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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<li><a href="#assignment" id="toc-assignment" class="nav-link active" data-scroll-target="#assignment"> <span class="header-section-number">2.1</span> Assignment</a>
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<li><a href="#context" id="toc-context" class="nav-link" data-scroll-target="#context"> <span class="header-section-number">2.3</span> Context</a></li>
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<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/variables.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>
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<h1 class="title d-none d-lg-block"><span class="chapter-number">2</span> <span class="chapter-title">Variables</span></h1>
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<section id="assignment" class="level2" data-number="2.1">
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<h2 data-number="2.1" class="anchored" data-anchor-id="assignment"><span class="header-section-number">2.1</span> Assignment</h2>
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<div class="quarto-figure quarto-figure-center">
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<figure class="figure">
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<p><img src="../precalc/figures/calculator.png" class="img-fluid figure-img"></p>
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<p></p><figcaption class="figure-caption">Screenshot of a calculator provided by the Google search engine.</figcaption><p></p>
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</figure>
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</div>
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<p>The Google calculator has a button <code>Ans</code> to refer to the answer to the previous evaluation. This is a form of memory. The last answer is stored in a specific place in memory for retrieval when <code>Ans</code> is used. In some calculators, more advanced memory features are possible. For some, it is possible to push values onto a stack of values for them to be referred to at a later time. This proves useful for complicated expressions, say, as the expression can be broken into smaller intermediate steps to be computed. These values can then be appropriately combined. This strategy is a good one, though the memory buttons can make its implementation a bit cumbersome.</p>
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<p>With <code>Julia</code>, as with other programming languages, it is very easy to refer to past evaluations. This is done by <em>assignment</em> whereby a computed value stored in memory is associated with a name. The name can be used to look up the value later. Assignment does not change the value of the object being assigned, it only introduces a reference to it.</p>
|
||
<p>Assignment in <code>Julia</code> is handled by the equals sign and takes the general form <code>variable_name = value</code>. For example, here we assign values to the variables <code>x</code> and <code>y</code></p>
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<div class="cell" data-execution_count="4">
|
||
<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>x <span class="op">=</span> <span class="fu">sqrt</span>(<span class="fl">2</span>)</span>
|
||
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>y <span class="op">=</span> <span class="fl">42</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="5">
|
||
<pre><code>42</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>In an assignment, the right hand side is always returned, so it appears nothing has happened. However, the values are there, as can be checked by typing their name</p>
|
||
<div class="cell" data-execution_count="5">
|
||
<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>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="6">
|
||
<pre><code>1.4142135623730951</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>Just typing a variable name (without a trailing semicolon) causes the assigned value to be displayed.</p>
|
||
<p>Variable names can be reused, as here, where we redefine <code>x</code>:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="6">
|
||
<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>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="7">
|
||
<pre><code>2</code></pre>
|
||
</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 <code>Pluto</code> interface for <code>Julia</code> is idiosyncratic, as variables are <em>reactive</em>. This interface allows changes to a variable <code>x</code> to propogate to all other cells referring to <code>x</code>. Consequently, the variable name can only be assigned <em>once</em> per notebook <strong>unless</strong> the name is in some other namespace, which can be arranged by including the assignment inside a function or a <code>let</code> block.</p>
|
||
</div>
|
||
</div>
|
||
<p><code>Julia</code> is referred to as a “dynamic language” which means (in most cases) that a variable can be reassigned with a value of a different type, as we did with <code>x</code> where first it was assigned to a floating point value then to an integer value. (Though we meet some cases - generic functions - where <code>Julia</code> balks at reassigning a variable if the type if different.)</p>
|
||
<p>More importantly than displaying a value, is the use of variables to build up more complicated expressions. For example, to compute</p>
|
||
<p><span class="math display">\[
|
||
\frac{1 + 2 \cdot 3^4}{5 - 6/7}
|
||
\]</span></p>
|
||
<p>we might break it into the grouped pieces implied by the mathematical notation:</p>
|
||
<div class="cell" data-execution_count="7">
|
||
<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>top <span class="op">=</span> <span class="fl">1</span> <span class="op">+</span> <span class="fl">2</span><span class="op">*</span><span class="fl">3</span><span class="op">^</span><span class="fl">4</span></span>
|
||
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>bottom <span class="op">=</span> <span class="fl">5</span> <span class="op">-</span> <span class="fl">6</span><span class="op">/</span><span class="fl">7</span></span>
|
||
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>top<span class="op">/</span>bottom</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">
|
||
<pre><code>39.34482758620689</code></pre>
|
||
</div>
|
||
</div>
|
||
<section id="examples" class="level3" data-number="2.1.1">
|
||
<h3 data-number="2.1.1" class="anchored" data-anchor-id="examples"><span class="header-section-number">2.1.1</span> Examples</h3>
|
||
<section id="example" class="level5">
|
||
<h5 class="anchored" data-anchor-id="example">Example</h5>
|
||
<p>Imagine we have the following complicated expression related to the trajectory of a <a href="http://www.researchgate.net/publication/230963032_On_the_trajectories_of_projectiles_depicted_in_early_ballistic_woodcuts">projectile</a> with wind resistance:</p>
|
||
<p><span class="math display">\[
|
||
\left(\frac{g}{k v_0\cos(\theta)} + \tan(\theta) \right) t + \frac{g}{k^2}\ln\left(1 - \frac{k}{v_0\cos(\theta)} t \right)
|
||
\]</span></p>
|
||
<p>Here <span class="math inline">\(g\)</span> is the gravitational constant <span class="math inline">\(9.8\)</span> and <span class="math inline">\(v_0\)</span>, <span class="math inline">\(\theta\)</span> and <span class="math inline">\(k\)</span> parameters, which we take to be <span class="math inline">\(200\)</span>, <span class="math inline">\(45\)</span> degrees, and <span class="math inline">\(1/2\)</span> respectively. With these values, the above expression can be computed when <span class="math inline">\(s=100\)</span>:</p>
|
||
<div class="cell" data-execution_count="8">
|
||
<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>g <span class="op">=</span> <span class="fl">9.8</span></span>
|
||
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>v0 <span class="op">=</span> <span class="fl">200</span></span>
|
||
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a>theta <span class="op">=</span> <span class="fl">45</span></span>
|
||
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a>k <span class="op">=</span> <span class="fl">1</span><span class="op">/</span><span class="fl">2</span></span>
|
||
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a>t <span class="op">=</span> <span class="fl">100</span></span>
|
||
<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a>a <span class="op">=</span> v0 <span class="op">*</span> <span class="fu">cosd</span>(theta)</span>
|
||
<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a>(g<span class="op">/</span>(k<span class="op">*</span>a) <span class="op">+</span> <span class="fu">tand</span>(theta))<span class="op">*</span> t <span class="op">+</span> (g<span class="op">/</span>k<span class="op">^</span><span class="fl">2</span>) <span class="op">*</span> <span class="fu">log</span>(<span class="fl">1</span> <span class="op">-</span> (k<span class="op">/</span>a)<span class="op">*</span>t)</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>96.75771791632161</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>By defining a new variable <code>a</code> to represent a value that is repeated a few times in the expression, the last command is greatly simplified. Doing so makes it much easier to check for accuracy against the expression to compute.</p>
|
||
</section>
|
||
<section id="example-1" class="level5">
|
||
<h5 class="anchored" data-anchor-id="example-1">Example</h5>
|
||
<p>A common expression in mathematics is a polynomial expression, for example <span class="math inline">\(-16s^2 + 32s - 12\)</span>. Translating this to <code>Julia</code> at <span class="math inline">\(s =3\)</span> we might have:</p>
|
||
<div class="cell" data-execution_count="9">
|
||
<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>s <span class="op">=</span> <span class="fl">3</span></span>
|
||
<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a><span class="op">-</span><span class="fl">16</span><span class="op">*</span>s<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> <span class="fl">32</span><span class="op">*</span>s <span class="op">-</span> <span class="fl">12</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="10">
|
||
<pre><code>-60</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>This looks nearly identical to the mathematical expression, but we inserted <code>*</code> to indicate multiplication between the constant and the variable. In fact, this step is not needed as Julia allows numeric literals to have an implied multiplication:</p>
|
||
<div class="cell" data-execution_count="10">
|
||
<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="op">-</span><span class="fl">16</span>s<span class="op">^</span><span class="fl">2</span> <span class="op">+</span> <span class="fl">32</span>s <span class="op">-</span> <span class="fl">12</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="11">
|
||
<pre><code>-60</code></pre>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
</section>
|
||
</section>
|
||
<section id="where-math-and-computer-notations-diverge" class="level2" data-number="2.2">
|
||
<h2 data-number="2.2" class="anchored" data-anchor-id="where-math-and-computer-notations-diverge"><span class="header-section-number">2.2</span> Where math and computer notations diverge</h2>
|
||
<p>It is important to recognize that <code>=</code> to <code>Julia</code> is not in analogy to how <span class="math inline">\(=\)</span> is used in mathematical notation. The following <code>Julia</code> code is not an equation:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="11">
|
||
<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>x <span class="op">=</span> <span class="fl">3</span></span>
|
||
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a>x <span class="op">=</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="12">
|
||
<pre><code>9</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>What happens instead? The right hand side is evaluated (<code>x</code> is squared), the result is stored and bound to the variable <code>x</code> (so that <code>x</code> will end up pointing to the new value, <code>9</code>, and not the original one, <code>3</code>); finally the value computed on the right-hand side is returned and in this case displayed, as there is no trailing semicolon to suppress the output.</p>
|
||
<p>This is completely unlike the mathematical equation <span class="math inline">\(x = x^2\)</span> which is typically solved for values of <span class="math inline">\(x\)</span> that satisfy the equation (<span class="math inline">\(0\)</span> and <span class="math inline">\(1\)</span>).</p>
|
||
<section id="example-2" class="level5">
|
||
<h5 class="anchored" data-anchor-id="example-2">Example</h5>
|
||
<p>Having <code>=</code> as assignment is usefully exploited when modeling sequences. For example, an application of Newton’s method might end up with this expression:</p>
|
||
<p><span class="math display">\[
|
||
x_{i+1} = x_i - \frac{x_i^2 - 2}{2x_i}
|
||
\]</span></p>
|
||
<p>As a mathematical expression, for each <span class="math inline">\(i\)</span> this defines a new value for <span class="math inline">\(x_{i+1}\)</span> in terms of a known value <span class="math inline">\(x_i\)</span>. This can be used to recursively generate a sequence, provided some starting point is known, such as <span class="math inline">\(x_0 = 2\)</span>.</p>
|
||
<p>The above might be written instead with:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="12">
|
||
<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>x <span class="op">=</span> <span class="fl">2</span></span>
|
||
<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a>x <span class="op">=</span> x <span class="op">-</span> (x<span class="op">^</span><span class="fl">2</span> <span class="op">-</span> <span class="fl">2</span>) <span class="op">/</span> (<span class="fl">2</span>x)</span>
|
||
<span id="cb17-3"><a href="#cb17-3" aria-hidden="true" tabindex="-1"></a>x <span class="op">=</span> x <span class="op">-</span> (x<span class="op">^</span><span class="fl">2</span> <span class="op">-</span> <span class="fl">2</span>) <span class="op">/</span> (<span class="fl">2</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="13">
|
||
<pre><code>1.4166666666666667</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>Repeating this last line will generate new values of <code>x</code> based on the previous one - no need for subscripts. This is exactly what the mathematical notation indicates is to be done.</p>
|
||
</section>
|
||
</section>
|
||
<section id="context" class="level2" data-number="2.3">
|
||
<h2 data-number="2.3" class="anchored" data-anchor-id="context"><span class="header-section-number">2.3</span> Context</h2>
|
||
<p>The binding of a value to a variable name happens within some context. For our simple illustrations, we are assigning values, as though they were typed at the command line. This stores the binding in the <code>Main</code> module. <code>Julia</code> looks for variables in this module when it encounters an expression and the value is substituted. Other uses, such as when variables are defined within a function, involve different contexts which may not be visible within the <code>Main</code> module.</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>The <code>varinfo</code> function will list the variables currently defined in the main workspace. There is no mechanism to delete a single variable.</p>
|
||
</div>
|
||
</div>
|
||
<div class="callout-warning 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">
|
||
Warning
|
||
</div>
|
||
</div>
|
||
<div class="callout-body-container callout-body">
|
||
<p><strong>Shooting oneselves in the foot.</strong> <code>Julia</code> allows us to locally redefine variables that are built in, such as the value for <code>pi</code> or the function object assigned to <code>sin</code>. For example, this is a perfectly valid command <code>sin=3</code>. However, it will overwrite the typical value of <code>sin</code> so that <code>sin(3)</code> will be an error. At the terminal, the binding to <code>sin</code> occurs in the <code>Main</code> module. This shadows that value of <code>sin</code> bound in the <code>Base</code> module. Even if redefined in <code>Main</code>, the value in base can be used by fully qualifying the name, as in <code>Base.sin(pi)</code>. This uses the notation <code>module_name.variable_name</code> to look up a binding in a module.</p>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
<section id="variable-names" class="level2" data-number="2.4">
|
||
<h2 data-number="2.4" class="anchored" data-anchor-id="variable-names"><span class="header-section-number">2.4</span> Variable names</h2>
|
||
<p><code>Julia</code> has a very wide set of possible <a href="https://docs.julialang.org/en/stable/manual/variables/#Allowed-Variable-Names-1">names</a> for variables. Variables are case sensitive and their names can include many <a href="http://en.wikipedia.org/wiki/List_of_Unicode_characters">Unicode</a> characters. Names must begin with a letter or an appropriate Unicode value (but not a number). There are some reserved words, such as <code>try</code> or <code>else</code> which can not be assigned to. However, many built-in names can be locally overwritten. Conventionally, variable names are lower case. For compound names, it is not unusual to see them squished together, joined with underscores, or written in camelCase.</p>
|
||
<div class="cell" data-execution_count="13">
|
||
<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>value_1 <span class="op">=</span> <span class="fl">1</span></span>
|
||
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a>a_long_winded_variable_name <span class="op">=</span> <span class="fl">2</span></span>
|
||
<span id="cb19-3"><a href="#cb19-3" aria-hidden="true" tabindex="-1"></a>sinOfX <span class="op">=</span> <span class="fu">sind</span>(<span class="fl">45</span>)</span>
|
||
<span id="cb19-4"><a href="#cb19-4" aria-hidden="true" tabindex="-1"></a>__private <span class="op">=</span> <span class="fl">2</span> <span class="co"># a convention</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">
|
||
<pre><code>2</code></pre>
|
||
</div>
|
||
</div>
|
||
<section id="unicode-names" class="level3" data-number="2.4.1">
|
||
<h3 data-number="2.4.1" class="anchored" data-anchor-id="unicode-names"><span class="header-section-number">2.4.1</span> Unicode names</h3>
|
||
<p>Julia allows variable names to use Unicode identifiers. Such names allow <code>julia</code> notation to mirror that of many mathematical texts. For example, in calculus the variable <span class="math inline">\(\epsilon\)</span> is often used to represent some small number. We can assign to a symbol that looks like <span class="math inline">\(\epsilon\)</span> using <code>Julia</code>’s LaTeX input mode. Typing <code>\epsilon[tab]</code> will replace the text with the symbol within <code>IJulia</code> or the command line.</p>
|
||
<div class="cell" data-execution_count="14">
|
||
<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>ϵ <span class="op">=</span> <span class="fl">1e-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="15">
|
||
<pre><code>1.0e-10</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>Entering Unicode names follows the pattern of “slash” + LaTeX name + <code>[tab]</code> key. Some other ones that are useful are <code>\delta[tab]</code>, <code>\alpha[tab]</code>, and <code>\beta[tab]</code>, though there are <a href="https://github.com/JuliaLang/julia/blob/master/stdlib/REPL/src/latex_symbols.jl">hundreds</a> of other values defined.</p>
|
||
<p>For example, we could have defined <code>theta</code> (<code>\theta[tab]</code>) and <code>v0</code> (<code>v\_0[tab]</code>) using Unicode to make them match more closely the typeset math:</p>
|
||
<div class="cell" data-execution_count="15">
|
||
<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>θ <span class="op">=</span> <span class="fl">45</span>; v₀ <span class="op">=</span> <span class="fl">200</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="16">
|
||
<pre><code>200</code></pre>
|
||
</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">
|
||
Unicode
|
||
</div>
|
||
</div>
|
||
<div class="callout-body-container callout-body">
|
||
<p>These notes can be presented as HTML files <em>or</em> as <code>Pluto</code> notebooks. They often use Unicode alternatives to avoid the <code>Pluto</code> requirement of a single use of assigning to a variable name in a notebook without placing the assignment in a <code>let</code> block or a function body.</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">
|
||
Emojis
|
||
</div>
|
||
</div>
|
||
<div class="callout-body-container callout-body">
|
||
<p>There is even support for tab-completion of <a href="https://github.com/JuliaLang/julia/blob/master/stdlib/REPL/src/emoji_symbols.jl">emojis</a> such as <code>\\:snowman:[tab]</code> or <code>\\:koala:[tab]</code></p>
|
||
</div>
|
||
</div>
|
||
<section id="example-3" class="level5">
|
||
<h5 class="anchored" data-anchor-id="example-3">Example</h5>
|
||
<p>As mentioned the value of <span class="math inline">\(e\)</span> is bound to the Unicode value <code>\euler[tab]</code> and not the letter <code>e</code>, so Unicode entry is required to access this constant This isn’t quite true. The <code>MathConstants</code> module defines <code>e</code>, as well as a few other values accessed via Unicode. When the <code>CalculusWithJulia</code> package is loaded, as will often be done in these notes, a value of <code>exp(1)</code> is assigned to <code>e</code>.</p>
|
||
</section>
|
||
</section>
|
||
</section>
|
||
<section id="tuple-assignment" class="level2" data-number="2.5">
|
||
<h2 data-number="2.5" class="anchored" data-anchor-id="tuple-assignment"><span class="header-section-number">2.5</span> Tuple assignment</h2>
|
||
<p>It is a common task to define more than one variable. Multiple definitions can be done in one line, using semicolons to break up the commands, as with:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="16">
|
||
<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>a <span class="op">=</span> <span class="fl">1</span>; b <span class="op">=</span> <span class="fl">2</span>; c<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="17">
|
||
<pre><code>3</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>For convenience, <code>Julia</code> allows an alternate means to define more than one variable at a time. The syntax is similar:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="17">
|
||
<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>a, b, c <span class="op">=</span> <span class="fl">1</span>, <span class="fl">2</span>, <span class="fl">3</span></span>
|
||
<span id="cb27-2"><a href="#cb27-2" aria-hidden="true" tabindex="-1"></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="18">
|
||
<pre><code>2</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>This sets <code>a=1</code>, <code>b=2</code>, and <code>c=3</code>, as suggested. This construct relies on <em>tuple destructuring</em>. The expression on the right hand side forms a tuple of values. A tuple is a container for different types of values, and in this case the tuple has 3 values. When the same number of variables match on the left-hand side as those in the container on the right, the names are assigned one by one.</p>
|
||
<p>The value on the right hand side is evaluated, then the assignment occurs. The following exploits this to swap the values assigned to <code>a</code> and <code>b</code>:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="18">
|
||
<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>a, b <span class="op">=</span> <span class="fl">1</span>, <span class="fl">2</span></span>
|
||
<span id="cb29-2"><a href="#cb29-2" aria-hidden="true" tabindex="-1"></a>a, b <span class="op">=</span> b, a</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">
|
||
<pre><code>(2, 1)</code></pre>
|
||
</div>
|
||
</div>
|
||
<section id="example-finding-the-slope" class="level4">
|
||
<h4 class="anchored" data-anchor-id="example-finding-the-slope">Example, finding the slope</h4>
|
||
<p>Find the slope of the line connecting the points <span class="math inline">\((1,2)\)</span> and <span class="math inline">\((4,6)\)</span>. We begin by defining the values and then applying the slope formula:</p>
|
||
<div class="cell" data-execution_count="19">
|
||
<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>x0, y0 <span class="op">=</span> <span class="fl">1</span>, <span class="fl">2</span></span>
|
||
<span id="cb31-2"><a href="#cb31-2" aria-hidden="true" tabindex="-1"></a>x1, y1 <span class="op">=</span> <span class="fl">4</span>, <span class="fl">6</span></span>
|
||
<span id="cb31-3"><a href="#cb31-3" aria-hidden="true" tabindex="-1"></a>m <span class="op">=</span> (y1 <span class="op">-</span> y0) <span class="op">/</span> (x1 <span class="op">-</span> x0)</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">
|
||
<pre><code>1.3333333333333333</code></pre>
|
||
</div>
|
||
</div>
|
||
<p>Of course, this could be computed directly with <code>(6-2) / (4-1)</code>, but by using familiar names for the values we can be certain we apply the formula properly.</p>
|
||
</section>
|
||
</section>
|
||
<section id="questions" class="level2" data-number="2.6">
|
||
<h2 data-number="2.6" class="anchored" data-anchor-id="questions"><span class="header-section-number">2.6</span> Questions</h2>
|
||
<section id="question" class="level6">
|
||
<h6 class="anchored" data-anchor-id="question">Question</h6>
|
||
<p>Let <span class="math inline">\(a=10\)</span>, <span class="math inline">\(b=2.3\)</span>, and <span class="math inline">\(c=8\)</span>. Find the value of <span class="math inline">\((a-b)/(a-c)\)</span>.</p>
|
||
<div class="cell" data-hold="true" data-execution_count="20">
|
||
<div class="cell-output cell-output-display" data-execution_count="21">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="7051172625682084957" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_7051172625682084957">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="7051172625682084957" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="7051172625682084957_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("7051172625682084957").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - 3.85) <= 0.001);
|
||
var msgBox = document.getElementById('7051172625682084957_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_7051172625682084957")
|
||
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_7051172625682084957")
|
||
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 <code>x = 4</code>. Compute <span class="math inline">\(y=100 - 2x - x^2\)</span>. What is the value:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="21">
|
||
<div class="cell-output cell-output-display" data-execution_count="22">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="12903064133376115655" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_12903064133376115655">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="12903064133376115655" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="12903064133376115655_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("12903064133376115655").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - -124) <= 0.1);
|
||
var msgBox = document.getElementById('12903064133376115655_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_12903064133376115655")
|
||
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_12903064133376115655")
|
||
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>What is the answer to this computation?</p>
|
||
<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>a <span class="op">=</span> <span class="fl">3.2</span>; b<span class="op">=</span><span class="fl">2.3</span></span>
|
||
<span id="cb33-2"><a href="#cb33-2" aria-hidden="true" tabindex="-1"></a>a<span class="op">^</span>b <span class="op">-</span> b<span class="op">^</span>a</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<div class="cell" data-hold="true" data-execution_count="23">
|
||
<div class="cell-output cell-output-display" data-execution_count="23">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="3248336723261914111" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_3248336723261914111">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="3248336723261914111" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="3248336723261914111_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("3248336723261914111").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - 0.14354012963861962) <= 0.001);
|
||
var msgBox = document.getElementById('3248336723261914111_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_3248336723261914111")
|
||
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_3248336723261914111")
|
||
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>For longer computations, it can be convenient to do them in parts, as this makes it easier to check for mistakes.</p>
|
||
<p>For example, to compute</p>
|
||
<p><span class="math display">\[
|
||
\frac{p - q}{\sqrt{p(1-p)}}
|
||
\]</span></p>
|
||
<p>for <span class="math inline">\(p=0.25\)</span> and <span class="math inline">\(q=0.2\)</span> we might do:</p>
|
||
<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>p, q <span class="op">=</span> <span class="fl">0.25</span>, <span class="fl">0.2</span></span>
|
||
<span id="cb34-2"><a href="#cb34-2" aria-hidden="true" tabindex="-1"></a>top <span class="op">=</span> p <span class="op">-</span> q</span>
|
||
<span id="cb34-3"><a href="#cb34-3" aria-hidden="true" tabindex="-1"></a>bottom <span class="op">=</span> <span class="fu">sqrt</span>(<span class="fu">p*</span>(<span class="fl">1</span><span class="op">-</span>p))</span>
|
||
<span id="cb34-4"><a href="#cb34-4" aria-hidden="true" tabindex="-1"></a><span class="kw">ans</span> <span class="op">=</span> top<span class="op">/</span>bottom</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>What is the result of the above?</p>
|
||
<div class="cell" data-hold="true" data-execution_count="25">
|
||
<div class="cell-output cell-output-display" data-execution_count="24">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="6375215055384604190" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_6375215055384604190">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="6375215055384604190" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="6375215055384604190_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("6375215055384604190").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - 0.11547005383792514) <= 0.001);
|
||
var msgBox = document.getElementById('6375215055384604190_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_6375215055384604190")
|
||
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_6375215055384604190")
|
||
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>Using variables to record the top and the bottom of the expression, compute the following for <span class="math inline">\(x=3\)</span>:</p>
|
||
<p><span class="math display">\[
|
||
y = \frac{x^2 - 2x - 8}{x^2 - 9x - 20}.
|
||
\]</span></p>
|
||
<div class="cell" data-hold="true" data-execution_count="26">
|
||
<div class="cell-output cell-output-display" data-execution_count="25">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="11310553385683392797" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_11310553385683392797">
|
||
<div style="padding-top: 5px">
|
||
<br>
|
||
<div class="input-group">
|
||
<input id="11310553385683392797" type="number" class="form-control" placeholder="Numeric answer">
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="11310553385683392797_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.getElementById("11310553385683392797").addEventListener("change", function() {
|
||
var correct = (Math.abs(this.value - 0.13157894736842105) <= 0.001);
|
||
var msgBox = document.getElementById('11310553385683392797_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_11310553385683392797")
|
||
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_11310553385683392797")
|
||
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>Which if these is not a valid variable name (identifier) in <code>Julia</code>:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="27">
|
||
<div class="cell-output cell-output-display" data-execution_count="26">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="8960286572301564312" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_8960286572301564312">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_8960286572301564312_1">
|
||
<input class="form-check-input" type="radio" name="radio_8960286572301564312" id="radio_8960286572301564312_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
<code>some_really_long_name_that_is_no_fun_to_type</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_8960286572301564312_2">
|
||
<input class="form-check-input" type="radio" name="radio_8960286572301564312" id="radio_8960286572301564312_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
<code>5degreesbelowzero</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_8960286572301564312_3">
|
||
<input class="form-check-input" type="radio" name="radio_8960286572301564312" id="radio_8960286572301564312_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
<code>aMiXeDcAsEnAmE</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_8960286572301564312_4">
|
||
<input class="form-check-input" type="radio" name="radio_8960286572301564312" id="radio_8960286572301564312_4" value="4">
|
||
|
||
<span class="label-body px-1">
|
||
<code>fahrenheit451</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="8960286572301564312_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_8960286572301564312"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 2;
|
||
var msgBox = document.getElementById('8960286572301564312_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_8960286572301564312")
|
||
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_8960286572301564312")
|
||
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>Which of these symbols is one of <code>Julia</code>’s built-in math constants?</p>
|
||
<div class="cell" data-hold="true" data-execution_count="28">
|
||
<div class="cell-output cell-output-display" data-execution_count="27">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="17218705638908257379" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_17218705638908257379">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_17218705638908257379_1">
|
||
<input class="form-check-input" type="radio" name="radio_17218705638908257379" id="radio_17218705638908257379_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
<code>pi</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_17218705638908257379_2">
|
||
<input class="form-check-input" type="radio" name="radio_17218705638908257379" id="radio_17218705638908257379_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
<code>oo</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_17218705638908257379_3">
|
||
<input class="form-check-input" type="radio" name="radio_17218705638908257379" id="radio_17218705638908257379_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
<code>E</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_17218705638908257379_4">
|
||
<input class="form-check-input" type="radio" name="radio_17218705638908257379" id="radio_17218705638908257379_4" value="4">
|
||
|
||
<span class="label-body px-1">
|
||
<code>I</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="17218705638908257379_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_17218705638908257379"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 1;
|
||
var msgBox = document.getElementById('17218705638908257379_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_17218705638908257379")
|
||
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_17218705638908257379")
|
||
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>What key sequence will produce this assignment</p>
|
||
<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>δ <span class="op">=</span> <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" data-hold="true" data-execution_count="30">
|
||
<div class="cell-output cell-output-display" data-execution_count="28">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="2007827740981226356" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_2007827740981226356">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_2007827740981226356_1">
|
||
<input class="form-check-input" type="radio" name="radio_2007827740981226356" id="radio_2007827740981226356_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
<code>\delta[tab] = 1/10</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_2007827740981226356_2">
|
||
<input class="form-check-input" type="radio" name="radio_2007827740981226356" id="radio_2007827740981226356_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
<code>$\\delta$ = 1/10</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_2007827740981226356_3">
|
||
<input class="form-check-input" type="radio" name="radio_2007827740981226356" id="radio_2007827740981226356_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
<code>delta[tab] = 1/10</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="2007827740981226356_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_2007827740981226356"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 1;
|
||
var msgBox = document.getElementById('2007827740981226356_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_2007827740981226356")
|
||
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_2007827740981226356")
|
||
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>Which of these three statements will <strong>not</strong> be a valid way to assign three variables at once:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="31">
|
||
<div class="cell-output cell-output-display" data-execution_count="29">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="6479211455394549920" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_6479211455394549920">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_6479211455394549920_1">
|
||
<input class="form-check-input" type="radio" name="radio_6479211455394549920" id="radio_6479211455394549920_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
<code>a=1, b=2, c=3</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_6479211455394549920_2">
|
||
<input class="form-check-input" type="radio" name="radio_6479211455394549920" id="radio_6479211455394549920_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
<code>a,b,c = 1,2,3</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_6479211455394549920_3">
|
||
<input class="form-check-input" type="radio" name="radio_6479211455394549920" id="radio_6479211455394549920_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
<code>a=1; b=2; c=3</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="6479211455394549920_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_6479211455394549920"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 1;
|
||
var msgBox = document.getElementById('6479211455394549920_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_6479211455394549920")
|
||
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_6479211455394549920")
|
||
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>The fact that assignment <em>always</em> returns the value of the right hand side <em>and</em> the fact that the <code>=</code> sign associates from right to left means that the following idiom:</p>
|
||
<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>x <span class="op">=</span> y <span class="op">=</span> z <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>
|
||
<p>Will always:</p>
|
||
<div class="cell" data-hold="true" data-execution_count="33">
|
||
<div class="cell-output cell-output-display" data-execution_count="30">
|
||
<form class="mx-2 my-3 mw-100" name="WeaveQuestion" data-id="4775253384779770468" data-controltype="">
|
||
<div class="form-group ">
|
||
<div class="controls">
|
||
<div class="form" id="controls_4775253384779770468">
|
||
<div style="padding-top: 5px">
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_4775253384779770468_1">
|
||
<input class="form-check-input" type="radio" name="radio_4775253384779770468" id="radio_4775253384779770468_1" value="1">
|
||
|
||
<span class="label-body px-1">
|
||
Create \(3\) linked values that will stay synced when any value changes
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_4775253384779770468_2">
|
||
<input class="form-check-input" type="radio" name="radio_4775253384779770468" id="radio_4775253384779770468_2" value="2">
|
||
|
||
<span class="label-body px-1">
|
||
Throw an error
|
||
</span>
|
||
</label>
|
||
</div>
|
||
<div class="form-check">
|
||
<label class="form-check-label" for="radio_4775253384779770468_3">
|
||
<input class="form-check-input" type="radio" name="radio_4775253384779770468" id="radio_4775253384779770468_3" value="3">
|
||
|
||
<span class="label-body px-1">
|
||
Assign all three variables at once to a value of <code>3</code>
|
||
</span>
|
||
</label>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<div id="4775253384779770468_message" style="padding-bottom: 15px"></div>
|
||
</div>
|
||
</div>
|
||
</form>
|
||
|
||
<script text="text/javascript">
|
||
document.querySelectorAll('input[name="radio_4775253384779770468"]').forEach(function(rb) {
|
||
rb.addEventListener("change", function() {
|
||
var correct = rb.value == 3;
|
||
var msgBox = document.getElementById('4775253384779770468_message');
|
||
if(correct) {
|
||
msgBox.innerHTML = "<div class='pluto-output admonition note alert alert-success'><span> 👍 Correct </span></div>";
|
||
var explanation = document.getElementById("explanation_4775253384779770468")
|
||
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_4775253384779770468")
|
||
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");
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||
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|
||
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||
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const bsSheetEl = window.document.querySelector("link#quarto-bootstrap");
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if (bsSheetEl) {
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|
||
const icon = "";
|
||
const anchorJS = new window.AnchorJS();
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||
anchorJS.options = {
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||
placement: 'right',
|
||
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|
||
};
|
||
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 = {
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||
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||
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