Gradients

Gradients.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "fc73d74c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "('answercheck.py', <http.client.HTTPMessage at 0x7fc9a8612220>)"
+      ]
+     },
+     "execution_count": 32,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "##ANSWER##\n",
+    "#Install answercheck in current director\n",
+    "from urllib.request import urlretrieve\n",
+    "urlretrieve('https://raw.githubusercontent.com/colbrydi/jupytercheck/master/answercheck.py', filename='answercheck.py')\n",
+    "##ANSWER##"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3c2a4f39",
+   "metadata": {},
+   "source": [
+    "# Gradients\n",
+    "Pandas is a python library used to analyze data."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "71e867d9",
+   "metadata": {},
+   "source": [
+    "## Learning Goal\n",
+    "To _**understand**_ how to take a multivariable/partial derivative.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5d237ca9",
+   "metadata": {},
+   "source": [
+    "## Training Materials\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "21f9b14e",
+   "metadata": {},
+   "source": [
+    "For a general understanding of gradients, check out the following website:\n",
+    "\n",
+    "https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivative-and-gradient-articles/a/the-gradient#:~:text=In%20the%20case%20of%20scalar,partial%20derivatives%20into%20a%20vector.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1e57b578",
+   "metadata": {},
+   "source": [
+    "## Self Assessment\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1b047470",
+   "metadata": {},
+   "source": [
+    "&#9989; **<span style=\"color:red\">Question:</span>**  Find (how do I make a $\\nabla$f  for the following equations:\n",
+    "\n",
+    "\n",
+    "1. $f(x, y) = x^3 - y^2$\n",
+    "2. $f(x,y) = xy^2 + 2x^4y$\n",
+    "3. $f(x,y) = cos(xy) - xsin(y)$\n",
+    "4. $f(x,y,z) = z^3 + (x/y) - 2xz$\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3b8e33ef",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Add you answers as sympy matricies.\n",
+    "a1= \n",
+    "a2=\n",
+    "a3=\n",
+    "a4=\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "08acf30a",
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "SyntaxError",
+     "evalue": "invalid syntax (20810275.py, line 5)",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;36m  Input \u001b[0;32mIn [7]\u001b[0;36m\u001b[0m\n\u001b[0;31m    a1=sym.Matrix([[3x**2] ,[-2y]])\u001b[0m\n\u001b[0m                     ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
+     ]
+    }
+   ],
+   "source": [
+    "\n",
+    "##ANSWER##\n",
+    "x=2.2\n",
+    "y=2.3\n",
+    "\n",
+    "a1=sym.Matrix([[3x**2] ,[-2y]])\n",
+    "a2=sym.Matrix([[y^2+8yx^3] ,[2xy+2x^4])\n",
+    "a3=sym.Matrix([-sin(xy)y -sin(y)], [-sin(xy)x - xcos(y)])\n",
+    "a4=sym.Matrix([(1/y)-2z],[ -x/y^2], [3z^2-2x])\n",
+    "\n",
+    "##ANSWER##"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dd9c7fa5",
+   "metadata": {},
+   "source": [
+    "\\&#9989; **<span style=\"color:red\">Question:</span>**  Example answercheck question: What is $x = 2+2$?\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "64684dfd",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Put your answer here"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "id": "619a2259",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "##ANSWER##\n",
+    "x = 4\n",
+    "##ANSWER##"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "id": "9cc2b34a",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "CheckWarning: passed variable is <class 'int'> and not a numpy.matrix.\n",
+      "    Trying to convert to a array matrix using ```A = np.matrix(A)```.\n",
+      "\n",
+      "\n",
+      "CheckWarning: passed matrix is int64 and not <class 'numpy.float64'>...\n",
+      "    Trying to convert to float using ```A = A.astype(float)```.\n",
+      "\n",
+      "Testing [[4.]]\n",
+      "Answer seems to be correct\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "from answercheck import checkanswer\n",
+    "checkanswer.vector(x,'2cab95d1b144d663bad1ce5c51020ae0')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "44b461a0",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "\n",
+    "Written by <<YOUR NAME HERE>>, Michigan State University  \n",
+    "As part of the Data Science Bridge Project \n",
+    "    \n",
+    "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc/4.0/88x31.png\" /></a><br />This work is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc/4.0/\">Creative Commons Attribution-NonCommercial 4.0 International License</a>."
+   ]
+  }
+ ],
+ "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": "3.9.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}