Repo re-org

1 files changed, 184 insertions, 0 deletions

diff --git a/notebooks/gauss_derivations.ipynb b/notebooks/gauss_derivations.ipynb
new file mode 100644
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+++ 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"
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+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}