{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from sympy import *\n", "import math\n", "init_printing()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This first exercise is just verifying some properties of statistics ( namely $\\sigma^2 = < j^2 > - < j > ^2$ )" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "count 14.000000\n", "mean 21.000000\n", "std 4.472136\n", "min 14.000000\n", "25% 16.000000\n", "50% 23.000000\n", "75% 25.000000\n", "max 25.000000\n", "dtype: float64" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ages = pd.Series([14,15, 16, 16, 16, 22,22,24, 24, 25, 25, 25, 25, 25])\n", "ages.describe()\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "count 14.000000\n", "mean 459.571429\n", "std 178.445301\n", "min 196.000000\n", "25% 256.000000\n", "50% 530.000000\n", "75% 625.000000\n", "max 625.000000\n", "dtype: float64" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(ages**2).describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Pandas standard deviation formula divides by N - 1 , not N, so we have to compensate for that." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$$4.472135954999578$$" ], "text/plain": [ "4.472135954999578" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "math.sqrt(((ages**2).mean() - ages.mean()**2)*14/13)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# facecolor - makes graph non transparent\n", "fig=plt.figure(facecolor='white')\n", "ax=fig.gca()\n", "ax.set_xlabel('age')\n", "ax.set_ylabel('freq')\n", "ax.set_title('Griffiths Problem 1.1')\n", "ages.plot(kind='hist', legend=False, ax=ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dropping a rock off a cliff that covers a distance given by $ x(t) = \\frac{1}{2}gt^2 $" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [], "source": [ "idx = np.linspace(0,1,11)\n", "dist = pd.Series([ 0.5*9.8*t**2/4.9 for t in idx], index=idx)\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# facecolor - makes graph non transparent\n", "fig=plt.figure(facecolor='white')\n", "ax=fig.gca()\n", "ax.set_xlabel('time')\n", "ax.set_ylabel('distance')\n", "ax.set_title('rock dropped')\n", "dist.plot(kind='line', x=idx, legend=False, ax=ax)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "s1=pd.Series(np.random.ranf(10000))\n", "s1.plot(kind='hist')" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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"text/latex": [ "$$0.285455411085$$" ], "text/plain": [ "0.28545541108511119" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s1.std()" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$$0.331662681289$$" ], "text/plain": [ "0.33166268128906645" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(s1**2).mean()" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$$0.29427097342$$" ], "text/plain": [ "0.29427097342047642" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(s1**2).std()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "g,t,x, h = symbols('g t x h')" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\frac{g h^{3}}{6}$$" ], "text/plain": [ " 3\n", "g⋅h \n", "────\n", " 6 " ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = integrate(g*t**2/2,t)\n", "f.subs(t,h)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$$\\mathbb{R} \\cap \\left\\{- \\sqrt{2} \\sqrt{\\frac{x}{g}}, \\sqrt{2} \\sqrt{\\frac{x}{g}}\\right\\}$$" ], "text/plain": [ " ⎧ ___ ___⎫\n", " ⎪ ╱ x ╱ x ⎪\n", "ℝ ∩ ⎨-√2⋅ ╱ ─ , √2⋅ ╱ ─ ⎬\n", " ⎪ ╲╱ g ╲╱ g ⎪\n", " ⎩ ⎭" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solveset(Eq(g*t**2/2, x), t, domain=S.Reals)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }