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Diffstat (limited to 'notebooks/gauss_derivations.ipynb')
| -rw-r--r-- | notebooks/gauss_derivations.ipynb | 184 |
1 files changed, 184 insertions, 0 deletions
diff --git a/notebooks/gauss_derivations.ipynb b/notebooks/gauss_derivations.ipynb new file mode 100644 index 0000000..6e0dcd8 --- /dev/null +++ b/notebooks/gauss_derivations.ipynb @@ -0,0 +1,184 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "\\[\\tag{${\\it \\%o}_{2}$}f\\left(a , \\mu , \\sigma , x\\right):=a\\,\\exp \\left(\\frac{-\\left(x-\\mu\\right)^2}{2\\,\\sigma^2}\\right)\\]" + ], + "text/plain": [ + " 2\n", + " - (x - mu)\n", + "(%o2) f(a, mu, sigma, x) := a exp(-----------)\n", + " 2\n", + " 2 sigma" + ], + "text/x-maxima": [ + "f(a,mu,sigma,x):=a*exp((-(x-mu)^2)/(2*sigma^2))" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f(a, mu, sigma, x) := a*exp(-(x-mu)^2/(2*sigma^2));" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "\\[\\tag{${\\it \\%o}_{11}$}-\\frac{a\\,\\left(x-\\mu\\right)\\,e^ {- \\frac{\\left(x-\\mu\\right)^2}{2\\,\\sigma^2} }}{\\sigma^2}\\]" + ], + "text/plain": [ + " 2\n", + " (x - mu)\n", + " - ---------\n", + " 2\n", + " 2 sigma\n", + " a (x - mu) %e\n", + "(%o11) - ------------------------\n", + " 2\n", + " sigma" + ], + "text/x-maxima": [ + "-(a*(x-mu)*%e^-((x-mu)^2/(2*sigma^2)))/sigma^2" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "diff(f(a, mu, sigma, x), x);" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "\\[\\tag{${\\it \\%o}_{12}$}e^ {- \\frac{\\left(x-\\mu\\right)^2}{2\\,\\sigma^2} }\\]" + ], + "text/plain": [ + " 2\n", + " (x - mu)\n", + " - ---------\n", + " 2\n", + " 2 sigma\n", + "(%o12) %e" + ], + "text/x-maxima": [ + "%e^-((x-mu)^2/(2*sigma^2))" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "diff(f(a, mu, sigma, x), a);" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "\\[\\tag{${\\it \\%o}_{13}$}\\frac{a\\,\\left(x-\\mu\\right)\\,e^ {- \\frac{\\left(x-\\mu\\right)^2}{2\\,\\sigma^2} }}{\\sigma^2}\\]" + ], + "text/plain": [ + " 2\n", + " (x - mu)\n", + " - ---------\n", + " 2\n", + " 2 sigma\n", + " a (x - mu) %e\n", + "(%o13) ------------------------\n", + " 2\n", + " sigma" + ], + "text/x-maxima": [ + "(a*(x-mu)*%e^-((x-mu)^2/(2*sigma^2)))/sigma^2" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "diff(f(a, mu, sigma, x), mu);" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "\\[\\tag{${\\it \\%o}_{14}$}\\frac{a\\,\\left(x-\\mu\\right)^2\\,e^ {- \\frac{\\left(x-\\mu\\right)^2}{2\\,\\sigma^2} }}{\\sigma^3}\\]" + ], + "text/plain": [ + " 2\n", + " (x - mu)\n", + " - ---------\n", + " 2\n", + " 2 2 sigma\n", + " a (x - mu) %e\n", + "(%o14) -------------------------\n", + " 3\n", + " sigma" + ], + "text/x-maxima": [ + "(a*(x-mu)^2*%e^-((x-mu)^2/(2*sigma^2)))/sigma^3" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "diff(f(a, mu, sigma, x), sigma);" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Maxima", + "language": "maxima", + "name": "maxima" + }, + "language_info": { + "codemirror_mode": "maxima", + "file_extension": ".mac", + "mimetype": "text/x-maxima", + "name": "maxima", + "pygments_lexer": "maxima", + "version": "5.43.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} |