id":"GH0_1VUQJd_M","colab_type":"text"},"source":["> Пример #12
\n","
\n","Давайте снова посмотрим на график функции из предыдущих примеров:
\n","$x^4 + 5x^3 - 10x$ на интервале $x \\in[-5, 2]$: "]},{"cell_type":"code","metadata":{"id":"RBNGDaMzJd_N","colab_type":"code","outputId":"b356b371-9762-4c4b-bef2-a32d2ff2097c","colab":{}},"source":["def F(x):\n"," return x**4 + 5*x**3 - 10*x\n","\n","x = np.linspace(-5, 2, 100)\n","y = list(map(F, x))\n","\n","plt.plot(x, y)\n","plt.ylabel(\"Y\")\n","plt.xlabel(\"X\")\n","plt.scatter([-0.9439], [F(-0.9439)])\n","plt.scatter([2], [F(2)])\n","plt.scatter([-0.5], [F(-0.5)])"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":[""]},"metadata":{"tags":[]},"execution_count":66},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"yS4vcRkMJd_Q","colab_type":"text"},"source":["> посмотрим на синюю точку. В этой точке функция непрерывна — если мы возьмем оранжевую точке и будем двигать ее по графику функции по направлению к синей точке, то с какого-то момента (например, когда оранжевая точка совпадет с зеленой) при приближении оранжевой точки к синей значение функции в оранжевой точке будет все ближе к значению функции в синей точке, и в конце концов значения функции в синей и оранжевой точках совпадут.
\n","
\n","Как несложно понять, эта функция непрерывна во всех точках."]},{"cell_type":"markdown","metadata":{"id":"zvmrkD_TJd_R","colab_type":"text"},"source":["> Пример #13
\n","
\n","F = $F(x) = \\left\\{\\begin{array}{l}-x, x < -1\\\\x = 0, x \\in [-1, 1] \\\\ x, x > 1\\end{array}\\right.$: "]},{"cell_type":"code","metadata":{"id":"i6oE5uo4Jd_S","colab_type":"code","outputId":"b6ae7517-6dce-4fad-f835-ba9c831e1cf3","colab":{}},"source":["x = np.linspace(-2, -1, 100)\n","y = list(map(lambda x: -x, x))\n","plt.plot(x, y, c='b')\n","\n","x = np.linspace(-1, 1, 100)\n","y = list(map(lambda x: 0, x))\n","plt.plot(x, y, c='b')\n","\n","x = np.linspace(1, 2, 100)\n","y = list(map(lambda x: x, x))\n","plt.plot(x, y, c='b')\n","\n","plt.ylabel(\"Y\")\n","plt.xlabel(\"X\")"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["Text(0.5, 0, 'X')"]},"metadata":{"tags":[]},"execution_count":70},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"zYJ-MUoxJd_V","colab_type":"text"},"source":["> здесь в точках -1 и 1 функция имеет **разрыв** (не непрерывна). Действительно, возьмем $\\delta =0.5$. Не существует такого $\\Delta x$, что для всех точек $x' \\in [-1 - \\Delta x, -1]$ выполнялось бы $|F(x') - F(-1)| < \\delta$.
\n","
\n","Во всех остальных точках функция непрерывна."]},{"cell_type":"markdown","metadata":{"id":"8qd-Pgd2Jd_W","colab_type":"text"},"source":["## Предел функции в точке\n","\n"]},{"cell_type":"markdown","metadata":{"id":"c7n7BUDwJd_X","colab_type":"text"},"source":["В этом разделе мы в самых общих чертах, не вдаваясь в подробности, познакомимся с понятиями пределов функции и последовательности."]},{"cell_type":"markdown","metadata":{"id":"4hhUZmacJd_X","colab_type":"text"},"source":["### Предел последовательности"]},{"cell_type":"markdown","metadata":{"id":"xtd9qTk_Jd_X","colab_type":"text"},"source":["Рассмотрим некоторую бесконечную последовательность чисел
\n","$x_1, x_2, \\dots, x_n, \\dots$\n","\n","Число $x$ является **пределом последовательности**, если для любого числа $\\delta > 0$ сушествует такой номер $n$, что для любого числа $N > n$ выполняется: $|x - x_N| < \\delta$
\n","Если $x$ является **пределом последовательности**, то говорят, что последовательность **стремится** к $x$.\n","\n","Обозначается стремление так:
\n","$x_1, x_2, \\dots, x_n, \\dots, \\to x$ (последовательность стремится к $x$)\n","\n","То есть, у последовательности есть предел $x$, если для сколь угодно малого числа $\\delta > 0$ можно найти член последовательности такой, что все члены после него ближе к пределу $x$, чем $\\delta$"]},{"cell_type":"markdown","metadata":{"id":"haqlK3McJd_Y","colab_type":"text"},"source":["> Пример #14
\n","
\n"," Рассмотрим последовательность чисел:
\n"," $1, \\frac{1}{2}, \\frac{1}{3}, \\frac{1}{4}, \\dots, \\frac{1}{n}, \\dots$
\n","
\n"," Предел этой последовательности — число 0. Думаю, вы легко убедитесь в этом сами."]},{"cell_type":"markdown","metadata":{"id":"0FbmDevVJd_Y","colab_type":"text"},"source":["> Пример #15
\n","
\n"," Рассмотрим последовательность чисел:
\n"," 1, -2, 3, -4, $\\dots$
\n","
\n","У этой последовательности предела не существует."]},{"cell_type":"markdown","metadata":{"id":"nWushvWwJd_Z","colab_type":"text"},"source":["### Предел функции в точке"]},{"cell_type":"markdown","metadata":{"id":"4XKH0vyEJd_a","colab_type":"text"},"source":["С понятием непрерывности функции тесно связано понятие предела функции в точке. \n","\n","Число $y$ является **пределом функции $F$ в точке** $x$, если для любого числа \\delta > 0 можно найти такое $\\Delta x > 0$, что для любой точки $x' \\in [x - \\Delta x, x + \\Delta x]$ выполняется: $|F(x') - y| < \\delta$
"]},{"cell_type":"markdown","metadata":{"id":"GlZPIW4tJd_a","colab_type":"text"},"source":["Очень похоже на определение непрерывности в точке. Отличие в том, что предел функции в точке не обязан совпадать со значением функции в точке. Более того, значения функции в точке $x$, в которой ищется предел, может вообще не существовать.\n","\n","Если же значение в точке $x$ функции $F$ существует, то чаще всего предел функции в точке соврадает со значением функции в этой точке."]},{"cell_type":"markdown","metadata":{"id":"ppCuQvRFJd_b","colab_type":"text"},"source":["Интуитивно определение предела функции в точке можно понимать так:
\n","Допустим, мы хотим найти предел функции $F$ в точке $x$. Построим последовательность точек $x_1, x_2, \\dots$, стремящуюся к $x$. Значения функции в точках этой последовательности также образуют последовательность:\n","$F(x_1), F(x_2), \\dots$. Если у последовательности значений функций есть предел $y$, то он является пределом функции в точке $x$.\n","\n","Обозначается $F(x_i) \\to y при x_i \\to x$ (значение функции стремится к $y$ при значениях аргемента, стремящихся к $x$)"]},{"cell_type":"markdown","metadata":{"id":"fwYE8BPuJd_b","colab_type":"text"},"source":["> Пример #16
\n","
\n"," У непрерывной функции существует редел в любой точке и он равен значению функции в этой точке."]},{"cell_type":"markdown","metadata":{"id":"dCydmYhAJd_c","colab_type":"text"},"source":["> Пример #17
\n","
\n"," Пример функции, которая не непрерывна в точке 0, но имеет в точке 0 предел, равный 0:
\n"," F = $F(x) = \\left\\{\\begin{array}{l}-x, x < -0\\\\x = 1, x = 0 \\\\ x, x > 0\\end{array}\\right.$: "]},{"cell_type":"code","metadata":{"id":"ZClCOf-RJd_d","colab_type":"code","outputId":"c762e2c3-2d27-48c7-cf37-0853d6e01e01","colab":{}},"source":["x = np.linspace(-2, 0, 100)\n","y = list(map(lambda x: -x, x))\n","plt.plot(x, y, c='b')\n","\n","plt.scatter(0, 1, c='b')\n","\n","x = np.linspace(0, 2, 100)\n","y = list(map(lambda x: x, x))\n","plt.plot(x, y, c='b')\n","\n","plt.ylabel(\"Y\")\n","plt.xlabel(\"X\")"],"execution_count":0,"outputs":[{"output_type":"execute_result","data":{"text/plain":["Text(0.5, 0, 'X')"]},"metadata":{"tags":[]},"execution_count":78},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"MUb8P1X9Jd_f","colab_type":"text"},"source":["В этом разделе мы познакомились с понятиями пределов последовательности и функции. Эти понятия пригодятся нам в другом ноутбуке, посвященном производным. Более детальное изучение выходит за рамки данного материала."]},{"cell_type":"markdown","metadata":{"id":"c3qquhmTJd_f","colab_type":"text"},"source":["# Функции многих переменных"]},{"cell_type":"markdown","metadata":{"id":"GhV2iHFZJd_g","colab_type":"text"},"source":["Выше мы рассмотрели функции, которые отображают одну переменную $x$ в одну переменную $y$. Теперь рассмотрим функции, которые отображают несколько переменных $x_1, x_2, \\dots$ в одну переменную $y$."]},{"cell_type":"markdown","metadata":{"id":"FO_L3f5vJd_h","colab_type":"text"},"source":["В самом начале ноутбука в примере с высотой дома мы рассматривали функцию зависимости высоты дома от одной переменной -- количества этажей в доме. Высоту одного этажа мы принимали за константу, поэтому наша функция выглядела так:\n","\n","$F(x) = 2x+1$\n","\n","где $x$ — количество этажей,
2 — высота одного этажа,
1 — высота фундамента,
$F(x)$ — итоговая высота дома."]},{"cell_type":"markdown","metadata":{"id":"pbLeyN0GJd_i","colab_type":"text"},"source":["Но мы понимаем, что в реальной жизни дома бывают разные и высота одного этажа во дворце и в жилой хрущевке может отличаться. То есть, высота одного этажа — это тоже переменная величина. Давайте отразим этой. внашей функции высоты дома:"]},{"cell_type":"markdown","metadata":{"id":"sldofhleJd_i","colab_type":"text"},"source":["$F(x) = yx+1$\n","\n","где $x$ — количество этажей,
$y$ — высота одного этажа,
1 — высота фундамента,
$F(x)$ — итоговая высота дома."]},{"cell_type":"markdown","metadata":{"id":"G0Ci4bwoJd_k","colab_type":"text"},"source":["Теперь это функция с **двумя переменными**. Мы можем изменять значения $x$ и $y$, подставлять их в функцию и получать разные значения.\n","\n","Точно так же можно сделать переменной и высоту фундамента — функция пример вид:\n","\n","$F(x) = yx+z$\n","\n","где $x$ — количество этажей,
$y$ — высота одного этажа,
$z$ — высота фундамента,
$F(x)$ — итоговая высота дома.\n","\n","...и будет уже функцией от трех переменных."]},{"cell_type":"markdown","metadata":{"id":"uvy9yDr_Jd_m","colab_type":"text"},"source":["Понятно, что функции бывают от скольки угодно переменных. И чаще всего в жизни встречаются функции от довольно большого числа переменных. Например, нейронная сеть — это функция от тысяч или даже миллионов параметров."]},{"cell_type":"markdown","metadata":{"id":"T_og3llPJd_m","colab_type":"text"},"source":["> Пример #18
\n","
\n"," Функции двух переменных тоже можно рисовать — они представляют собой трехмерную поверхность (задаваемую двумя переменным и значениями функции).
\n","
\n"," Функции с тремя и более переменными, к сожалению, изобразить нельзя (они соответствуют 4-хмерной и еще более многомерным телам, а мы живем в трехмерном мире, эх)"]},{"cell_type":"code","metadata":{"id":"xWrl4Vr8Jd_n","colab_type":"code","outputId":"e6644721-1ff7-491a-f559-252c54ec40bb","colab":{}},"source":["from mpl_toolkits.mplot3d import Axes3D\n","import matplotlib.pyplot as plt\n","from matplotlib import cm\n","from matplotlib.ticker import LinearLocator, FormatStrFormatter\n","import numpy as np\n","\n","\n","fig = plt.figure()\n","ax = fig.gca(projection='3d')\n","\n","# Make data.\n","X = np.arange(-5, 5, 0.25)\n","Y = np.arange(-5, 5, 0.25)\n","X, Y = np.meshgrid(X, Y)\n","R = np.sqrt(X**2 + Y**2)\n","Z = np.sin(R)\n","\n","# Plot the surface.\n","surf = ax.plot_surface(X, Y, Z,\n"," linewidth=0, antialiased=False)\n","\n","# Customize the z axis.\n","ax.set_zlim(-1.01, 1.01)\n","ax.zaxis.set_major_locator(LinearLocator(10))\n","ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))\n","\n","plt.show()"],"execution_count":0,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"tags":[],"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"dBk2xqiSJd_p","colab_type":"text"},"source":["Как же с такими функциями работать? На самом деле, точно так же, как и с функциями одной переменной:"]},{"cell_type":"markdown","metadata":{"id":"FWZVLil6Jd_p","colab_type":"text"},"source":["### Область значений и область определения функции многих переменных"]},{"cell_type":"markdown","metadata":{"id":"O7_jMtbFJd_q","colab_type":"text"},"source":["Рассмотрим функцию с двумя переменными:\n","\n","$F(x_1, x_2) = \\sqrt{x_1} + x_2 $\n","\n","Так как мы работаем только с действительными числами ($\\mathbb{R}$), то переменная $x_1$ может принимать только положительные значения, т.е. определена на $\\mathbb{R_+}$. Переменная же $x_2$ может принимать любые значения на $\\mathbb{R}$. \n","Обозначается область определения функции с двумя переменными так:\n","\n","$\\mathbb{R_+} \\times \\mathbb{R}$\n","\n","Область значения нашей функции — $\\mathbb{R}$. Итого функция \n","\n","$F: \\mathbb{R_+} \\times \\mathbb{R} \\to \\mathbb{R}$ "]},{"cell_type":"markdown","metadata":{"id":"Nx9zzWHWJd_r","colab_type":"text"},"source":["### Исследование функций многих переменных"]},{"cell_type":"markdown","metadata":{"id":"GZLCXO51Jd_r","colab_type":"text"},"source":["В разделе про исследования функций многих переменных мы говорили про поиски минимума/максимума, возрастание/убывание функции и непрерывность. Эти понятия легко обобщаются на функции многих переменных:\n","\n","Рассмотрим функцию $n$ переменныx $F(x_1, x_2, \\dots, x_n)$."]},{"cell_type":"markdown","metadata":{"id":"l47r5FTRJd_r","colab_type":"text"},"source":["1. **Минимум и максимум**:\n","\n","Задача поиска минимумов (как локальных, так и глобальных) в случае функции многих переменных ставится так же, как и в случае функции одной переменной: нужно найти такое значение аргумента (аргументов), что соответствубщее значение функции минимально/максимально.\n","\n","То есть, в случае функции $F$ нам надо найти такие $x_1, x_2, \\dots, x_n$, что $F(x_1, x_2, \\dots, x_n)$ минимально/максимально.\n","\n","2. **Возрастание и убывание функции**\n","\n","Рассмотрим некоторую фиксированную \"точку\" — набор параметров $(x'_1, x'_2, \\dots, x'_n)$. В случае функции многих переменных мы не можем сказать, возрастает или убывает функция $F$ в этой точке, потому что при изменении разных переменных функция может вести себя по разному.\n","\n","Другими словами: давайте зафиксируем все координаты $x'_2, \\dots, x'_n$ и будем изменять только $x_1$. Мы как бы получим функцию одной переменной — так как мы зафиксировали $x'_2, \\dots, x'_n$, то их мы модем считать константами. И вот функция одной переменной в точке $x'_1$ может возрастать, убывать или вообще иметь экстремум.\n","\n","Теперь сделаем то же самое, только завиксируем все координаты, кроме второй. Менять будем только $x_2$. Опять получим функцию одной переменной, но уже другую, не как при изменении $x_1$. Опять же, в точке $x'_2$ эта функция может возрастать, убывать или вообще иметь экстремум.\n","\n","Аналогично со всеми остальными координатами. Получается, что, находясь в одной точке $(x'_1, x'_2, \\dots, x'_n)$, функция может вырасти при изменении одной координаты и уменьшиться при изменении другой. Поэтому определение возрастания/удывания функции многих переменных в точке определено только **покоординатно**. \n","\n","3. **Непрерывность и предел**\n"," Здесь ситуация схожа с первым пунктом: понятие непрерывности и предела очень просто обобщается на функцию многих переменных. \n"," \n"," Вспомним определение непрерывности для функции одной переменной:\n"," \n"," Функция F **непрерывна в точке** x, если:
\n"," 1. F определена в точке x\n"," 2. Для любого числа $\\delta$ > 0 можно найти такое $\\Delta x > 0$, что для любой точки $x' \\in [x - \\Delta x, x + \\Delta x]$ выполняется: $|F(x') - F(x)| < \\delta$
\n","\n","Для непрерывности функции многих переменных остается сказать, что пункт B должен выполняться по каждой координате функции.\n","Это значит, что мы у функции $F(x_1, x_2, \\dots, x_n)$ фиксируем все координаты, кроме одной, и для полученной функции одной переменной должно выполняться условие непрерывности."]},{"cell_type":"markdown","metadata":{"id":"SSboPhEoJd_s","colab_type":"text"},"source":["# Примеры функций в реальной жизни\n","\n","\n"]},{"cell_type":"markdown","metadata":{"id":"rmJR35-BJxuP","colab_type":"text"},"source":["Для того, чтобы понимать, что функции присутствуют практически везде в нашей жизни, приведем несколько примеров:\n","\n","Давайте рассмотрим несколько примеров функций из экономики и финансов:"]},{"cell_type":"markdown","metadata":{"id":"0ndyk2HyJd_s","colab_type":"text"},"source":[" > Пример #19
\n","
\n"," Функция спроса.
\n"," Допустим, мы торгуем определенным товаром, например, толстовками. Обозначим за Q количество купленного товара, за P -- цену одной кдиницы товара. Тогда функция спроса в нашем случае может выглядеть так:
\n"," $Q = 7 - P$
\n"," $Q$ и $P$ здесь -- переменные ( как $x$ и $y$ в предыдущих примерах)"]},{"cell_type":"markdown","metadata":{"id":"S2HLYbXHJd_t","colab_type":"text"},"source":[" > Пример #20
\n","
\n"," Расчет излишка потребителя.
\n"," Формула расчета излишка потребителя выглядит так:
\n"," $S_{PEP1} = [(P_1 – P) \\times Q] / 2$
\n"," Здесь $S_{PEP1}$ — излишек покупателя,
\n"," $P_1$ — цена спроса,
\n"," $P$ — рыночная цена,
\n"," $Q$ — объем продаж.
\n","
\n"," Это функция 3 переменных."]},{"cell_type":"markdown","metadata":{"id":"bz28vZabJd_u","colab_type":"text"},"source":[" > Пример #21
\n","
\n"," Функция зависимости скорости тела от времени (из физики):
\n"," $v = v_0 + at$,
\n"," $v$ — скорость,
\n"," $v_0$ — начальная скорость,
\n"," $a$ — ускорение,
\n"," $t$ — время."]},{"cell_type":"code","metadata":{"id":"9CpSHO6aJd_u","colab_type":"code","colab":{}},"source":[""],"execution_count":0,"outputs":[]}]}