{ "cells": [ { "cell_type": "markdown", "id": "51e496b1-c39e-443f-ace9-3383baf97074", "metadata": {}, "source": [ "# Задачи для практического занятия по курсу:\n", "\n", "## \"ПРОГРАММИРОВАНИЕ\" 👩‍💻\n", "\n", "### Лабораторная работа по теме \"Суммирование функциональных рядов\" 📝\n", "\n", "#### Преподаватель практики: Т.Ф. Долгих, каф. ВМ и МФ, мехмат ЮФУ 👩‍🏫\n", "\n", "-----------\n", "\n", "**Переименовать файл:** File -> Rename... -> поменять NameStud на свою фамилию, записанную латинскими буквами -> нажать Rename.\n", "\n", "-----------\n", "\n", "Для визуализации формул можно использовать сайт https://www.processon.io/ru/visual \n", "\n", "-----------\n", "\n", "📜 **Пример 1.**\n", "Дано $x \\in \\mathbb{R}$.\n", "Вычислить приближенное значение бесконечной суммы\n", "$$\n", "\\sin x = x - \\frac{x^3}{3!} + \\frac{x^5}{5!} - \\frac{x^7}{7!} + \\ldots\n", "$$\n", "\n", "На печать выдавать значение суммы, посчитанное с заданной точностью $\\varepsilon = 10^{-5}$, и значение функции.\n", "\n", "*Указание.* Используйте рекуррентные соотношения." ] }, { "attachments": { "1398c324-907c-4acb-934b-ba299534390f.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "e2ff860a-b6df-4730-92cb-6da37cc25926", "metadata": {}, "source": [ "***РЕКУРРЕНТНЫЕ ФОРМУЛЫ***\n", "\n", "![image.png](attachment:1398c324-907c-4acb-934b-ba299534390f.png)" ] }, { "cell_type": "code", "execution_count": 1, "id": "c147a5e0-acf2-4421-b2b6-867582e13898", "metadata": {}, "outputs": [ { "name": "stdin", "output_type": "stream", "text": [ " -0.25\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "summa = -0.24740\n", "sin = -0.24740\n" ] } ], "source": [ "# программа\n", "\n", "from math import sin\n", "\n", "x = float(input())\n", "\n", "eps = 1e-5\n", "\n", "s = 0\n", "i = 1\n", "a = x\n", "while abs(a) >= eps:\n", " s += a\n", " i += 1\n", " a *= - x * x / (2 * i - 2) / (2 * i - 1)\n", "\n", "print('summa = %7.5f' %s)\n", "\n", "f = sin(x)\n", "print('sin = %7.5f' %f)" ] }, { "cell_type": "markdown", "id": "407f1270-93dd-49cc-ade5-1f8255659a78", "metadata": {}, "source": [ "💻 **Задание 1.**\n", "Дано $x \\in \\left( \\dfrac{1}{2}; +\\infty \\right)$.\n", "Вычислить приближенное значение бесконечной суммы\n", "$$\n", "\\ln x = \\frac{x - 1}{x} + \\frac{(x - 1)^2}{2x^2} + \\frac{(x - 1)^3}{3x^3} + \\frac{(x - 1)^4}{4x^4} + \\ldots\n", "$$\n", "\n", "На печать выдавать значение суммы, посчитанное с заданной точностью $\\varepsilon = 10^{-6}$, и значение функции.\n", "\n", "*Указание.* Используйте рекуррентные соотношения." ] }, { "cell_type": "markdown", "id": "b5201243-ec2b-488a-9b97-7297f9e7b83c", "metadata": {}, "source": [ "***РЕКУРРЕНТНЫЕ ФОРМУЛЫ***\n" ] }, { "cell_type": "code", "execution_count": null, "id": "8b2d11d6-1916-4ef4-b004-d45cfb248c6b", "metadata": {}, "outputs": [], "source": [ "# программа" ] }, { "cell_type": "markdown", "id": "99c34c68-7f04-441a-8115-cbcc5050fefd", "metadata": {}, "source": [ "💻 **Задание 2.**\n", "Дано $x \\in \\mathbb{R}$.\n", "Вычислить приближенное значение бесконечной суммы\n", "$$\n", "\\mathrm{ch} x = 1 + \\frac{x^2}{2!} + \\frac{x^4}{4!} + \\frac{x^6}{6!} + \\ldots\n", "$$\n", "\n", "На печать выдавать значение суммы, посчитанное с заданной точностью $\\varepsilon = 10^{-4}$, и значение функции.\n", "\n", "*Указание.* Используйте рекуррентные соотношения." ] }, { "cell_type": "markdown", "id": "9ba4ad4b-e7d2-4f2a-a2bd-1ca75f465cac", "metadata": {}, "source": [ "***РЕКУРРЕНТНЫЕ ФОРМУЛЫ***\n" ] }, { "cell_type": "code", "execution_count": null, "id": "bc1a0764-a952-4a4d-8394-6ac197196f28", "metadata": {}, "outputs": [], "source": [ "# программа" ] }, { "cell_type": "markdown", "id": "e5174dbb-99ac-499d-bc81-6887be0216e0", "metadata": {}, "source": [ "💻 **Задание 3.**\n", "Дано $x \\in \\mathbb{R}$.\n", "Вычислить приближенное значение бесконечной суммы\n", "$$\n", "\\sin^2 x = \\frac{2 \\cdot x^2}{2!} - \\frac{2^3 \\cdot x^4}{4!} + \\frac{2^5 \\cdot x^6}{6!} - \\frac{2^7 \\cdot x^8}{8!} + \\ldots\n", "$$\n", "\n", "На печать выдавать значение суммы, посчитанное с заданной точностью $\\varepsilon = 10^{-5}$, и значение функции.\n", "\n", "*Указание.* Используйте рекуррентные соотношения." ] }, { "cell_type": "markdown", "id": "c41dcf6c-0dcb-4024-95a4-daa88ed2a410", "metadata": {}, "source": [ "***РЕКУРРЕНТНЫЕ ФОРМУЛЫ***\n" ] }, { "cell_type": "code", "execution_count": null, "id": "ec0d9731-7161-4c63-9cb5-c94766be7d9f", "metadata": {}, "outputs": [], "source": [ "# программа" ] }, { "cell_type": "markdown", "id": "380f773b-f86b-4ed4-96f7-cb918f8f29c0", "metadata": {}, "source": [ "💻 **Задание 4.**\n", "Дано $x \\in (-1; 1]$.\n", "Вычислить приближенное значение бесконечной суммы\n", "$$\n", "\\ln(1 + x) = x - \\frac{x^2}{2} + \\frac{x^3}{3} - \\frac{x^4}{4} + \\ldots\n", "$$\n", "\n", "На печать выдавать значение суммы, посчитанное с заданной точностью $\\varepsilon = 5 \\cdot 10^{-5}$, и значение функции.\n", "\n", "*Указание.* Используйте рекуррентные соотношения." ] }, { "cell_type": "markdown", "id": "297ea67d-0fb0-491f-a96c-1962791359ef", "metadata": {}, "source": [ "***РЕКУРРЕНТНЫЕ ФОРМУЛЫ***\n" ] }, { "cell_type": "code", "execution_count": null, "id": "7d30ce40-b580-43b1-b250-01fce22dc164", "metadata": {}, "outputs": [], "source": [ "# программа" ] }, { "cell_type": "markdown", "id": "9371b024-a2cd-4ea8-b886-a00673e35355", "metadata": {}, "source": [ "💻 **Задание 5.**\n", "Дано $x \\in \\mathbb{R}$.\n", "Напечатать таблицу значений элементов ряда\n", "$$\n", "1, \\quad \\frac{x}{1!}, \\quad \\frac{x^2}{2!}, \\quad \\frac{x^3}{3!}, \\ldots,\n", "$$\n", "которые по абсолютной величине больше $\\varepsilon = 10^{-4}$.\n", "\n", "Сначала печатать номер элемента, затем его значение.\n", "\n", "*Указание.* Используйте рекуррентные соотношения." ] }, { "cell_type": "markdown", "id": "992821f9-047d-4372-984f-7b78a9b640b9", "metadata": {}, "source": [ "***РЕКУРРЕНТНЫЕ ФОРМУЛЫ***" ] }, { "cell_type": "code", "execution_count": null, "id": "9d06c580-14ed-4272-adcc-96a324dd4287", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "4ef8b846-f5d6-4a69-b9c7-a0b7ba407cd2", "metadata": {}, "source": [ "💻 🔥 **Задание 6.**\n", "Вычислить отрицательный корень уравнения\n", "$$\n", "x^3 - x + 0{,}5 = 0,\n", "$$\n", "используя рекуррентную формулу \n", "$$\n", "x_i = \\sqrt[3]{x_{i-1} - 0{,}5}, \\quad i = 1, 2, 3,\\ldots\n", "$$\n", "Вычисления прекратить при $|x_i - x_{i-1}| < \\varepsilon$, $\\varepsilon = 10^{-4}$. \n", "Определить количество итераций.\n", "\n", "*Указание.* Начальное значение $x_0$ определите при помощи модуля `sympy`: постройте график функции $y = x^3 − x + 0{,}5$ и возьмите значение, близкое к искомому отрицательному корню и инициализируйте его в программе." ] }, { "cell_type": "code", "execution_count": null, "id": "f2566004-54cc-4aaa-a616-d04d567ca8dc", "metadata": {}, "outputs": [], "source": [ "# график" ] }, { "cell_type": "code", "execution_count": null, "id": "c7f26754-fcf5-483e-8a9a-19ce399a601e", "metadata": {}, "outputs": [], "source": [ "# программа с решением уравнения" ] } ], 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