{ "cells": [ { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# This is Davide's code for the Taylor series activity\n", "# first I import the libraries that I need\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# first I calculate the true unction\n", "x=np.arange(-1,3.00001,.01)\n", "y=np.exp(x)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# here I calculate the 3rd order expansion around x=0\n", "def taylor3(x):\n", " y=x*0\n", " for i in range(4):\n", " y = y + np.exp(0)/np.math.factorial(i)*x**i\n", " return(y)\n", "tay3=taylor3(x)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(x,y,label='y=exp(x)')\n", "plt.plot(x,tay3,label=r'3$^{rd}$ order expansion')\n", "plt.xlabel('x')\n", "plt.ylabel('f(x)')\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# redoing the taylor expansion to allow for expansion to arbitrary\n", "# order around arbitrary point\n", "def taylorn(x,x0,order):\n", " y=x*0\n", " for i in range(order+1):\n", " y = y + np.exp(x0)/np.math.factorial(i)*(x-x0)**i\n", " return(y)" ] }, { "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": [ "# plotting various orders around x0=1.5\n", "# I am going to use a thick line for the real function to makes it stand out\n", "plt.plot(x,y,label='y=exp(x)',lw=4)\n", "stringy=['th','st','nd','rd','th']\n", "plt.plot(1.5,np.exp(1.5),'o',ms=14,label='Expansion point')\n", "for i in range(5):\n", " plt.plot(x,taylorn(x,1.5,i),label=str(i)+r'$^{'+stringy[i]+'}$ order expansion')\n", "plt.xlabel('x')\n", "plt.ylabel('f(x)')\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }