2465 lines
457 KiB
HTML
2465 lines
457 KiB
HTML
<!DOCTYPE html>
|
||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head>
|
||
|
||
<meta charset="utf-8">
|
||
<meta name="generator" content="quarto-1.0.32">
|
||
|
||
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
|
||
|
||
|
||
<title>Calculus with Julia - 11 Polynomials</title>
|
||
<style>
|
||
code{white-space: pre-wrap;}
|
||
span.smallcaps{font-variant: small-caps;}
|
||
span.underline{text-decoration: underline;}
|
||
div.column{display: inline-block; vertical-align: top; width: 50%;}
|
||
div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
|
||
ul.task-list{list-style: none;}
|
||
pre > code.sourceCode { white-space: pre; position: relative; }
|
||
pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
|
||
pre > code.sourceCode > span:empty { height: 1.2em; }
|
||
.sourceCode { overflow: visible; }
|
||
code.sourceCode > span { color: inherit; text-decoration: inherit; }
|
||
div.sourceCode { margin: 1em 0; }
|
||
pre.sourceCode { margin: 0; }
|
||
@media screen {
|
||
div.sourceCode { overflow: auto; }
|
||
}
|
||
@media print {
|
||
pre > code.sourceCode { white-space: pre-wrap; }
|
||
pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
|
||
}
|
||
pre.numberSource code
|
||
{ counter-reset: source-line 0; }
|
||
pre.numberSource code > span
|
||
{ position: relative; left: -4em; counter-increment: source-line; }
|
||
pre.numberSource code > span > a:first-child::before
|
||
{ content: counter(source-line);
|
||
position: relative; left: -1em; text-align: right; vertical-align: baseline;
|
||
border: none; display: inline-block;
|
||
-webkit-touch-callout: none; -webkit-user-select: none;
|
||
-khtml-user-select: none; -moz-user-select: none;
|
||
-ms-user-select: none; user-select: none;
|
||
padding: 0 4px; width: 4em;
|
||
color: #aaaaaa;
|
||
}
|
||
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; }
|
||
div.sourceCode
|
||
{ }
|
||
@media screen {
|
||
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
|
||
}
|
||
code span.al { color: #ff0000; font-weight: bold; } /* Alert */
|
||
code span.an { color: #60a0b0; font-weight: bold; font-style: italic; } /* Annotation */
|
||
code span.at { color: #7d9029; } /* Attribute */
|
||
code span.bn { color: #40a070; } /* BaseN */
|
||
code span.bu { } /* BuiltIn */
|
||
code span.cf { color: #007020; font-weight: bold; } /* ControlFlow */
|
||
code span.ch { color: #4070a0; } /* Char */
|
||
code span.cn { color: #880000; } /* Constant */
|
||
code span.co { color: #60a0b0; font-style: italic; } /* Comment */
|
||
code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; } /* CommentVar */
|
||
code span.do { color: #ba2121; font-style: italic; } /* Documentation */
|
||
code span.dt { color: #902000; } /* DataType */
|
||
code span.dv { color: #40a070; } /* DecVal */
|
||
code span.er { color: #ff0000; font-weight: bold; } /* Error */
|
||
code span.ex { } /* Extension */
|
||
code span.fl { color: #40a070; } /* Float */
|
||
code span.fu { color: #06287e; } /* Function */
|
||
code span.im { } /* Import */
|
||
code span.in { color: #60a0b0; font-weight: bold; font-style: italic; } /* Information */
|
||
code span.kw { color: #007020; font-weight: bold; } /* Keyword */
|
||
code span.op { color: #666666; } /* Operator */
|
||
code span.ot { color: #007020; } /* Other */
|
||
code span.pp { color: #bc7a00; } /* Preprocessor */
|
||
code span.sc { color: #4070a0; } /* SpecialChar */
|
||
code span.ss { color: #bb6688; } /* SpecialString */
|
||
code span.st { color: #4070a0; } /* String */
|
||
code span.va { color: #19177c; } /* Variable */
|
||
code span.vs { color: #4070a0; } /* VerbatimString */
|
||
code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */
|
||
</style>
|
||
|
||
|
||
<script src="../site_libs/quarto-nav/quarto-nav.js"></script>
|
||
<script src="../site_libs/quarto-nav/headroom.min.js"></script>
|
||
<script src="../site_libs/clipboard/clipboard.min.js"></script>
|
||
<script src="../site_libs/quarto-search/autocomplete.umd.js"></script>
|
||
<script src="../site_libs/quarto-search/fuse.min.js"></script>
|
||
<script src="../site_libs/quarto-search/quarto-search.js"></script>
|
||
<meta name="quarto:offset" content="../">
|
||
<link href="../precalc/polynomial_roots.html" rel="next">
|
||
<link href="../precalc/inversefunctions.html" rel="prev">
|
||
<script src="../site_libs/quarto-html/quarto.js"></script>
|
||
<script src="../site_libs/quarto-html/popper.min.js"></script>
|
||
<script src="../site_libs/quarto-html/tippy.umd.min.js"></script>
|
||
<script src="../site_libs/quarto-html/anchor.min.js"></script>
|
||
<link href="../site_libs/quarto-html/tippy.css" rel="stylesheet">
|
||
<link href="../site_libs/quarto-html/quarto-syntax-highlighting.css" rel="stylesheet" id="quarto-text-highlighting-styles">
|
||
<script src="../site_libs/bootstrap/bootstrap.min.js"></script>
|
||
<link href="../site_libs/bootstrap/bootstrap-icons.css" rel="stylesheet">
|
||
<link href="../site_libs/bootstrap/bootstrap.min.css" rel="stylesheet" id="quarto-bootstrap" data-mode="light">
|
||
<script id="quarto-search-options" type="application/json">{
|
||
"location": "navbar",
|
||
"copy-button": false,
|
||
"collapse-after": 3,
|
||
"panel-placement": "end",
|
||
"type": "overlay",
|
||
"limit": 20,
|
||
"language": {
|
||
"search-no-results-text": "No results",
|
||
"search-matching-documents-text": "matching documents",
|
||
"search-copy-link-title": "Copy link to search",
|
||
"search-hide-matches-text": "Hide additional matches",
|
||
"search-more-match-text": "more match in this document",
|
||
"search-more-matches-text": "more matches in this document",
|
||
"search-clear-button-title": "Clear",
|
||
"search-detached-cancel-button-title": "Cancel",
|
||
"search-submit-button-title": "Submit"
|
||
}
|
||
}</script>
|
||
<script async="" src="https://hypothes.is/embed.js"></script>
|
||
<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" integrity="sha512-c3Nl8+7g4LMSTdrm621y7kf9v3SDPnhxLNhcjFJbKECVnmZHTdo+IRO05sNLTH/D3vA6u1X32ehoLC7WFVdheg==" crossorigin="anonymous"></script>
|
||
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.5.1/jquery.min.js" integrity="sha512-bLT0Qm9VnAYZDflyKcBaQ2gg0hSYNQrJ8RilYldYQ1FxQYoCLtUjuuRuZo+fjqhx/qtq/1itJ0C2ejDxltZVFg==" crossorigin="anonymous"></script>
|
||
<script type="application/javascript">define('jquery', [],function() {return window.jQuery;})</script>
|
||
|
||
<script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml-full.js" type="text/javascript"></script>
|
||
|
||
</head>
|
||
|
||
<body class="nav-sidebar floating nav-fixed">
|
||
|
||
<div id="quarto-search-results"></div>
|
||
<header id="quarto-header" class="headroom fixed-top">
|
||
<nav class="navbar navbar-expand-lg navbar-dark ">
|
||
<div class="navbar-container container-fluid">
|
||
<a class="navbar-brand" href="../index.html">
|
||
<img src="../logo.png" alt="">
|
||
<span class="navbar-title">Calculus with Julia</span>
|
||
</a>
|
||
<div id="quarto-search" class="" title="Search"></div>
|
||
</div> <!-- /container-fluid -->
|
||
</nav>
|
||
<nav class="quarto-secondary-nav" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar" aria-controls="quarto-sidebar" aria-expanded="false" aria-label="Toggle sidebar navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
|
||
<div class="container-fluid d-flex justify-content-between">
|
||
<h1 class="quarto-secondary-nav-title"><span class="chapter-number">11</span> <span class="chapter-title">Polynomials</span></h1>
|
||
<button type="button" class="quarto-btn-toggle btn" aria-label="Show secondary navigation">
|
||
<i class="bi bi-chevron-right"></i>
|
||
</button>
|
||
</div>
|
||
</nav>
|
||
</header>
|
||
<!-- content -->
|
||
<div id="quarto-content" class="quarto-container page-columns page-rows-contents page-layout-article page-navbar">
|
||
<!-- sidebar -->
|
||
<nav id="quarto-sidebar" class="sidebar collapse sidebar-navigation floating overflow-auto">
|
||
<div class="mt-2 flex-shrink-0 align-items-center">
|
||
<div class="sidebar-search">
|
||
<div id="quarto-search" class="" title="Search"></div>
|
||
</div>
|
||
</div>
|
||
<div class="sidebar-menu-container">
|
||
<ul class="list-unstyled mt-1">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../index.html" class="sidebar-item-text sidebar-link">Preface</a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-1" aria-expanded="true">Precalculus Concepts</a>
|
||
<a class="sidebar-item-toggle text-start" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-1" aria-expanded="true">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
||
</a>
|
||
</div>
|
||
<ul id="quarto-sidebar-section-1" class="collapse list-unstyled sidebar-section depth1 show">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/calculator.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">1</span> <span class="chapter-title">From calculator to computer</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/variables.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">2</span> <span class="chapter-title">Variables</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/numbers_types.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">3</span> <span class="chapter-title">Number systems</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/logical_expressions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">4</span> <span class="chapter-title">Inequalities, Logical expressions</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/vectors.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">5</span> <span class="chapter-title">Vectors</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/ranges.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">6</span> <span class="chapter-title">Ranges and Sets</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">7</span> <span class="chapter-title">Functions</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/plotting.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">8</span> <span class="chapter-title">The Graph of a Function</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/transformations.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">9</span> <span class="chapter-title">Function manipulations</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/inversefunctions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">10</span> <span class="chapter-title">The Inverse of a Function</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/polynomial.html" class="sidebar-item-text sidebar-link active"><span class="chapter-number">11</span> <span class="chapter-title">Polynomials</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/polynomial_roots.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">12</span> <span class="chapter-title">Roots of a polynomial</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/polynomials_package.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">13</span> <span class="chapter-title">The Polynomials package</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/rational_functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">14</span> <span class="chapter-title">Rational functions</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/exp_log_functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">15</span> <span class="chapter-title">Exponential and logarithmic functions</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/trig_functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">16</span> <span class="chapter-title">Trigonometric functions</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../precalc/julia_overview.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">17</span> <span class="chapter-title">Overview of Julia commands</span></a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-2" aria-expanded="false">Limits</a>
|
||
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-2" aria-expanded="false">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
||
</a>
|
||
</div>
|
||
<ul id="quarto-sidebar-section-2" class="collapse list-unstyled sidebar-section depth1 ">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../limits/limits.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">18</span> <span class="chapter-title">Limits</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../limits/limits_extensions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">19</span> <span class="chapter-title">Limits, issues, extensions of the concept</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../limits/continuity.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">20</span> <span class="chapter-title">Continuity</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../limits/intermediate_value_theorem.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">21</span> <span class="chapter-title">Implications of continuity</span></a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-3" aria-expanded="false">Derivatives</a>
|
||
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-3" aria-expanded="false">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
||
</a>
|
||
</div>
|
||
<ul id="quarto-sidebar-section-3" class="collapse list-unstyled sidebar-section depth1 ">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/derivatives.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">22</span> <span class="chapter-title">Derivatives</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/numeric_derivatives.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">23</span> <span class="chapter-title">Numeric derivatives</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/symbolic_derivatives.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">24</span> <span class="chapter-title">Symbolic derivatives</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/mean_value_theorem.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">25</span> <span class="chapter-title">The mean value theorem for differentiable functions.</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/optimization.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">26</span> <span class="chapter-title">Optimization</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/first_second_derivatives.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">27</span> <span class="chapter-title">The first and second derivatives</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/curve_sketching.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">28</span> <span class="chapter-title">Curve Sketching</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/linearization.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">29</span> <span class="chapter-title">Linearization</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/newtons_method.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">30</span> <span class="chapter-title">Newton’s method</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/more_zeros.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">31</span> <span class="chapter-title">Derivative-free alternatives to Newton’s method</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/lhospitals_rule.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">32</span> <span class="chapter-title">L’Hospital’s Rule</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/implicit_differentiation.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">33</span> <span class="chapter-title">Implicit Differentiation</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/related_rates.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">34</span> <span class="chapter-title">Related rates</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../derivatives/taylor_series_polynomials.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">35</span> <span class="chapter-title">Taylor Polynomials and other Approximating Polynomials</span></a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-4" aria-expanded="false">Integrals</a>
|
||
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-4" aria-expanded="false">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
||
</a>
|
||
</div>
|
||
<ul id="quarto-sidebar-section-4" class="collapse list-unstyled sidebar-section depth1 ">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/area.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">36</span> <span class="chapter-title">Area under a curve</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/ftc.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">37</span> <span class="chapter-title">Fundamental Theorem or Calculus</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/substitution.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">38</span> <span class="chapter-title">Substitution</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/integration_by_parts.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">39</span> <span class="chapter-title">Integration By Parts</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/partial_fractions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">40</span> <span class="chapter-title">Partial Fractions</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/improper_integrals.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">41</span> <span class="chapter-title">Improper Integrals</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/mean_value_theorem.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">42</span> <span class="chapter-title">Mean value theorem for integrals</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/area_between_curves.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">43</span> <span class="chapter-title">Area between two curves</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/center_of_mass.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">44</span> <span class="chapter-title">Center of Mass</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/volumes_slice.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">45</span> <span class="chapter-title">Volumes by slicing</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/arc_length.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">46</span> <span class="chapter-title">Arc length</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integrals/surface_area.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">47</span> <span class="chapter-title">Surface Area</span></a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-5" aria-expanded="false">ODEs</a>
|
||
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-5" aria-expanded="false">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
||
</a>
|
||
</div>
|
||
<ul id="quarto-sidebar-section-5" class="collapse list-unstyled sidebar-section depth1 ">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../ODEs/odes.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">48</span> <span class="chapter-title">ODEs</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../ODEs/euler.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">49</span> <span class="chapter-title">Euler’s method</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../ODEs/solve.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">50</span> <span class="chapter-title">The problem-algorithm-solve interface</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../ODEs/differential_equations.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">51</span> <span class="chapter-title">The <code>DifferentialEquations</code> suite</span></a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-6" aria-expanded="false">Differential vector calculus</a>
|
||
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-6" aria-expanded="false">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
||
</a>
|
||
</div>
|
||
<ul id="quarto-sidebar-section-6" class="collapse list-unstyled sidebar-section depth1 ">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/polar_coordinates.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">52</span> <span class="chapter-title">Polar Coordinates and Curves</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/vectors.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">53</span> <span class="chapter-title">Vectors and matrices</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/vector_valued_functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">54</span> <span class="chapter-title">Vector-valued functions, <span class="math inline">\(f:R \rightarrow R^n\)</span></span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/scalar_functions.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">55</span> <span class="chapter-title">Scalar functions</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/scalar_functions_applications.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">56</span> <span class="chapter-title">Applications with scalar functions</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/vector_fields.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">57</span> <span class="chapter-title">Functions <span class="math inline">\(R^n \rightarrow R^m\)</span></span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../differentiable_vector_calculus/plots_plotting.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">58</span> <span class="chapter-title">2D and 3D plots in Julia with Plots</span></a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-7" aria-expanded="false">Integral vector calculus</a>
|
||
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-7" aria-expanded="false">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
||
</a>
|
||
</div>
|
||
<ul id="quarto-sidebar-section-7" class="collapse list-unstyled sidebar-section depth1 ">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integral_vector_calculus/double_triple_integrals.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">59</span> <span class="chapter-title">Multi-dimensional integrals</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integral_vector_calculus/line_integrals.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">60</span> <span class="chapter-title">Line and Surface Integrals</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integral_vector_calculus/div_grad_curl.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">61</span> <span class="chapter-title">The Gradient, Divergence, and Curl</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integral_vector_calculus/stokes_theorem.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">62</span> <span class="chapter-title">Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../integral_vector_calculus/review.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">63</span> <span class="chapter-title">Quick Review of Vector Calculus</span></a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-8" aria-expanded="false">Alternatives</a>
|
||
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-8" aria-expanded="false">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
||
</a>
|
||
</div>
|
||
<ul id="quarto-sidebar-section-8" class="collapse list-unstyled sidebar-section depth1 ">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../alternatives/plotly_plotting.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">64</span> <span class="chapter-title">JavaScript based plotting libraries</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../alternatives/makie_plotting.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">65</span> <span class="chapter-title">Calculus plots with Makie</span></a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-9" aria-expanded="false">Appendices</a>
|
||
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-9" aria-expanded="false">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
||
</a>
|
||
</div>
|
||
<ul id="quarto-sidebar-section-9" class="collapse list-unstyled sidebar-section depth1 ">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../misc/getting_started_with_julia.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">66</span> <span class="chapter-title">Getting started with Julia</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../misc/julia_interfaces.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">67</span> <span class="chapter-title">Julia interfaces</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../misc/calculus_with_julia.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">68</span> <span class="chapter-title">The <code>CalculusWithJulia</code> package</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../misc/unicode.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">69</span> <span class="chapter-title">Usages of Unicode symbols</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../misc/quick_notes.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">70</span> <span class="chapter-title">Quick introduction to Calculus with Julia</span></a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../references.html" class="sidebar-item-text sidebar-link">References</a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</div>
|
||
</nav>
|
||
<!-- margin-sidebar -->
|
||
<div id="quarto-margin-sidebar" class="sidebar margin-sidebar">
|
||
<nav id="TOC" role="doc-toc">
|
||
<h2 id="toc-title">Table of contents</h2>
|
||
|
||
<ul>
|
||
<li><a href="#linear-polynomials" id="toc-linear-polynomials" class="nav-link active" data-scroll-target="#linear-polynomials"> <span class="header-section-number">11.1</span> Linear polynomials</a></li>
|
||
<li><a href="#symbolic-math-in-julia" id="toc-symbolic-math-in-julia" class="nav-link" data-scroll-target="#symbolic-math-in-julia"> <span class="header-section-number">11.2</span> Symbolic math in Julia</a></li>
|
||
<li><a href="#substitution-subs-replace" id="toc-substitution-subs-replace" class="nav-link" data-scroll-target="#substitution-subs-replace"> <span class="header-section-number">11.3</span> Substitution: subs, replace</a>
|
||
<ul class="collapse">
|
||
<li><a href="#conversion-of-symbolic-numbers-to-julia-numbers" id="toc-conversion-of-symbolic-numbers-to-julia-numbers" class="nav-link" data-scroll-target="#conversion-of-symbolic-numbers-to-julia-numbers"> <span class="header-section-number">11.3.1</span> Conversion of symbolic numbers to Julia numbers</a></li>
|
||
<li><a href="#converting-symbolic-expressions-into-julia-functions" id="toc-converting-symbolic-expressions-into-julia-functions" class="nav-link" data-scroll-target="#converting-symbolic-expressions-into-julia-functions"> <span class="header-section-number">11.3.2</span> Converting symbolic expressions into Julia functions</a></li>
|
||
</ul></li>
|
||
<li><a href="#graphical-properties-of-polynomials" id="toc-graphical-properties-of-polynomials" class="nav-link" data-scroll-target="#graphical-properties-of-polynomials"> <span class="header-section-number">11.4</span> Graphical properties of polynomials</a>
|
||
<ul class="collapse">
|
||
<li><a href="#leading-term-dominates" id="toc-leading-term-dominates" class="nav-link" data-scroll-target="#leading-term-dominates"> <span class="header-section-number">11.4.1</span> Leading term dominates</a></li>
|
||
</ul></li>
|
||
<li><a href="#factoring-polynomials" id="toc-factoring-polynomials" class="nav-link" data-scroll-target="#factoring-polynomials"> <span class="header-section-number">11.5</span> Factoring polynomials</a>
|
||
<ul class="collapse">
|
||
<li><a href="#polynomial-functions-and-polynomials." id="toc-polynomial-functions-and-polynomials." class="nav-link" data-scroll-target="#polynomial-functions-and-polynomials."> <span class="header-section-number">11.5.1</span> Polynomial functions and polynomials.</a></li>
|
||
</ul></li>
|
||
<li><a href="#questions" id="toc-questions" class="nav-link" data-scroll-target="#questions"> <span class="header-section-number">11.6</span> Questions</a></li>
|
||
</ul>
|
||
<div class="toc-actions"><div><i class="bi bi-github"></i></div><div class="action-links"><p><a href="https://github.com/jverzani/CalculusWithJuliaNotes.jl/edit/main/quarto/precalc/polynomial.qmd" class="toc-action">Edit this page</a></p><p><a href="https://github.com/jverzani/CalculusWithJuliaNotes.jl/issues/new" class="toc-action">Report an issue</a></p></div></div></nav>
|
||
</div>
|
||
<!-- main -->
|
||
<main class="content" id="quarto-document-content">
|
||
|
||
<header id="title-block-header" class="quarto-title-block default">
|
||
<div class="quarto-title">
|
||
<h1 class="title d-none d-lg-block"><span class="chapter-number">11</span> <span class="chapter-title">Polynomials</span></h1>
|
||
</div>
|
||
|
||
|
||
|
||
<div class="quarto-title-meta">
|
||
|
||
|
||
|
||
</div>
|
||
|
||
|
||
</header>
|
||
|
||
<p>In this section we use the following add-on packages:</p>
|
||
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">SymPy</span></span>
|
||
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">Plots</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<hr>
|
||
<p>Polynomials are a particular class of expressions that are simple enough to have many properties that can be analyzed. In particular, the key concepts of calculus: limits, continuity, derivatives, and integrals are all relatively trivial for polynomial functions. However, polynomials are flexible enough that they can be used to approximate a wide variety of functions. Indeed, though we don’t pursue this, we mention that <code>Julia</code>’s <code>ApproxFun</code> package exploits this to great advantage.</p>
|
||
<p>Here we discuss some vocabulary and basic facts related to polynomials and show how the add-on <code>SymPy</code> package can be used to model polynomial expressions within <code>SymPy</code>. <code>SymPy</code> provides a Computer Algebra System (CAS) for <code>Julia</code>. In this case, by leveraging a mature <code>Python</code> package <a href="https://www.sympy.org/">SymPy</a>. Later we will discuss the <code>Polynomials</code> package for polynomials.</p>
|
||
<p>For our purposes, a <em>monomial</em> is simply a non-negative integer power of <span class="math inline">\(x\)</span> (or some other indeterminate symbol) possibly multiplied by a scalar constant. For example, <span class="math inline">\(5x^4\)</span> is a monomial, as are constants, such as <span class="math inline">\(-2=-2x^0\)</span> and the symbol itself, as <span class="math inline">\(x = x^1\)</span>. In general, one may consider restrictions on where the constants can come from, and consider more than one symbol, but we won’t pursue this here, restricting ourselves to the case of a single variable and real coefficients.</p>
|
||
<p>A <em>polynomial</em> is a sum of monomials. After combining terms with same powers, a non-zero polynomial may be written uniquely as:</p>
|
||
<p><span class="math display">\[
|
||
a_n x^n + a_{n-1}x^{n-1} + \cdots a_1 x + a_0, \quad a_n \neq 0
|
||
\]</span></p>
|
||
<div class="cell" data-cache="true" data-hold="true" data-execution_count="4">
|
||
<div class="cell-output cell-output-display" data-execution_count="5">
|
||
<div class="d-flex justify-content-center"> <figure class="figure"> <img src="data:image/gif;base64,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" class="card-img-top figure-img" alt="A Figure">
|
||
<figcaption class="figure-caption"><div class="markdown"><p>Polynomials of varying even degrees over \([-1,1]\).</p>
|
||
</div> </figcaption>
|
||
</figure>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>The numbers <span class="math inline">\(a_0, a_1, \dots, a_n\)</span> are the <strong>coefficients</strong> of the polynomial in the standard basis. With the identifications that <span class="math inline">\(x=x^1\)</span> and <span class="math inline">\(1 = x^0\)</span>, the monomials above have their power match their coefficient’s index, e.g., <span class="math inline">\(a_ix^i\)</span>. Outside of the coefficient <span class="math inline">\(a_n\)</span>, the other coefficients may be negative, positive, <em>or</em> <span class="math inline">\(0\)</span>. Except for the zero polynomial, the largest power <span class="math inline">\(n\)</span> is called the <a href="https://en.wikipedia.org/wiki/Degree_of_a_polynomial">degree</a>. The degree of the <a href="http://tinyurl.com/he6eg6s">zero</a> polynomial is typically not defined or defined to be <span class="math inline">\(-1\)</span>, so as to make certain statements easier to express. The term <span class="math inline">\(a_n\)</span> is called the <strong>leading coefficient</strong>. When the leading coefficient is <span class="math inline">\(1\)</span>, the polynomial is called a <strong>monic polynomial</strong>. The monomial <span class="math inline">\(a_n x^n\)</span> is the <strong>leading term</strong>.</p>
|
||
<p>For example, the polynomial <span class="math inline">\(-16x^2 - 32x + 100\)</span> has degree <span class="math inline">\(2\)</span>, leading coefficient <span class="math inline">\(-16\)</span> and leading term <span class="math inline">\(-16x^2\)</span>. It is not monic, as the leading coefficient is not <span class="math inline">\(1\)</span>.</p>
|
||
<p>Lower degree polynomials have special names: a degree <span class="math inline">\(0\)</span> polynomial (<span class="math inline">\(a_0\)</span>) is a non-zero constant, a degree <span class="math inline">\(1\)</span> polynomial (<span class="math inline">\(a_0+a_1x\)</span>) is called linear, a degree <span class="math inline">\(2\)</span> polynomial is quadratic, and a degree <span class="math inline">\(3\)</span> polynomial is called cubic.</p>
|
||
<section id="linear-polynomials" class="level2" data-number="11.1">
|
||
<h2 data-number="11.1" class="anchored" data-anchor-id="linear-polynomials"><span class="header-section-number">11.1</span> Linear polynomials</h2>
|
||
<p>A special place is reserved for polynomials with degree <span class="math inline">\(1\)</span>. These are linear, as their graphs are straight lines. The general form,</p>
|
||
<p><span class="math display">\[
|
||
a_1 x + a_0, \quad a_1 \neq 0,
|
||
\]</span></p>
|
||
<p>is often written as <span class="math inline">\(mx + b\)</span>, which is the <strong>slope-intercept</strong> form. The slope of a line determines how steeply it rises. The value of <span class="math inline">\(m\)</span> can be found from two points through the well-known formula:</p>
|
||
<p><span class="math display">\[
|
||
m = \frac{y_1 - y_0}{x_1 - x_0} = \frac{\text{rise}}{\text{run}}
|
||
\]</span></p>
|
||
<div class="cell" data-cache="true" data-hold="true" data-execution_count="5">
|
||
<div class="cell-output cell-output-display" data-execution_count="6">
|
||
<div class="d-flex justify-content-center"> <figure class="figure"> <img src="data:image/gif;base64,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" class="card-img-top figure-img" alt="A Figure">
|
||
<figcaption class="figure-caption"><div class="markdown"><p>Graphs of y = mx for different values of m</p>
|
||
</div> </figcaption>
|
||
</figure>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>The intercept, <span class="math inline">\(b\)</span>, comes from the fact that when <span class="math inline">\(x=0\)</span> the expression is <span class="math inline">\(b\)</span>. That is the graph of the function <span class="math inline">\(f(x) = mx + b\)</span> will have <span class="math inline">\((0,b)\)</span> as a point on it.</p>
|
||
<p>More generally, we have the <strong>point-slope</strong> form of a line, written as a polynomial through</p>
|
||
<p><span class="math display">\[
|
||
y_0 + m \cdot (x - x_0).
|
||
\]</span></p>
|
||
<p>The slope is <span class="math inline">\(m\)</span> and the point <span class="math inline">\((x_0, y_0)\)</span>. Again, the line graphing this as a function of <span class="math inline">\(x\)</span> would have the point <span class="math inline">\((x_0,y_0)\)</span> on it and have slope <span class="math inline">\(m\)</span>. This form is more useful in calculus, as the information we have convenient is more likely to be related to a specific value of <span class="math inline">\(x\)</span>, not the special value <span class="math inline">\(x=0\)</span>.</p>
|
||
<p>Thinking in terms of transformations, this looks like the function <span class="math inline">\(f(x) = x\)</span> (whose graph is a line with slope <span class="math inline">\(1\)</span>) stretched in the <span class="math inline">\(y\)</span> direction by a factor of <span class="math inline">\(m\)</span> then shifted right by <span class="math inline">\(x_0\)</span> units, and then shifted up by <span class="math inline">\(y_0\)</span> units. When <span class="math inline">\(m>1\)</span>, this means the line grows faster. When <span class="math inline">\(m< 0\)</span>, the line <span class="math inline">\(f(x)=x\)</span> is flipped through the <span class="math inline">\(x\)</span>-axis so would head downwards, not upwards like <span class="math inline">\(f(x) = x\)</span>.</p>
|
||
</section>
|
||
<section id="symbolic-math-in-julia" class="level2" data-number="11.2">
|
||
<h2 data-number="11.2" class="anchored" data-anchor-id="symbolic-math-in-julia"><span class="header-section-number">11.2</span> Symbolic math in Julia</h2>
|
||
<p>The indeterminate value <code>x</code> (or some other symbol) in a polynomial, is like a variable in a function and unlike a variable in <code>Julia</code>. Variables in <code>Julia</code> are identifiers, just a means to look up a specific, already determined, value. Rather, the symbol <code>x</code> is not yet determined, it is essentially a place holder for a future value. Although we have seen that <code>Julia</code> makes it very easy to work with mathematical functions, it is not the case that base <code>Julia</code> makes working with expressions of algebraic symbols easy. This makes sense, <code>Julia</code> is primarily designed for technical computing, where numeric approaches rule the day. However, symbolic math can be used from within <code>Julia</code> through add-on packages.</p>
|
||
<p>Symbolic math programs include well-known ones like the commercial programs Mathematica and Maple. Mathematica powers the popular <a href="www.wolframalpha.com">WolframAlpha</a> website, which turns “natural” language into the specifics of a programming language. The open-source Sage project is an alternative to these two commercial giants. It includes a wide-range of open-source math projects available within its umbrella framework. (<code>Julia</code> can even be run from within the free service <a href="https://cloud.sagemath.com/projects">cloud.sagemath.com</a>.) A more focused project for symbolic math, is the <a href="www.sympy.org">SymPy</a> Python library. SymPy is also used within Sage. However, SymPy provides a self-contained library that can be used standalone within a Python session. That is great for <code>Julia</code> users, as the <code>PyCall</code> and <code>PythonCall</code> packages glue <code>Julia</code> to Python in a seamless manner. This allows the <code>Julia</code> package <code>SymPy</code> to provide functionality from SymPy within <code>Julia</code>.</p>
|
||
<div class="callout-note callout callout-style-default callout-captioned">
|
||
<div class="callout-header d-flex align-content-center">
|
||
<div class="callout-icon-container">
|
||
<i class="callout-icon"></i>
|
||
</div>
|
||
<div class="callout-caption-container flex-fill">
|
||
Note
|
||
</div>
|
||
</div>
|
||
<div class="callout-body-container callout-body">
|
||
<p>When <code>SymPy</code> is installed through the package manger, the underlying <code>Python</code> libraries will also be installed.</p>
|
||
</div>
|
||
</div>
|
||
<div class="callout-note callout callout-style-default callout-captioned">
|
||
<div class="callout-header d-flex align-content-center">
|
||
<div class="callout-icon-container">
|
||
<i class="callout-icon"></i>
|
||
</div>
|
||
<div class="callout-caption-container flex-fill">
|
||
Note
|
||
</div>
|
||
</div>
|
||
<div class="callout-body-container callout-body">
|
||
<p>The <a href="../alternatives/symbolics"><code>Symbolics</code></a> package is a rapidly developing <code>Julia</code>-only packge that provides symbolic math options.</p>
|
||
</div>
|
||
</div>
|
||
<hr>
|
||
<p>To use <code>SymPy</code>, we create symbolic objects to be our indeterminate symbols. The <code>symbols</code> function does this. However, we will use the more convenient <code>@syms</code> macro front end for <code>symbols</code>.</p>
|
||
<div class="cell" data-execution_count="6">
|
||
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="pp">@syms</span> a, b, c, x<span class="op">::</span><span class="dt">real</span>, zs[<span class="fl">1</span><span class="op">:</span><span class="fl">10</span>]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="7">
|
||
<pre><code>(a, b, c, x, Sym[zs₁, zs₂, zs₃, zs₄, zs₅, zs₆, zs₇, zs₈, zs₉, zs₁₀])</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>The above shows that multiple symbols can be defined at once. The annotation <code>x::real</code> instructs <code>SymPy</code> to assume the <code>x</code> is real, as otherwise it assumes it is possibly complex. There are many other <a href="http://docs.sympy.org/dev/modules/core.html#module-sympy.core.assumptions">assumptions</a> that can be made. The <code>@syms</code> macro documentation lists them. The <code>zs[1:10]</code> tensor notation creates a container with <span class="math inline">\(10\)</span> different symbols. The <em>macro</em> <code>@syms</code> does not need assignment, as the variable(s) are created behind the scenes by the macro.</p>
|
||
<div class="callout-note callout callout-style-default callout-captioned">
|
||
<div class="callout-header d-flex align-content-center">
|
||
<div class="callout-icon-container">
|
||
<i class="callout-icon"></i>
|
||
</div>
|
||
<div class="callout-caption-container flex-fill">
|
||
Note
|
||
</div>
|
||
</div>
|
||
<div class="callout-body-container callout-body">
|
||
<p>Macros in <code>Julia</code> are just transformations of the syntax into other syntax. The <code>@</code> indicates they behave differently than regular function calls.</p>
|
||
</div>
|
||
</div>
|
||
<p>The <code>SymPy</code> package does three basic things:</p>
|
||
<ul>
|
||
<li>It imports some of the functionality provided by <code>SymPy</code>, including the ability to create symbolic variables.</li>
|
||
<li>It overloads many <code>Julia</code> functions to work seamlessly with symbolic expressions. This makes working with polynomials quite natural.</li>
|
||
<li>It gives access to a wide range of SymPy’s functionality through the <code>sympy</code> object.</li>
|
||
</ul>
|
||
<p>To illustrate, using the just defined <code>x</code>, here is how we can create the polynomial <span class="math inline">\(-16x^2 + 100\)</span>:</p>
|
||
<div class="cell" data-execution_count="7">
|
||
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>𝒑 <span class="op">=</span> <span class="op">-</span><span class="fl">16</span>x<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> <span class="fl">100</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="8">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
100 - 16 x^{2}
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>That is, the expression is created just as you would create it within a function body. But here the result is still a symbolic object. We have assigned this expression to a variable <code>p</code>, and have not defined it as a function <code>p(x)</code>. Mentally keeping the distinction between symbolic expressions and functions is very important.</p>
|
||
<p>The <code>typeof</code> function shows that <code>𝒑</code> is of a symbolic type (<code>Sym</code>):</p>
|
||
<div class="cell" data-execution_count="8">
|
||
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="fu">typeof</span>(𝒑)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="9">
|
||
<pre><code>Sym</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>We can mix and match symbolic objects. This command creates an arbitrary quadratic polynomial:</p>
|
||
<div class="cell" data-execution_count="9">
|
||
<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>quad <span class="op">=</span> a<span class="op">*</span>x<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> b<span class="op">*</span>x <span class="op">+</span> c</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="10">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
a x^{2} + b x + c
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>Again, this is entered in a manner nearly identical to how we see such expressions typeset (<span class="math inline">\(ax^2 + bx+c\)</span>), though we must remember to explicitly place the multiplication operator, as the symbols are not numeric literals.</p>
|
||
<p>We can apply many of <code>Julia</code>’s mathematical functions and the result will still be symbolic:</p>
|
||
<div class="cell" data-execution_count="10">
|
||
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="fu">sin</span>(<span class="fu">a*</span>(x <span class="op">-</span> b<span class="op">*</span><span class="cn">pi</span>) <span class="op">+</span> c)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="11">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
\sin{\left(a \left(- \pi b + x\right) + c \right)}
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>Another example, might be the following combination:</p>
|
||
<div class="cell" data-execution_count="11">
|
||
<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>quad <span class="op">+</span> quad<span class="op">^</span><span class="fl">2</span> <span class="op">-</span> quad<span class="op">^</span><span class="fl">3</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="12">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
a x^{2} + b x + c - \left(a x^{2} + b x + c\right)^{3} + \left(a x^{2} + b x + c\right)^{2}
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>One way to create symbolic expressions is simply to call a <code>Julia</code> function with symbolic arguments. The first line in the next example defines a function, the second evaluates it at the symbols <code>x</code>, <code>a</code>, and <code>b</code> resulting in a symbolic expression <code>ex</code>:</p>
|
||
<div class="cell" data-execution_count="12">
|
||
<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="fu">f</span>(x, m, b) <span class="op">=</span> m<span class="op">*</span>x <span class="op">+</span> b</span>
|
||
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>ex <span class="op">=</span> <span class="fu">f</span>(x, a, b)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="13">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
a x + b
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="substitution-subs-replace" class="level2" data-number="11.3">
|
||
<h2 data-number="11.3" class="anchored" data-anchor-id="substitution-subs-replace"><span class="header-section-number">11.3</span> Substitution: subs, replace</h2>
|
||
<p>Algebraically working with symbolic expressions is straightforward. A different symbolic task is substitution. For example, replacing each instance of <code>x</code> in a polynomial, with, say, <code>(x-1)^2</code>. Substitution requires three things to be specified: an expression to work on, a variable to substitute, and a value to substitute in.</p>
|
||
<p>SymPy provides its <code>subs</code> function for this. This function is available in <code>Julia</code>, but it is easier to use notation reminiscent of function evaluation.</p>
|
||
<p>To illustrate, to do the task above for the polynomial <span class="math inline">\(-16x^2 + 100\)</span> we could have:</p>
|
||
<div class="cell" data-execution_count="13">
|
||
<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="fu">𝒑</span>(x <span class="op">=></span> (x<span class="op">-</span><span class="fl">1</span>)<span class="op">^</span><span class="fl">2</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="14">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
100 - 16 \left(x - 1\right)^{4}
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>This “call” notation takes pairs (designated by <code>a=>b</code>) where the left-hand side is the variable to substitute for, and the right-hand side the new value. The value to substitute can depend on the variable, as illustrated; be a different variable; or be a numeric value, such as <span class="math inline">\(2\)</span>:</p>
|
||
<div class="cell" data-execution_count="14">
|
||
<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>𝒚 <span class="op">=</span> <span class="fu">𝒑</span>(x<span class="op">=></span><span class="fl">2</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="15">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
36
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>The result will always be of a symbolic type, even if the answer is just a number:</p>
|
||
<div class="cell" data-execution_count="15">
|
||
<div class="sourceCode cell-code" id="cb13"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="fu">typeof</span>(𝒚)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="16">
|
||
<pre><code>Sym</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>If there is just one free variable in an expression, the pair notation can be dropped:</p>
|
||
<div class="cell" data-execution_count="16">
|
||
<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="fu">𝒑</span>(<span class="fl">4</span>) <span class="co"># substitutes x=>4</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="17">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
-156
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<section id="example" class="level5">
|
||
<h5 class="anchored" data-anchor-id="example">Example</h5>
|
||
<p>Suppose we have the polynomial <span class="math inline">\(p = ax^2 + bx +c\)</span>. What would it look like if we shifted right by <span class="math inline">\(E\)</span> units and up by <span class="math inline">\(F\)</span> units?</p>
|
||
<div class="cell" data-execution_count="17">
|
||
<div class="sourceCode cell-code" id="cb16"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="pp">@syms</span> E F</span>
|
||
<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a>p₂ <span class="op">=</span> a<span class="op">*</span>x<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> b<span class="op">*</span>x <span class="op">+</span> c</span>
|
||
<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a><span class="fu">p₂</span>(x <span class="op">=></span> x<span class="op">-</span>E) <span class="op">+</span> F</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="18">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
F + a \left(- E + x\right)^{2} + b \left(- E + x\right) + c
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>And expanded this becomes:</p>
|
||
<div class="cell" data-execution_count="18">
|
||
<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="fu">expand</span>(<span class="fu">p₂</span>(x <span class="op">=></span> x<span class="op">-</span>E) <span class="op">+</span> F)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="19">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
E^{2} a - 2 E a x - E b + F + a x^{2} + b x + c
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="conversion-of-symbolic-numbers-to-julia-numbers" class="level3" data-number="11.3.1">
|
||
<h3 data-number="11.3.1" class="anchored" data-anchor-id="conversion-of-symbolic-numbers-to-julia-numbers"><span class="header-section-number">11.3.1</span> Conversion of symbolic numbers to Julia numbers</h3>
|
||
<p>In the above, we substituted <code>2</code> in for <code>x</code> to get <code>y</code>:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="19">
|
||
<div class="sourceCode cell-code" id="cb18"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>p <span class="op">=</span> <span class="op">-</span><span class="fl">16</span>x<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> <span class="fl">100</span></span>
|
||
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a>y <span class="op">=</span> <span class="fu">p</span>(<span class="fl">2</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="20">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
36
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>The value, <span class="math inline">\(36\)</span> is still symbolic, but clearly an integer. If we are just looking at the output, we can easily translate from the symbolic value to an integer, as they print similarly. However the conversion to an integer, or another type of number, does not happen automatically. If a number is needed to pass along to another <code>Julia</code> function, it may need to be converted. In general, conversions between different types are handled through various methods of <code>convert</code>. However, with <code>SymPy</code>, the <code>N</code> function will attempt to do the conversion for you:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="20">
|
||
<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>p <span class="op">=</span> <span class="op">-</span><span class="fl">16</span>x<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> <span class="fl">100</span></span>
|
||
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a><span class="fu">N</span>(<span class="fu">p</span>(<span class="fl">2</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="21">
|
||
<pre><code>36</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>Where <code>convert(T,x)</code> requires a specification of the type to convert <code>x</code> to, <code>N</code> attempts to match the data type used by SymPy to store the number. As such, the output type of <code>N</code> may vary (rational, a BigFloat, a float, etc.) For getting more digits of accuracy, a precision can be passed to <code>N</code>. The following command will take the symbolic value for <span class="math inline">\(\pi\)</span>, <code>PI</code>, and produce about <span class="math inline">\(60\)</span> digits worth as a <code>BigFloat</code> value:</p>
|
||
<div class="cell" data-execution_count="21">
|
||
<div class="sourceCode cell-code" id="cb21"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a><span class="fu">N</span>(PI, <span class="fl">60</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="22">
|
||
<pre><code>3.141592653589793238462643383279502884197169399375105820974939</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>Conversion by <code>N</code> will fail if the value to be converted contains free symbols, as would be expected.</p>
|
||
</section>
|
||
<section id="converting-symbolic-expressions-into-julia-functions" class="level3" data-number="11.3.2">
|
||
<h3 data-number="11.3.2" class="anchored" data-anchor-id="converting-symbolic-expressions-into-julia-functions"><span class="header-section-number">11.3.2</span> Converting symbolic expressions into Julia functions</h3>
|
||
<p>Evaluating a symbolic expression and returning a numeric value can be done by composing the two just discussed concepts. For example:</p>
|
||
<div class="cell" data-execution_count="22">
|
||
<div class="sourceCode cell-code" id="cb23"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a>𝐩 <span class="op">=</span> <span class="fl">200</span> <span class="op">-</span> <span class="fl">16</span>x<span class="op">^</span><span class="fl">2</span></span>
|
||
<span id="cb23-2"><a href="#cb23-2" aria-hidden="true" tabindex="-1"></a><span class="fu">N</span>(<span class="fu">𝐩</span>(<span class="fl">2</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="23">
|
||
<pre><code>136</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>This approach is direct, but can be slow <em>if</em> many such evaluations were needed (such as with a plot). An alternative is to turn the symbolic expression into a <code>Julia</code> function and then evaluate that as usual.</p>
|
||
<p>The <code>lambdify</code> function turns a symbolic expression into a <code>Julia</code> function</p>
|
||
<div class="cell" data-hold="true" data-execution_count="23">
|
||
<div class="sourceCode cell-code" id="cb25"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a>pp <span class="op">=</span> <span class="fu">lambdify</span>(𝐩)</span>
|
||
<span id="cb25-2"><a href="#cb25-2" aria-hidden="true" tabindex="-1"></a><span class="fu">pp</span>(<span class="fl">2</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="24">
|
||
<pre><code>136</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>The <code>lambdify</code> function uses the name of the similar <code>SymPy</code> function which is named after Pythons convention of calling anoynmous function “lambdas.” The use above is straightforward. Only slightly more complicated is the use when there are multiple symbolic values. For example:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="24">
|
||
<div class="sourceCode cell-code" id="cb27"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a>p <span class="op">=</span> a<span class="op">*</span>x<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> b</span>
|
||
<span id="cb27-2"><a href="#cb27-2" aria-hidden="true" tabindex="-1"></a>pp <span class="op">=</span> <span class="fu">lambdify</span>(p)</span>
|
||
<span id="cb27-3"><a href="#cb27-3" aria-hidden="true" tabindex="-1"></a><span class="fu">pp</span>(<span class="fl">1</span>,<span class="fl">2</span>,<span class="fl">3</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="25">
|
||
<pre><code>11</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>This evaluation matches <code>a</code> with <code>1</code>, <code>b</code> with<code>2</code>, and <code>x</code> with <code>3</code> as that is the order returned by the function call <code>free_symbols(p)</code>. To adjust that, a second <code>vars</code> argument can be given:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="25">
|
||
<div class="sourceCode cell-code" id="cb29"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a>pp <span class="op">=</span> <span class="fu">lambdify</span>(p, (x,a,b))</span>
|
||
<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a><span class="fu">pp</span>(<span class="fl">1</span>,<span class="fl">2</span>,<span class="fl">3</span>) <span class="co"># computes 2*1^2 + 3</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="26">
|
||
<pre><code>5</code></pre>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
</section>
|
||
<section id="graphical-properties-of-polynomials" class="level2" data-number="11.4">
|
||
<h2 data-number="11.4" class="anchored" data-anchor-id="graphical-properties-of-polynomials"><span class="header-section-number">11.4</span> Graphical properties of polynomials</h2>
|
||
<p>Consider the graph of the polynomial <code>x^5 - x + 1</code>:</p>
|
||
<div class="cell" data-execution_count="26">
|
||
<div class="sourceCode cell-code" id="cb31"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb31-1"><a href="#cb31-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(x<span class="op">^</span><span class="fl">5</span> <span class="op">-</span> x <span class="op">+</span> <span class="fl">1</span>, <span class="op">-</span><span class="fl">3</span><span class="op">/</span><span class="fl">2</span>, <span class="fl">3</span><span class="op">/</span><span class="fl">2</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="27">
|
||
<p><img src="polynomial_files/figure-html/cell-27-output-1.svg" class="img-fluid"></p>
|
||
</div>
|
||
</div>
|
||
<p>(Plotting symbolic expressions is similar to plotting a function, in that the expression is passed in as the first argument. The expression must have only one free variable, as above, or an error will occur.)</p>
|
||
<p>This graph illustrates the key features of polynomial graphs:</p>
|
||
<ul>
|
||
<li>there may be values for <code>x</code> where the graph crosses the <span class="math inline">\(x\)</span> axis (real roots of the polynomial);</li>
|
||
<li>there may be peaks and valleys (local maxima and local minima)</li>
|
||
<li>except for constant polynomials, the ultimate behaviour for large values of <span class="math inline">\(\lvert x\rvert\)</span> is either both sides of the graph going to positive infinity, or negative infinity, or as in this graph one to the positive infinity and one to negative infinity. In particular, there is no <em>horizontal asymptote</em>.</li>
|
||
</ul>
|
||
<p>To investigate this last point, let’s consider the case of the monomial <span class="math inline">\(x^n\)</span>. When <span class="math inline">\(n\)</span> is even, the following animation shows that larger values of <span class="math inline">\(n\)</span> have greater growth once outside of <span class="math inline">\([-1,1]\)</span>:</p>
|
||
<div class="cell" data-cache="true" data-hold="true" data-execution_count="27">
|
||
<div class="cell-output cell-output-display" data-execution_count="28">
|
||
<div class="d-flex justify-content-center"> <figure class="figure"> <img src="data:image/gif;base64,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" class="card-img-top figure-img" alt="A Figure">
|
||
<figcaption class="figure-caption"><div class="markdown"><p>Demonstration that \(x^{10}\) grows faster than \(x^8\), ... and \(x^2\) grows faster than \(x^0\) (which is constant).</p>
|
||
</div> </figcaption>
|
||
</figure>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>Of course, this is expected, as, for example, <span class="math inline">\(2^2 < 2^4 < 2^6 < \cdots\)</span>. The general shape of these terms is similar - <span class="math inline">\(U\)</span> shaped, and larger powers dominate the smaller powers as <span class="math inline">\(\lvert x\rvert\)</span> gets big.</p>
|
||
<p>For odd powers of <span class="math inline">\(n\)</span>, the graph of the monomial <span class="math inline">\(x^n\)</span> is no longer <span class="math inline">\(U\)</span> shaped, but rather constantly increasing. This graph of <span class="math inline">\(x^5\)</span> is typical:</p>
|
||
<div class="cell" data-execution_count="28">
|
||
<div class="sourceCode cell-code" id="cb32"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb32-1"><a href="#cb32-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(x<span class="op">^</span><span class="fl">5</span>, <span class="op">-</span><span class="fl">2</span>, <span class="fl">2</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="29">
|
||
<p><img src="polynomial_files/figure-html/cell-29-output-1.svg" class="img-fluid"></p>
|
||
</div>
|
||
</div>
|
||
<p>Again, for larger powers the shape is similar, but the growth is faster.</p>
|
||
<section id="leading-term-dominates" class="level3" data-number="11.4.1">
|
||
<h3 data-number="11.4.1" class="anchored" data-anchor-id="leading-term-dominates"><span class="header-section-number">11.4.1</span> Leading term dominates</h3>
|
||
<p>To see the roots and/or the peaks and valleys of a polynomial requires a judicious choice of viewing window, as ultimately the leading term will dominate the graph. The following animation of the graph of <span class="math inline">\((x-5)(x-3)(x-2)(x-1)\)</span> illustrates. Subsequent images show a widening of the plot window until the graph appears U-shaped.</p>
|
||
<div class="cell" data-cache="true" data-hold="true" data-execution_count="29">
|
||
<div class="cell-output cell-output-display" data-execution_count="30">
|
||
<div class="d-flex justify-content-center"> <figure class="figure"> <img src="data:image/gif;base64,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" class="card-img-top figure-img" alt="A Figure">
|
||
<figcaption class="figure-caption"><div class="markdown"><p>The previous graph is highlighted in red. Ultimately the leading term (\(x^4\) here) dominates the graph.</p>
|
||
</div> </figcaption>
|
||
</figure>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>The leading term in the animation is <span class="math inline">\(x^4\)</span>, of even degree, so the graphic is U-shaped, were the leading term of odd degree the left and right sides would each head off to different signs of infinity.</p>
|
||
<p>To illustrate analytically why the leading term dominates, consider the polynomial <span class="math inline">\(2x^5 - x + 1\)</span> and then factor out the largest power, <span class="math inline">\(x^5\)</span>, leaving a product:</p>
|
||
<p><span class="math display">\[
|
||
x^5 \cdot (2 - \frac{1}{x^4} + \frac{1}{x^5}).
|
||
\]</span></p>
|
||
<p>For large <span class="math inline">\(\lvert x\rvert\)</span>, the last two terms in the product on the right get close to <span class="math inline">\(0\)</span>, so this expression is <em>basically</em> just <span class="math inline">\(2x^5\)</span> - the leading term.</p>
|
||
<hr>
|
||
<p>The following graphic illustrates the <span class="math inline">\(4\)</span> basic <em>overall</em> shapes that can result when plotting a polynomials as <span class="math inline">\(x\)</span> grows without bound:</p>
|
||
<div class="cell" data-execution_count="30">
|
||
<div class="cell-output cell-output-display" data-execution_count="31">
|
||
<p><img src="polynomial_files/figure-html/cell-31-output-1.svg" class="img-fluid"></p>
|
||
</div>
|
||
</div>
|
||
<section id="example-1" class="level5">
|
||
<h5 class="anchored" data-anchor-id="example-1">Example</h5>
|
||
<p>Suppose <span class="math inline">\(p = a_n x^n + \cdots + a_1 x + a_0\)</span> with <span class="math inline">\(a_n > 0\)</span>. Then by the above, eventually for large <span class="math inline">\(x > 0\)</span> we have <span class="math inline">\(p > 0\)</span>, as that is the behaviour of <span class="math inline">\(a_n x^n\)</span>. Were <span class="math inline">\(a_n < 0\)</span>, then eventually for large <span class="math inline">\(x>0\)</span>, <span class="math inline">\(p < 0\)</span>.</p>
|
||
<p>Now consider the related polynomial, <span class="math inline">\(q\)</span>, where we multiply <span class="math inline">\(p\)</span> by <span class="math inline">\(x^n\)</span> and substitute in <span class="math inline">\(1/x\)</span> for <span class="math inline">\(x\)</span>. This is the “reversed” polynomial, as we see in this illustration for <span class="math inline">\(n=2\)</span>:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="31">
|
||
<div class="sourceCode cell-code" id="cb33"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb33-1"><a href="#cb33-1" aria-hidden="true" tabindex="-1"></a>p <span class="op">=</span> a<span class="op">*</span>x<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> b<span class="op">*</span>x <span class="op">+</span> c</span>
|
||
<span id="cb33-2"><a href="#cb33-2" aria-hidden="true" tabindex="-1"></a>n <span class="op">=</span> <span class="fl">2</span> <span class="co"># the degree of p</span></span>
|
||
<span id="cb33-3"><a href="#cb33-3" aria-hidden="true" tabindex="-1"></a>q <span class="op">=</span> <span class="fu">expand</span>(x<span class="op">^</span>n <span class="op">*</span> <span class="fu">p</span>(x <span class="op">=></span> <span class="fl">1</span><span class="op">/</span>x))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="32">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
a + b x + c x^{2}
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>In particular, from the reversal, the behavior of <span class="math inline">\(q\)</span> for large <span class="math inline">\(x\)</span> depends on the sign of <span class="math inline">\(a_0\)</span>. As well, due to the <span class="math inline">\(1/x\)</span>, the behaviour of <span class="math inline">\(q\)</span> for large <span class="math inline">\(x>0\)</span> is the same as the behaviour of <span class="math inline">\(p\)</span> for small <em>positive</em> <span class="math inline">\(x\)</span>. In particular if <span class="math inline">\(a_n > 0\)</span> but <span class="math inline">\(a_0 < 0\)</span>, then <code>p</code> is eventually positive and <code>q</code> is eventually negative.</p>
|
||
<p>That is, if <span class="math inline">\(p\)</span> has <span class="math inline">\(a_n > 0\)</span> but <span class="math inline">\(a_0 < 0\)</span> then the graph of <span class="math inline">\(p\)</span> must cross the <span class="math inline">\(x\)</span> axis.</p>
|
||
<p>This observation is the start of Descartes’ rule of <a href="http://sepwww.stanford.edu/oldsep/stew/descartes.pdf">signs</a>, which counts the change of signs of the coefficients in <code>p</code> to say something about how many possible crossings there are of the <span class="math inline">\(x\)</span> axis by the graph of the polynomial <span class="math inline">\(p\)</span>.</p>
|
||
</section>
|
||
</section>
|
||
</section>
|
||
<section id="factoring-polynomials" class="level2" data-number="11.5">
|
||
<h2 data-number="11.5" class="anchored" data-anchor-id="factoring-polynomials"><span class="header-section-number">11.5</span> Factoring polynomials</h2>
|
||
<p>Among numerous others, there are two common ways of representing a non-zero polynomial:</p>
|
||
<ul>
|
||
<li>expanded form, as in <span class="math inline">\(a_n x^n + a_{n-1}x^{n-1} + \cdots a_1 x + a_0, a_n \neq 0\)</span>; or</li>
|
||
<li>factored form, as in <span class="math inline">\(a\cdot(x-r_1)\cdot(x-r_2)\cdots(x-r_n), a \neq 0\)</span>.</li>
|
||
</ul>
|
||
<p>The latter writes <span class="math inline">\(p\)</span> as a product of linear factors, though this is only possible in general if we consider complex roots. With real roots only, then the factors are either linear or quadratic, as will be discussed later.</p>
|
||
<p>There are values to each representation. One value of the expanded form is that polynomial addition and scalar multiplication is much easier than in factored form. For example, adding polynomials just requires matching up the monomials of similar powers. For the factored form, polynomial multiplication is much easier than expanded form. For the factored form it is easy to read off <em>roots</em> of the polynomial (values of <span class="math inline">\(x\)</span> where <span class="math inline">\(p\)</span> is <span class="math inline">\(0\)</span>), as a product is <span class="math inline">\(0\)</span> only if a term is <span class="math inline">\(0\)</span>, so any zero must be a zero of a factor. Factored form has other technical advantages. For example, the polynomial <span class="math inline">\((x-1)^{1000}\)</span> can be compactly represented using the factored form, but would require <span class="math inline">\(1001\)</span> coefficients to store in expanded form. (As well, due to floating point differences, the two would evaluate quite differently as one would require over a <span class="math inline">\(1000\)</span> operations to compute, the other just two.)</p>
|
||
<p>Translating from factored form to expanded form can be done by carefully following the distributive law of multiplication. For example, with some care it can be shown that:</p>
|
||
<p><span class="math display">\[
|
||
(x-1) \cdot (x-2) \cdot (x-3) = x^3 - 6x^2 +11x - 6.
|
||
\]</span></p>
|
||
<p>The <code>SymPy</code> function <code>expand</code> will perform these algebraic manipulations without fuss:</p>
|
||
<div class="cell" data-execution_count="32">
|
||
<div class="sourceCode cell-code" id="cb34"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb34-1"><a href="#cb34-1" aria-hidden="true" tabindex="-1"></a><span class="fu">expand</span>((x<span class="op">-</span><span class="fl">1</span>)<span class="fu">*</span>(x<span class="op">-</span><span class="fl">2</span>)<span class="fu">*</span>(x<span class="op">-</span><span class="fl">3</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="33">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
x^{3} - 6 x^{2} + 11 x - 6
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>Factoring a polynomial is several weeks worth of lessons, as there is no one-size-fits-all algorithm to follow. There are some tricks that are taught: for example factoring differences of perfect squares, completing the square, the rational root theorem, <span class="math inline">\(\dots\)</span>. But in general the solution is not automated. The <code>SymPy</code> function <code>factor</code> will find all rational factors (terms like <span class="math inline">\((qx-p)\)</span>), but will leave terms that do not have rational factors alone. For example:</p>
|
||
<div class="cell" data-execution_count="33">
|
||
<div class="sourceCode cell-code" id="cb35"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb35-1"><a href="#cb35-1" aria-hidden="true" tabindex="-1"></a><span class="fu">factor</span>(x<span class="op">^</span><span class="fl">3</span> <span class="op">-</span> <span class="fl">6</span>x<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> <span class="fl">11</span>x <span class="op">-</span><span class="fl">6</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="34">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
\left(x - 3\right) \left(x - 2\right) \left(x - 1\right)
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>Or</p>
|
||
<div class="cell" data-execution_count="34">
|
||
<div class="sourceCode cell-code" id="cb36"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb36-1"><a href="#cb36-1" aria-hidden="true" tabindex="-1"></a><span class="fu">factor</span>(x<span class="op">^</span><span class="fl">5</span> <span class="op">-</span> <span class="fl">5</span>x<span class="op">^</span><span class="fl">4</span> <span class="op">+</span> <span class="fl">8</span>x<span class="op">^</span><span class="fl">3</span> <span class="op">-</span> <span class="fl">8</span>x<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> <span class="fl">7</span>x <span class="op">-</span> <span class="fl">3</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="35">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
\left(x - 3\right) \left(x - 1\right)^{2} \left(x^{2} + 1\right)
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>But will not factor things that are not hard to see:</p>
|
||
<div class="cell" data-execution_count="35">
|
||
<div class="sourceCode cell-code" id="cb37"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb37-1"><a href="#cb37-1" aria-hidden="true" tabindex="-1"></a>x<span class="op">^</span><span class="fl">2</span> <span class="op">-</span> <span class="fl">2</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="36">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
x^{2} - 2
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>The factoring <span class="math inline">\((x-\sqrt{2})\cdot(x + \sqrt{2})\)</span> is not found, as <span class="math inline">\(\sqrt{2}\)</span> is not rational.</p>
|
||
<p>(For those, it may be possible to solve to get the roots, which can then be used to produce the factored form.)</p>
|
||
<section id="polynomial-functions-and-polynomials." class="level3" data-number="11.5.1">
|
||
<h3 data-number="11.5.1" class="anchored" data-anchor-id="polynomial-functions-and-polynomials."><span class="header-section-number">11.5.1</span> Polynomial functions and polynomials.</h3>
|
||
<p>Our definition of a polynomial is in terms of algebraic expressions which are easily represented by <code>SymPy</code> objects, but not objects from base <code>Julia</code>. (Later we discuss the <code>Polynomials</code> package for representing polynomials. There is also the <code>AbstractAlbegra</code> package for a more algebraic treatment of polynomials.)</p>
|
||
<p>However, <em>polynomial functions</em> are easily represented by <code>Julia</code>, for example,</p>
|
||
<div class="cell" data-execution_count="36">
|
||
<div class="sourceCode cell-code" id="cb38"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb38-1"><a href="#cb38-1" aria-hidden="true" tabindex="-1"></a><span class="fu">f</span>(x) <span class="op">=</span> <span class="op">-</span><span class="fl">16</span>x<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> <span class="fl">100</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="37">
|
||
<pre><code>f (generic function with 2 methods)</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>The distinction is subtle, the expression is turned into a function just by adding the <code>f(x) =</code> preface. But to <code>Julia</code> there is a big distinction. The function form never does any computation until after a value of <span class="math inline">\(x\)</span> is passed to it. Whereas symbolic expressions can be manipulated quite freely before any numeric values are specified.</p>
|
||
<p>It is easy to create a symbolic expression from a function - just evaluate the function on a symbolic value:</p>
|
||
<div class="cell" data-execution_count="37">
|
||
<div class="sourceCode cell-code" id="cb40"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb40-1"><a href="#cb40-1" aria-hidden="true" tabindex="-1"></a><span class="fu">f</span>(x)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="38">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
100 - 16 x^{2}
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>This is easy - but can also be confusing. The function object is <code>f</code>, the expression is <code>f(x)</code> - the function evaluated on a symbolic object. Moreover, as seen, the symbolic expression can be evaluated using the same syntax as a function call:</p>
|
||
<div class="cell" data-execution_count="38">
|
||
<div class="sourceCode cell-code" id="cb41"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb41-1"><a href="#cb41-1" aria-hidden="true" tabindex="-1"></a>p <span class="op">=</span> <span class="fu">f</span>(x)</span>
|
||
<span id="cb41-2"><a href="#cb41-2" aria-hidden="true" tabindex="-1"></a><span class="fu">p</span>(<span class="fl">2</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell-output cell-output-display" data-execution_count="39">
|
||
<span class="math-left-align" style="padding-left: 4px; width:0; float:left;">
|
||
\[
|
||
36
|
||
\]
|
||
</span>
|
||
</div>
|
||
</div>
|
||
<p>For many uses, the distinction is unnecessary to make, as the many functions will work with any callable expression. One such is <code>plot</code> – either <code>plot(f, a, b)</code> or <code>plot(f(x),a, b)</code> will produce the same plot using the <code>Plots</code> package.</p>
|
||
</section>
|
||
</section>
|
||
<section id="questions" class="level2" data-number="11.6">
|
||
<h2 data-number="11.6" class="anchored" data-anchor-id="questions"><span class="header-section-number">11.6</span> Questions</h2>
|
||
<section id="question" class="level6">
|
||
<h6 class="anchored" data-anchor-id="question">Question</h6>
|
||
<p>Let <span class="math inline">\(p\)</span> be the polynomial <span class="math inline">\(3x^2 - 2x + 5\)</span>.</p>
|
||
<p>What is the degree of <span class="math inline">\(p\)</span>?</p>
|
||
<div class="cell" data-hold="true" data-execution_count="39">
|
||
<div class="cell-output cell-output-display" data-execution_count="40">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="14227349458571548855" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_14227349458571548855">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="14227349458571548855" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="14227349458571548855_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("14227349458571548855").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - 2) <= 0);
|
||
var msgBox = document.getElementById('14227349458571548855_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_14227349458571548855")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_14227349458571548855")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
<p>What is the leading coefficient of <span class="math inline">\(p\)</span>?</p>
|
||
<div class="cell" data-execution_count="40">
|
||
<div class="cell-output cell-output-display" data-execution_count="41">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="17428890841209197184" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_17428890841209197184">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="17428890841209197184" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="17428890841209197184_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("17428890841209197184").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - 3) <= 0);
|
||
var msgBox = document.getElementById('17428890841209197184_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_17428890841209197184")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_17428890841209197184")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
<p>The graph of <span class="math inline">\(p\)</span> would have what <span class="math inline">\(y\)</span>-intercept?</p>
|
||
<div class="cell" data-execution_count="41">
|
||
<div class="cell-output cell-output-display" data-execution_count="42">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="14303254114744292916" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_14303254114744292916">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="14303254114744292916" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="14303254114744292916_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("14303254114744292916").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - 5) <= 0);
|
||
var msgBox = document.getElementById('14303254114744292916_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_14303254114744292916")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_14303254114744292916")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
<p>Is <span class="math inline">\(p\)</span> a monic polynomial?</p>
|
||
<div class="cell" data-execution_count="42">
|
||
<div class="cell-output cell-output-display" data-execution_count="43">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="9617875952855429725" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_9617875952855429725">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_9617875952855429725_1">
|
||
<input class="form-check-input" type="radio" name="radio_9617875952855429725" id="radio_9617875952855429725_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
Yes
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_9617875952855429725_2">
|
||
<input class="form-check-input" type="radio" name="radio_9617875952855429725" id="radio_9617875952855429725_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
No
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="9617875952855429725_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_9617875952855429725"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 2;
|
||
var msgBox = document.getElementById('9617875952855429725_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_9617875952855429725")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_9617875952855429725")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
})});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
<p>Is <span class="math inline">\(p\)</span> a quadratic polynomial?</p>
|
||
<div class="cell" data-execution_count="43">
|
||
<div class="cell-output cell-output-display" data-execution_count="44">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="6536535233179182058" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_6536535233179182058">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_6536535233179182058_1">
|
||
<input class="form-check-input" type="radio" name="radio_6536535233179182058" id="radio_6536535233179182058_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
Yes
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_6536535233179182058_2">
|
||
<input class="form-check-input" type="radio" name="radio_6536535233179182058" id="radio_6536535233179182058_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
No
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="6536535233179182058_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_6536535233179182058"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 1;
|
||
var msgBox = document.getElementById('6536535233179182058_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_6536535233179182058")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_6536535233179182058")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
})});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
<p>The graph of <span class="math inline">\(p\)</span> would be <span class="math inline">\(U\)</span>-shaped?</p>
|
||
<div class="cell" data-execution_count="44">
|
||
<div class="cell-output cell-output-display" data-execution_count="45">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="4398266763210570906" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_4398266763210570906">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_4398266763210570906_1">
|
||
<input class="form-check-input" type="radio" name="radio_4398266763210570906" id="radio_4398266763210570906_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
Yes
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_4398266763210570906_2">
|
||
<input class="form-check-input" type="radio" name="radio_4398266763210570906" id="radio_4398266763210570906_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
No
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="4398266763210570906_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_4398266763210570906"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 1;
|
||
var msgBox = document.getElementById('4398266763210570906_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_4398266763210570906")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_4398266763210570906")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
})});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
<p>What is the leading term of <span class="math inline">\(p\)</span>?</p>
|
||
<div class="cell" data-hold="true" data-execution_count="45">
|
||
<div class="cell-output cell-output-display" data-execution_count="46">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="4948115528765244722" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_4948115528765244722">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_4948115528765244722_1">
|
||
<input class="form-check-input" type="radio" name="radio_4948115528765244722" id="radio_4948115528765244722_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
\(3\)
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_4948115528765244722_2">
|
||
<input class="form-check-input" type="radio" name="radio_4948115528765244722" id="radio_4948115528765244722_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
\(3x^2\)
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_4948115528765244722_3">
|
||
<input class="form-check-input" type="radio" name="radio_4948115528765244722" id="radio_4948115528765244722_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
\(-2x\)
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_4948115528765244722_4">
|
||
<input class="form-check-input" type="radio" name="radio_4948115528765244722" id="radio_4948115528765244722_4" value="4">
|
||
|
||
<span class="label-body px-1">
|
||
\(5\)
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="4948115528765244722_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_4948115528765244722"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 2;
|
||
var msgBox = document.getElementById('4948115528765244722_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_4948115528765244722")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_4948115528765244722")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
})});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="question-1" class="level6">
|
||
<h6 class="anchored" data-anchor-id="question-1">Question</h6>
|
||
<p>Let <span class="math inline">\(p = x^3 - 2x^2 +3x - 4\)</span>.</p>
|
||
<p>What is <span class="math inline">\(a_2\)</span>, using the standard numbering of coefficient?</p>
|
||
<div class="cell" data-execution_count="46">
|
||
<div class="cell-output cell-output-display" data-execution_count="47">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="217798504043531981" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_217798504043531981">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="217798504043531981" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="217798504043531981_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("217798504043531981").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - -2) <= 0);
|
||
var msgBox = document.getElementById('217798504043531981_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_217798504043531981")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_217798504043531981")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
<p>What is <span class="math inline">\(a_n\)</span>?</p>
|
||
<div class="cell" data-execution_count="47">
|
||
<div class="cell-output cell-output-display" data-execution_count="48">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="16394645662266939214" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_16394645662266939214">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="16394645662266939214" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="16394645662266939214_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("16394645662266939214").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - 1) <= 0);
|
||
var msgBox = document.getElementById('16394645662266939214_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_16394645662266939214")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_16394645662266939214")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
<p>What is <span class="math inline">\(a_0\)</span>?</p>
|
||
<div class="cell" data-execution_count="48">
|
||
<div class="cell-output cell-output-display" data-execution_count="49">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="10538694461509438566" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_10538694461509438566">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="10538694461509438566" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="10538694461509438566_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("10538694461509438566").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - -4) <= 0);
|
||
var msgBox = document.getElementById('10538694461509438566_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_10538694461509438566")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_10538694461509438566")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="question-2" class="level6">
|
||
<h6 class="anchored" data-anchor-id="question-2">Question</h6>
|
||
<p>The linear polynomial <span class="math inline">\(p = 2x + 3\)</span> is written in which form:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="49">
|
||
<div class="cell-output cell-output-display" data-execution_count="50">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="2798856811212515174" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_2798856811212515174">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_2798856811212515174_1">
|
||
<input class="form-check-input" type="radio" name="radio_2798856811212515174" id="radio_2798856811212515174_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
general form
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_2798856811212515174_2">
|
||
<input class="form-check-input" type="radio" name="radio_2798856811212515174" id="radio_2798856811212515174_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
point-slope form
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_2798856811212515174_3">
|
||
<input class="form-check-input" type="radio" name="radio_2798856811212515174" id="radio_2798856811212515174_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
slope-intercept form
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="2798856811212515174_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_2798856811212515174"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 3;
|
||
var msgBox = document.getElementById('2798856811212515174_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_2798856811212515174")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_2798856811212515174")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
})});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="question-3" class="level6">
|
||
<h6 class="anchored" data-anchor-id="question-3">Question</h6>
|
||
<p>The polynomial <code>p</code> is defined in <code>Julia</code> as follows:</p>
|
||
<div class="sourceCode cell-code" id="cb42"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb42-1"><a href="#cb42-1" aria-hidden="true" tabindex="-1"></a><span class="pp">@syms</span> x</span>
|
||
<span id="cb42-2"><a href="#cb42-2" aria-hidden="true" tabindex="-1"></a>p <span class="op">=</span> <span class="op">-</span><span class="fl">16</span>x<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> <span class="fl">64</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>What command will return the value of the polynomial when <span class="math inline">\(x=2\)</span>?</p>
|
||
<div class="cell" data-hold="true" data-execution_count="51">
|
||
<div class="cell-output cell-output-display" data-execution_count="51">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="9976305713579571914" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_9976305713579571914">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_9976305713579571914_1">
|
||
<input class="form-check-input" type="radio" name="radio_9976305713579571914" id="radio_9976305713579571914_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
<code>p_2</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_9976305713579571914_2">
|
||
<input class="form-check-input" type="radio" name="radio_9976305713579571914" id="radio_9976305713579571914_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
<code>p[2]</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_9976305713579571914_3">
|
||
<input class="form-check-input" type="radio" name="radio_9976305713579571914" id="radio_9976305713579571914_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
<code>p*2</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_9976305713579571914_4">
|
||
<input class="form-check-input" type="radio" name="radio_9976305713579571914" id="radio_9976305713579571914_4" value="4">
|
||
|
||
<span class="label-body px-1">
|
||
<code>p(x=>2)</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="9976305713579571914_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_9976305713579571914"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 4;
|
||
var msgBox = document.getElementById('9976305713579571914_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_9976305713579571914")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_9976305713579571914")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
})});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="question-4" class="level6">
|
||
<h6 class="anchored" data-anchor-id="question-4">Question</h6>
|
||
<p>In the large, the graph of <span class="math inline">\(p=x^{101} - x + 1\)</span> will</p>
|
||
<div class="cell" data-hold="true" data-execution_count="52">
|
||
<div class="cell-output cell-output-display" data-execution_count="52">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="13530449032116469889" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_13530449032116469889">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_13530449032116469889_1">
|
||
<input class="form-check-input" type="radio" name="radio_13530449032116469889" id="radio_13530449032116469889_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
Be \(U\)-shaped, opening upward
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_13530449032116469889_2">
|
||
<input class="form-check-input" type="radio" name="radio_13530449032116469889" id="radio_13530449032116469889_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
Be \(U\)-shaped, opening downward
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_13530449032116469889_3">
|
||
<input class="form-check-input" type="radio" name="radio_13530449032116469889" id="radio_13530449032116469889_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
Overall, go upwards from \(-\infty\) to \(+\infty\)
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_13530449032116469889_4">
|
||
<input class="form-check-input" type="radio" name="radio_13530449032116469889" id="radio_13530449032116469889_4" value="4">
|
||
|
||
<span class="label-body px-1">
|
||
Overall, go downwards from \(+\infty\) to \(-\infty\)
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="13530449032116469889_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_13530449032116469889"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 3;
|
||
var msgBox = document.getElementById('13530449032116469889_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_13530449032116469889")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_13530449032116469889")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
})});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="question-5" class="level6">
|
||
<h6 class="anchored" data-anchor-id="question-5">Question</h6>
|
||
<p>In the large, the graph of <span class="math inline">\(p=x^{102} - x^{101} + x + 1\)</span> will</p>
|
||
<div class="cell" data-hold="true" data-execution_count="53">
|
||
<div class="cell-output cell-output-display" data-execution_count="53">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="8298265012659132938" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_8298265012659132938">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_8298265012659132938_1">
|
||
<input class="form-check-input" type="radio" name="radio_8298265012659132938" id="radio_8298265012659132938_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
Be \(U\)-shaped, opening upward
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_8298265012659132938_2">
|
||
<input class="form-check-input" type="radio" name="radio_8298265012659132938" id="radio_8298265012659132938_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
Be \(U\)-shaped, opening downward
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_8298265012659132938_3">
|
||
<input class="form-check-input" type="radio" name="radio_8298265012659132938" id="radio_8298265012659132938_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
Overall, go upwards from \(-\infty\) to \(+\infty\)
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_8298265012659132938_4">
|
||
<input class="form-check-input" type="radio" name="radio_8298265012659132938" id="radio_8298265012659132938_4" value="4">
|
||
|
||
<span class="label-body px-1">
|
||
Overall, go downwards from \(+\infty\) to \(-\infty\)
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="8298265012659132938_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_8298265012659132938"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 1;
|
||
var msgBox = document.getElementById('8298265012659132938_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_8298265012659132938")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_8298265012659132938")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
})});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="question-6" class="level6">
|
||
<h6 class="anchored" data-anchor-id="question-6">Question</h6>
|
||
<p>In the large, the graph of <span class="math inline">\(p=-x^{10} + x^9 + x^8 + x^7 + x^6\)</span> will</p>
|
||
<div class="cell" data-hold="true" data-execution_count="54">
|
||
<div class="cell-output cell-output-display" data-execution_count="54">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="15561108228234012904" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_15561108228234012904">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_15561108228234012904_1">
|
||
<input class="form-check-input" type="radio" name="radio_15561108228234012904" id="radio_15561108228234012904_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
Be \(U\)-shaped, opening upward
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_15561108228234012904_2">
|
||
<input class="form-check-input" type="radio" name="radio_15561108228234012904" id="radio_15561108228234012904_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
Be \(U\)-shaped, opening downward
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_15561108228234012904_3">
|
||
<input class="form-check-input" type="radio" name="radio_15561108228234012904" id="radio_15561108228234012904_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
Overall, go upwards from \(-\infty\) to \(+\infty\)
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_15561108228234012904_4">
|
||
<input class="form-check-input" type="radio" name="radio_15561108228234012904" id="radio_15561108228234012904_4" value="4">
|
||
|
||
<span class="label-body px-1">
|
||
Overall, go downwards from \(+\infty\) to \(-\infty\)
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="15561108228234012904_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_15561108228234012904"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 2;
|
||
var msgBox = document.getElementById('15561108228234012904_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_15561108228234012904")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_15561108228234012904")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
})});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="question-7" class="level6">
|
||
<h6 class="anchored" data-anchor-id="question-7">Question</h6>
|
||
<p>Use <code>SymPy</code> to factor the polynomial <span class="math inline">\(x^{11} - x\)</span>. How many factors are found?</p>
|
||
<div class="cell" data-hold="true" data-execution_count="55">
|
||
<div class="cell-output cell-output-display" data-execution_count="55">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="16928029585630841431" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_16928029585630841431">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="16928029585630841431" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="16928029585630841431_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("16928029585630841431").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - 5) <= 0);
|
||
var msgBox = document.getElementById('16928029585630841431_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_16928029585630841431")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_16928029585630841431")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="question-8" class="level6">
|
||
<h6 class="anchored" data-anchor-id="question-8">Question</h6>
|
||
<p>Use <code>SymPy</code> to factor the polynomial <span class="math inline">\(x^{12} - 1\)</span>. How many factors are found?</p>
|
||
<div class="cell" data-hold="true" data-execution_count="56">
|
||
<div class="cell-output cell-output-display" data-execution_count="56">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="3772274614958833958" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_3772274614958833958">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="3772274614958833958" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="3772274614958833958_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("3772274614958833958").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - 6) <= 0);
|
||
var msgBox = document.getElementById('3772274614958833958_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_3772274614958833958")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_3772274614958833958")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="question-9" class="level6">
|
||
<h6 class="anchored" data-anchor-id="question-9">Question</h6>
|
||
<p>What is the monic polynomial with roots <span class="math inline">\(x=-1\)</span>, <span class="math inline">\(x=0\)</span>, and <span class="math inline">\(x=2\)</span>?</p>
|
||
<div class="cell" data-hold="true" data-execution_count="57">
|
||
<div class="cell-output cell-output-display" data-execution_count="57">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="1855149482095150509" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_1855149482095150509">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_1855149482095150509_1">
|
||
<input class="form-check-input" type="radio" name="radio_1855149482095150509" id="radio_1855149482095150509_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
<code>x^3 + x^2 - 2x</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_1855149482095150509_2">
|
||
<input class="form-check-input" type="radio" name="radio_1855149482095150509" id="radio_1855149482095150509_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
<code>x^3 - x^2 - 2x</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_1855149482095150509_3">
|
||
<input class="form-check-input" type="radio" name="radio_1855149482095150509" id="radio_1855149482095150509_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
<code>x^3 - 3x^2 + 2x</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_1855149482095150509_4">
|
||
<input class="form-check-input" type="radio" name="radio_1855149482095150509" id="radio_1855149482095150509_4" value="4">
|
||
|
||
<span class="label-body px-1">
|
||
<code>x^3 + x^2 + 2x</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="1855149482095150509_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_1855149482095150509"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 2;
|
||
var msgBox = document.getElementById('1855149482095150509_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_1855149482095150509")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_1855149482095150509")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
})});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="question-10" class="level6">
|
||
<h6 class="anchored" data-anchor-id="question-10">Question</h6>
|
||
<p>Use <code>expand</code> to expand the expression <code>((x-h)^3 - x^3) / h</code> where <code>x</code> and <code>h</code> are symbolic constants. What is the value:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="58">
|
||
<div class="cell-output cell-output-display" data-execution_count="58">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="16391561392778088233" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_16391561392778088233">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_16391561392778088233_1">
|
||
<input class="form-check-input" type="radio" name="radio_16391561392778088233" id="radio_16391561392778088233_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
<code>0</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_16391561392778088233_2">
|
||
<input class="form-check-input" type="radio" name="radio_16391561392778088233" id="radio_16391561392778088233_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
<code>-h^2 + 3hx - 3x^2</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_16391561392778088233_3">
|
||
<input class="form-check-input" type="radio" name="radio_16391561392778088233" id="radio_16391561392778088233_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
<code>h^3 + 3h^2x + 3hx^2 + x^3 -x^3/h</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_16391561392778088233_4">
|
||
<input class="form-check-input" type="radio" name="radio_16391561392778088233" id="radio_16391561392778088233_4" value="4">
|
||
|
||
<span class="label-body px-1">
|
||
<code>x^3 - x^3/h</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="16391561392778088233_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_16391561392778088233"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 2;
|
||
var msgBox = document.getElementById('16391561392778088233_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_16391561392778088233")
|
||
if (explanation != null) {
|
||
explanation.style.display = "none";
|
||
}
|
||
} else {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition alert alert-danger'><span>👎 Incorrect </span></div>";
|
||
var explanation = document.getElementById("explanation_16391561392778088233")
|
||
if (explanation != null) {
|
||
explanation.style.display = "block";
|
||
}
|
||
}
|
||
|
||
})});
|
||
|
||
</script>
|
||
</div>
|
||
</div>
|
||
|
||
|
||
</section>
|
||
</section>
|
||
|
||
</main> <!-- /main -->
|
||
<script id="quarto-html-after-body" type="application/javascript">
|
||
window.document.addEventListener("DOMContentLoaded", function (event) {
|
||
const toggleBodyColorMode = (bsSheetEl) => {
|
||
const mode = bsSheetEl.getAttribute("data-mode");
|
||
const bodyEl = window.document.querySelector("body");
|
||
if (mode === "dark") {
|
||
bodyEl.classList.add("quarto-dark");
|
||
bodyEl.classList.remove("quarto-light");
|
||
} else {
|
||
bodyEl.classList.add("quarto-light");
|
||
bodyEl.classList.remove("quarto-dark");
|
||
}
|
||
}
|
||
const toggleBodyColorPrimary = () => {
|
||
const bsSheetEl = window.document.querySelector("link#quarto-bootstrap");
|
||
if (bsSheetEl) {
|
||
toggleBodyColorMode(bsSheetEl);
|
||
}
|
||
}
|
||
toggleBodyColorPrimary();
|
||
const icon = "";
|
||
const anchorJS = new window.AnchorJS();
|
||
anchorJS.options = {
|
||
placement: 'right',
|
||
icon: icon
|
||
};
|
||
anchorJS.add('.anchored');
|
||
const clipboard = new window.ClipboardJS('.code-copy-button', {
|
||
target: function(trigger) {
|
||
return trigger.previousElementSibling;
|
||
}
|
||
});
|
||
clipboard.on('success', function(e) {
|
||
// button target
|
||
const button = e.trigger;
|
||
// don't keep focus
|
||
button.blur();
|
||
// flash "checked"
|
||
button.classList.add('code-copy-button-checked');
|
||
var currentTitle = button.getAttribute("title");
|
||
button.setAttribute("title", "Copied!");
|
||
setTimeout(function() {
|
||
button.setAttribute("title", currentTitle);
|
||
button.classList.remove('code-copy-button-checked');
|
||
}, 1000);
|
||
// clear code selection
|
||
e.clearSelection();
|
||
});
|
||
function tippyHover(el, contentFn) {
|
||
const config = {
|
||
allowHTML: true,
|
||
content: contentFn,
|
||
maxWidth: 500,
|
||
delay: 100,
|
||
arrow: false,
|
||
appendTo: function(el) {
|
||
return el.parentElement;
|
||
},
|
||
interactive: true,
|
||
interactiveBorder: 10,
|
||
theme: 'quarto',
|
||
placement: 'bottom-start'
|
||
};
|
||
window.tippy(el, config);
|
||
}
|
||
const noterefs = window.document.querySelectorAll('a[role="doc-noteref"]');
|
||
for (var i=0; i<noterefs.length; i++) {
|
||
const ref = noterefs[i];
|
||
tippyHover(ref, function() {
|
||
let href = ref.getAttribute('href');
|
||
try { href = new URL(href).hash; } catch {}
|
||
const id = href.replace(/^#\/?/, "");
|
||
const note = window.document.getElementById(id);
|
||
return note.innerHTML;
|
||
});
|
||
}
|
||
var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
|
||
for (var i=0; i<bibliorefs.length; i++) {
|
||
const ref = bibliorefs[i];
|
||
const cites = ref.parentNode.getAttribute('data-cites').split(' ');
|
||
tippyHover(ref, function() {
|
||
var popup = window.document.createElement('div');
|
||
cites.forEach(function(cite) {
|
||
var citeDiv = window.document.createElement('div');
|
||
citeDiv.classList.add('hanging-indent');
|
||
citeDiv.classList.add('csl-entry');
|
||
var biblioDiv = window.document.getElementById('ref-' + cite);
|
||
if (biblioDiv) {
|
||
citeDiv.innerHTML = biblioDiv.innerHTML;
|
||
}
|
||
popup.appendChild(citeDiv);
|
||
});
|
||
return popup.innerHTML;
|
||
});
|
||
}
|
||
var localhostRegex = new RegExp(/^(?:http|https):\/\/localhost\:?[0-9]*\//);
|
||
var filterRegex = new RegExp('/' + window.location.host + '/');
|
||
var isInternal = (href) => {
|
||
return filterRegex.test(href) || localhostRegex.test(href);
|
||
}
|
||
// Inspect non-navigation links and adorn them if external
|
||
var links = window.document.querySelectorAll('a:not(.nav-link):not(.navbar-brand):not(.toc-action):not(.sidebar-link):not(.sidebar-item-toggle):not(.pagination-link):not(.no-external)');
|
||
for (var i=0; i<links.length; i++) {
|
||
const link = links[i];
|
||
if (!isInternal(link.href)) {
|
||
// target, if specified
|
||
link.setAttribute("target", "_blank");
|
||
}
|
||
}
|
||
});
|
||
</script>
|
||
<nav class="page-navigation">
|
||
<div class="nav-page nav-page-previous">
|
||
<a href="../precalc/inversefunctions.html" class="pagination-link">
|
||
<i class="bi bi-arrow-left-short"></i> <span class="nav-page-text"><span class="chapter-number">10</span> <span class="chapter-title">The Inverse of a Function</span></span>
|
||
</a>
|
||
</div>
|
||
<div class="nav-page nav-page-next">
|
||
<a href="../precalc/polynomial_roots.html" class="pagination-link">
|
||
<span class="nav-page-text"><span class="chapter-number">12</span> <span class="chapter-title">Roots of a polynomial</span></span> <i class="bi bi-arrow-right-short"></i>
|
||
</a>
|
||
</div>
|
||
</nav>
|
||
</div> <!-- /content -->
|
||
<footer class="footer">
|
||
<div class="nav-footer">
|
||
<div class="nav-footer-center">Copyright 2022, John Verzani</div>
|
||
</div>
|
||
</footer>
|
||
|
||
|
||
|
||
</body></html> |