{ "cells": [ { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "# remember to include these two lines of code at the start of your document!\n", "from IPython.core.interactiveshell import InteractiveShell\n", "InteractiveShell.ast_node_interactivity = \"all\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# MATH1110 Lab 4: Errors" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 7 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = var('x')\n", "g1 = plot( sin(x), -2*pi, 2*pi, color = 'red', thickness = 2)\n", "g2 = plot( sin(x-pi/6), -2*pi, 2*pi, color = 'orange', thickness = 2)\n", "g3 = plot( sin(x-pi/3), -2*pi, 2*pi, color = 'yellow', thickness = 2)\n", "g4 = plot( sin(x-pi/2), -2*pi, 2*pi, color = 'limegreen', thickness = 2)\n", "g5 = plot( sin(x-2*pi/3), -2*pi, 2*pi, color = 'blue', thickness = 2, alpha = 0.6)\n", "g6 = plot( sin(x-5*pi/6), -2*pi, 2*pi, color = 'purple', thickness = 2, alpha = 0.7)\n", "show((g1+g2+g3+g4+g5+g6)+text('Welcome to Lab 4', (0, 0.4), fontsize = 23, color = 'black'), \\\n", " xmin = -2*pi, xmax = 2*pi, axes = False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Objectives for today:** This one's a little bit different...\n", "\n", "1. Review of solving\n", "2. Common error codes\n", "3. Find the errors!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Review of solving equations\n", "\n", "For Assignment 2 (which is due on friday), you'll have to know how to find the intersection of two curves by solving a system of equations. Here is another example of that process:\n", "\n", "Plot the two implicitly defined curves $f_1$ and $f_2$ in different colours for $-5 \\leq x \\leq 15, \\; -4 \\leq y \\leq 4$. Find their intersection using *solve()*." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "x = var('x')\n", "y = var('y')\n", "f1 = x==y^2+1\n", "f2 = tan(ln(y^3-x*y))==0\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clear as mud? Any questions here?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Common error codes\n", "\n", "Below are some examples of errors you'll commonly see while coding. Usually ***the very last line of the error message*** is most helpful." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "clear_vars()\n", "y = t-1\n", "# undefined variable ... \"name 't' is not defined\"" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "scrolled": true }, "outputs": [], "source": [ "clear_vars()\n", "x = var('x')\n", "h(x) = 4x+9/2\n", "# SyntaxError\n", "# missing a multiplication sign" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sage will sometimes put an arrow where the error was detected, or reference which line the problem occurred. Very handy!\n", "\n", "A NameError can also mean that the command being used is not recognized:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "Show(h)\n", "# anyone see the issue here?" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [], "source": [ "3*(cos( (2^4 - 1)*pi/6)\n", "# parentheses don't match\n", "# usually it says \"unexpected EOF while parsing\" if there's a close parenthesis missing from the end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that when you place your curser next to a set of parentheses, the complimenting one lights up in green.\n", "If there is not matching parenthesis, then it will be red.\n", "\n", "The error code looks different if there's a missing opening parenthesis:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "scrolled": true }, "outputs": [], "source": [ "3*cos( (2^4 - 1)*pi/6))" ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [], "source": [ "x = var('x')\n", "limit(sin(x))\n", "# a ValueError will occur when you're missing a mandatory entry within a command\n", "# it also gives you an example of what a correctly used limit command should look like!" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "plot(-x^2, colour = 'orange')\n", "# Sage is trying real hard but can't figure it out\n", "# A runtime error is produced when an option within a command isn't recognized (colour has the wrong spelling)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "plot(-x^2, color = orange)\n", "# and another NameError if you forget to put a bit of text in quotes/apostrophes that should be" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The trickiest errors to find are often those with parentheses, as sometimes the error code will point to the line *after* where the parenthsis was forgotten. Watch out for these instances!\n", "\n", "When in doubt, read the last line of the error code and see if Sage is giving you any arrows to hint at where the error is occuring." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Find the errors!\n", "\n", "Now it's your turn to work on those coding hawk eyes. Correct the following code and breifly describe in a #comment what the issue was. There may be more than one error to fix.\n", "\n", "If you don't get to them all, don't worry about it! It's just for practice." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#(1) Show the function\n", "r = var('r')\n", "b = log(r+1)\n", "show(B)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#(2) Plot the function\n", "plot(b, r, -10, 10, ymin -10, ymax = 10)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#(3) Show the function\n", "h = sin*(3*r)/cos*(r+1)\n", "show(h)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#(4) Expand the function g\n", "g = (r-1)(r+8)(2*r+1)(r-3)\n", "expand(g)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#(5) Plot the function\n", "a5 = log(4*r)-r^3\n", "plot(a5, 10, -10, ymin = -10, ymax = 10)\n" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "#(6) Plot the function\n", "plot=(a5, ymin = -10, ymax = 10, colour = purple)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#(7) Plot the two functions on the same graph\n", "clear_vars()\n", "x = var('x')\n", "f1 = (3*(cos(x)) - sin(1/x)\n", "f2 = cot( e^x ) # Note that e is a number\n", "plot( f1, f2, x, -pi, pi, ymin = -10, ymax = 10, detect_poles = 'show')\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#(8) Clear variables\n", "Clear_vars()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#(9) Find the derivative of y using the limit definition\n", "t = var('t') ; h = var('h')\n", "y = (t^2 +1) / ((t+3)*(t^2 - 2))\n", "d9 = ( y(t+h) - y(t) ) / h\n", "limit(t, h = 0)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#(10) Find the one-sided limits of y as t approaches -3\n", "limit(y, t = -3, dir = -)\n", "limit(y, t = -3, dir = +)\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#(11) Add (3/4)*s^3 to the function g\n", "clear_vars()\n", "s = vars('s')\n", "g = s^2 + (s^3)/4\n", "show( g – (3/4)*s^3 )\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#(12) Plot the function\n", "Plot( s*csc(s)) , s, -10, 10)\n" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [], "source": [ "#(13) Plot the lines together on a graph\n", "line1 = line( [(-1, -1), (1, 4)], color = 'pink')\n", "line2 = line( [(-3, -1), (3, 1)], color = 'orange')\n", "line3 = line( [(-3, 2), (4, 0)], color = 'navy')\n", "\n", "# no error code, but where is the graph?" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "#(14) Plot the four functions and points together on the graph\n", "clear_vars()\n", "ps = points( [(2.3, 2.8), (3.7, 2.8)], size = 70)\n", "x = var('x')\n", "curve1 = plot( (x-3)^2/2 + 1, x, 2.3, 3.7, thickness = 3, xmin = 0, xmax = 5)\n", "curve2 = plot( 4*(x-3)^2 + 2, x, 2.9, 3.1, \\\n", " title = \"I'm so sorry this was supposed to look nice but it's a bit scary .. Happy early Halloween!\")\n", "curve3 = plot( cos(x - 2.3) + 2.1, 2.2, 2.4)\n", "curve4 = plot( cos(x - 3.7) + 2.1, 3.6, 3.8)\n", "show(ps, curve1, curve2, curve3, curve4, xmin = 1, xmax = 5, ymin = 0, ymax = 4)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#(15) Show the function $f = \\large{ \\frac{ \\cos{(x-x^2)}\\sin{\\frac{x}{2}} }{ 3+x } }$" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "#(15) Show the function\n", "clear_vars()\n", "x = var('x')\n", "f = (cos(x-x^2))sin(x/2) / 3+x\n", "show(f)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reminders\n", "\n", "> Assignment 2 is due this friday. Submit a pdf of your code to Blackboard.\n", "\n", "> Be sure to save your work!" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.0", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }