From 6c1d7ceb164445b76b37db565ed100957dcc7382 Mon Sep 17 00:00:00 2001
From: ande2472 <ande2472@msu.edu>
Date: Tue, 28 Jun 2022 03:14:40 -0400
Subject: [PATCH] Upload New File
---
Gradients.ipynb | 226 ++++++++++++++++++++++++++++++++++++++++++++++++
1 file changed, 226 insertions(+)
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+{
+ "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": [
+ "✅ **<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": [
+ "\\✅ **<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
+}
--
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