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<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>
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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="../derivatives/implicit_differentiation.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">33</span> <span class="chapter-title">Implicit Differentiation</span></a>
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||||
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<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>
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<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>
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<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>
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<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>
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||||
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<a href="../integrals/substitution.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">38</span> <span class="chapter-title">Substitution</span></a>
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<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>
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<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>
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||||
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<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>
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<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>
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<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>
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<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>
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<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>
|
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<a href="../ODEs/odes.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">48</span> <span class="chapter-title">ODEs</span></a>
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||||
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<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>
|
||||
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||||
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<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>
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||||
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<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>
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|
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<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>
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<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>
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||||
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||||
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<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>
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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.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">55</span> <span class="chapter-title">Scalar functions</span></a>
|
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||||
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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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||||
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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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||||
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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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<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>
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||||
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<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>
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<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>
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<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>
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<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>
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<a href="../misc/calculus_with_julia.html" class="sidebar-item-text sidebar-link active"><span class="chapter-number">68</span> <span class="chapter-title">The <code>CalculusWithJulia</code> package</span></a>
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<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>
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<h2 id="toc-title">Table of contents</h2>
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<li><a href="#the-package-concept" id="toc-the-package-concept" class="nav-link active" data-scroll-target="#the-package-concept"> <span class="header-section-number">68.1</span> The package concept</a>
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<li><a href="#package-installation" id="toc-package-installation" class="nav-link" data-scroll-target="#package-installation"> <span class="header-section-number">68.1.1</span> Package installation</a></li>
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<li><a href="#using-a-package" id="toc-using-a-package" class="nav-link" data-scroll-target="#using-a-package"> <span class="header-section-number">68.1.2</span> Using a package</a></li>
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<li><a href="#package-details" id="toc-package-details" class="nav-link" data-scroll-target="#package-details"> <span class="header-section-number">68.1.3</span> Package details</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/misc/calculus_with_julia.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">68</span> <span class="chapter-title">The <code>CalculusWithJulia</code> package</span></h1>
|
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</div>
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|
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</header>
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||||
|
||||
<p>To run the commands in these notes, some external packages must be installed and loaded.</p>
|
||||
<p>The <code>Pluto</code> interface does this in the background, so there is nothing to do but execute the cells that call <code>using</code> or <code>import</code>. For <code>Julia</code> post version <code>1.7</code>, this installation will be initiated for you when <code>using</code> is called in the REPL terminal.</p>
|
||||
<p>For other interfaces, to use the <code>CalculusWithJulia</code> package requires first that it be installed. From the command line. This can be done with this key sequence:</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>] add CalculusWithJulia</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||||
<p>Or, using the <code>Pkg</code> package, the commands would be</p>
|
||||
<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="im">import</span> <span class="bu">Pkg</span></span>
|
||||
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="bu">Pkg</span>.<span class="fu">add</span>(<span class="st">"CalculusWithJulia"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||||
<p>Installation only needs to be done once.</p>
|
||||
<hr>
|
||||
<p>However, for each new <code>Julia</code> session, the package must be <em>loaded</em>, as with the following command:</p>
|
||||
<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><span class="im">using</span> <span class="bu">CalculusWithJulia</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||||
<p>That is all. The rest of this page just provides some details for the interested reader.</p>
|
||||
<section id="the-package-concept" class="level2" data-number="68.1">
|
||||
<h2 data-number="68.1" class="anchored" data-anchor-id="the-package-concept"><span class="header-section-number">68.1</span> The package concept</h2>
|
||||
<p>The <code>Julia</code> language provides the building blocks for the wider <code>Julia</code> ecosystem that enhance and extend the language’s applicability.</p>
|
||||
<p><code>Julia</code> is extended through “packages.” Some of these, such as packages for certain math constants and some linear algebra operations, are part of all <code>Julia</code> installations and must simple by loaded to be used. Others, such as packages for finding integrals or (automatic) derivatives are provided by users and must first be <em>installed</em> before being used.</p>
|
||||
<section id="package-installation" class="level3" data-number="68.1.1">
|
||||
<h3 data-number="68.1.1" class="anchored" data-anchor-id="package-installation"><span class="header-section-number">68.1.1</span> Package installation</h3>
|
||||
<p>Package installation is straightforward, as <code>Julia</code> has a package, <code>Pkg</code>, that facilitates this.</p>
|
||||
<p>Since <code>Julia</code> version 1.7, just attempting to load a package through <code>using PackageName</code> at the <em>command line</em> will either load an installed package <em>or</em> query for an uninstalled package to be installed before lading. So installation just requires confirming a prompt.</p>
|
||||
<p>For more control, the command line and <code>IJulia</code> provide access to the function in <code>Pkg</code> through the escape command <code>]</code>. For example, to find the status of all currently installed packages, the following command can be executed:</p>
|
||||
<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>] status</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||||
<p>External packages are <em>typically</em> installed from GitHub and if they are regisered, installation is as easy as calling <code>add</code>:</p>
|
||||
<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>] add QuadGK</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||||
<p>That command will consult <code>Julia</code>’s general registry for the location of the <code>QuadGK</code> package, use this location to download the necessary files, if necessary dependencies will be built and installed, and then the package available for use.</p>
|
||||
<p>For these notes, when the <code>CalculusWithJulia</code> package is installed it will also install many of the other packages that are needed.</p>
|
||||
<p>See <a href="https://docs.julialang.org/en/v1/stdlib/Pkg/index.html">Pkg</a> for more details, such as how to update the set of available packages.</p>
|
||||
</section>
|
||||
<section id="using-a-package" class="level3" data-number="68.1.2">
|
||||
<h3 data-number="68.1.2" class="anchored" data-anchor-id="using-a-package"><span class="header-section-number">68.1.2</span> Using a package</h3>
|
||||
<p>The features of an installed package are not available until the package is brought into the current session. A package need only be <em>installed</em> once, but must be loaded each session.</p>
|
||||
<p>To load a package, the <code>using</code> keyword is provided:</p>
|
||||
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">QuadGK</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||||
<p>The above command will make available all <em>exported</em> function names from the <code>QuadGK</code> package so they can be directly used, as in:</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><span class="fu">quadgk</span>(sin, <span class="fl">0</span>, <span class="cn">pi</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="6">
|
||||
<pre><code>(2.0, 1.7905676941154525e-12)</code></pre>
|
||||
</div>
|
||||
</div>
|
||||
<p>(A command to find an integral of <span class="math inline">\(f(x) = \sin(x)\)</span> over <span class="math inline">\([0, \pi]\)</span>.)</p>
|
||||
</section>
|
||||
<section id="package-details" class="level3" data-number="68.1.3">
|
||||
<h3 data-number="68.1.3" class="anchored" data-anchor-id="package-details"><span class="header-section-number">68.1.3</span> Package details</h3>
|
||||
<p>When a package is <em>first</em> loaded after installation, or some other change, it will go through a <em>pre-compilation</em> process. Depending on the package size, this can take a moment to several seconds. This won’t happen the second time a package is loaded.</p>
|
||||
<p>However, subsequent times a package is loaded some further compilation is done, so it can still take some time for a package to load. Mostly this is not noticeable, though with the plotting package used in these notes, it is.</p>
|
||||
<p>When a package is loaded, all of its dependent packages are also loaded, but their functions are not immediately available to the user.</p>
|
||||
<p>In <em>typical</em> <code>Julia</code> usage, each needed package is loaded on demand. This is faster and also keeps the namespace (the collection of variable and function names) smaller to avoid collisions. However, for these notes, the package <code>CalculusWithJulia</code> will load a few of the packages needed for the entire set of notes, not just the current section. This is to make it a bit <em>easier</em> for the <em>beginning</em> user.</p>
|
||||
<p>One issue with loading several packages is the possibility that more than one will export a function with the same name, causing a collision. Moreover, at times, there can be dependency conflicts between packages. A suggested workflow is to use projects and in each project use a minimal set of packages. In Pluto, this is done behind the scenes.</p>
|
||||
<p>The <code>Julia</code> language is designed around have several “generic” functions each with many different methods depending on their usage. This design allows many different implementations for operations such as addition or multiplication yet the user only needs to call one function name. Packages can easily extend these generic functions by providing their own methods for their own new types of data. For example, <code>SymPy</code>, which adds symbolic math features to <code>Julia</code> (using a Python package) extends both <code>+</code> and <code>*</code> for use with symbolic objects.</p>
|
||||
<p>This design works great when the “generic” usage matches the needs of the package authors, but there are two common issues that arise:</p>
|
||||
<ul>
|
||||
<li>The extension of a generic is for a type defined outside the author’s package. This is known as “type piracy” and is frowned on, as it can lead to subtle errors. The <code>CalculusWithJulia</code> package practices this for one case: using <code>'</code> to indicate derivatives for <code>Function</code> objects.</li>
|
||||
<li>The generic function concept is not part of base <code>Julia</code>. An example might be the <code>solve</code> function. This name has a well-defined mathematical usage (e.g., “solve for <span class="math inline">\(x\)</span>.”), but the generic concept is not part of base <code>Julia</code>. As it is used by <code>SymPy</code> and <code>DifferentialEquations</code>, among others, the ecosystem has a stub package <code>CommonSolve</code> allowing the sharing of this “verb.”</li>
|
||||
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<a href="../ODEs/odes.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">48</span> <span class="chapter-title">ODEs</span></a>
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||||
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<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>
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<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>
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||||
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||||
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||||
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<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>
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<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>
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<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>
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<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>
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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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</li>
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||||
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<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>
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</li>
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||||
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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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||||
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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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</li>
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||||
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||||
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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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|
||||
</ul>
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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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<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>
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||||
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||||
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<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>
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||||
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<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>
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||||
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<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>
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||||
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<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>
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<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>
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<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>
|
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|
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|
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<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>
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<a href="../misc/getting_started_with_julia.html" class="sidebar-item-text sidebar-link active"><span class="chapter-number">66</span> <span class="chapter-title">Getting started with Julia</span></a>
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<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>
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<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>
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<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>
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<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>
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<a href="../references.html" class="sidebar-item-text sidebar-link">References</a>
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<h2 id="toc-title">Table of contents</h2>
|
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|
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<ul>
|
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<li><a href="#running-julia-through-the-web" id="toc-running-julia-through-the-web" class="nav-link active" data-scroll-target="#running-julia-through-the-web"> <span class="header-section-number">66.1</span> Running Julia through the web</a></li>
|
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<li><a href="#installing-julia-locally" id="toc-installing-julia-locally" class="nav-link" data-scroll-target="#installing-julia-locally"> <span class="header-section-number">66.2</span> Installing Julia locally</a></li>
|
||||
<li><a href="#basic-interactive-usage" id="toc-basic-interactive-usage" class="nav-link" data-scroll-target="#basic-interactive-usage"> <span class="header-section-number">66.3</span> Basic interactive usage</a></li>
|
||||
<li><a href="#add-on-packages" id="toc-add-on-packages" class="nav-link" data-scroll-target="#add-on-packages"> <span class="header-section-number">66.4</span> Add-on packages</a></li>
|
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</ul>
|
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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/misc/getting_started_with_julia.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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<!-- main -->
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<main class="content" id="quarto-document-content">
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<div class="quarto-title">
|
||||
<h1 class="title d-none d-lg-block"><span class="chapter-number">66</span> <span class="chapter-title">Getting started with Julia</span></h1>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<div class="quarto-title-meta">
|
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||||
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||||
</header>
|
||||
|
||||
<p>Julia is a freely available, open-source programming language aimed at technical computing.</p>
|
||||
<p>As it is open source, indeed with a liberal MIT license, it can be installed for free on many types of computers (though not phones or tablets).</p>
|
||||
<section id="running-julia-through-the-web" class="level2" data-number="66.1">
|
||||
<h2 data-number="66.1" class="anchored" data-anchor-id="running-julia-through-the-web"><span class="header-section-number">66.1</span> Running Julia through the web</h2>
|
||||
<p>There are a few services for running <code>Julia</code> through the web. Mentioned here is <a href="https://mybinder.org">Binder</a>, which provides a web-based interface to <code>Julia</code> built around <code>Jupyter</code>. <code>Jupyter</code> is a wildly succesful platform for interacting with different open-source software programs.</p>
|
||||
<p><a href="https://mybinder.org/v2/gh/CalculusWithJulia/CwJScratchPad.git/master">lauch binder</a></p>
|
||||
<p>Clicking the launch link above will open a web page which provides a blank notebook, save for a package used by these notes. However, <code>Binder</code> is nowhere near as reliable as a local installation.</p>
|
||||
</section>
|
||||
<section id="installing-julia-locally" class="level2" data-number="66.2">
|
||||
<h2 data-number="66.2" class="anchored" data-anchor-id="installing-julia-locally"><span class="header-section-number">66.2</span> Installing Julia locally</h2>
|
||||
<p>Installing <code>Julia</code> locally is not more difficult than installing other software.</p>
|
||||
<p>Binaries of <code>Julia</code> are provided at <a href="http://julialang.org/downloads/">julialang.org</a>. Julia has an official released version and a developmental version. Unless there is a compelling reason, the latest released version should be downloaded and installed for use.</p>
|
||||
<p>For Windows users, there is a <code>juliaup</code> program for managing the installation of Julia.</p>
|
||||
<p>The base <code>Julia</code> provides a <em>command-line interface</em>, or REPL (read-evaluate-parse).</p>
|
||||
</section>
|
||||
<section id="basic-interactive-usage" class="level2" data-number="66.3">
|
||||
<h2 data-number="66.3" class="anchored" data-anchor-id="basic-interactive-usage"><span class="header-section-number">66.3</span> Basic interactive usage</h2>
|
||||
<p>Once installed, <code>Julia</code> can be started by clicking on an icon or typing <code>julia</code> at the command line. Either will open a <em>command line interface</em> for a user to interact with a <code>Julia</code> process. The basic workflow is easy: commands are typed then sent to a <code>Julia</code> process when the “return” key is pressed for a complete expression. Then the output is displayed.</p>
|
||||
<p>A command is typed following the <em>prompt</em>. An example might be <code>2 + 2</code>. To send the command to the <code>Julia</code> interpreter the “return” key is pressed. A complete expression or expressions will then be parsed and evaluated (executed). If the expression is not complete, <code>julia</code>’s prompt will still accept input to complete the expression. Type <code>2 +</code> to see. (The expression <code>2 +</code> is not complete, as the infix operator <code>+</code> expects two arguments, one on its left and one on its right.)</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>
|
||||
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a> _ _ <span class="fu">_</span>(_)_ <span class="op">|</span> Documentation<span class="op">:</span> https<span class="op">://</span>docs.julialang.org</span>
|
||||
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a> (_) <span class="op">|</span> (_) (_) <span class="op">|</span></span>
|
||||
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a> _ _ _<span class="op">|</span> <span class="op">|</span>_ __ _ <span class="op">|</span> <span class="dt">Type</span> <span class="st">"?"</span> <span class="cf">for</span> help, <span class="st">"]?"</span> <span class="cf">for</span> <span class="bu">Pkg</span> help.</span>
|
||||
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a> <span class="op">|</span> <span class="op">|</span> <span class="op">|</span> <span class="op">|</span> <span class="op">|</span> <span class="op">|</span> <span class="op">|/</span> _<span class="ss">` | |</span></span>
|
||||
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a> <span class="op">|</span> <span class="op">|</span> <span class="op">|</span>_<span class="op">|</span> <span class="op">|</span> <span class="op">|</span> <span class="op">|</span> (_<span class="op">|</span> <span class="op">|</span> <span class="op">|</span> Version <span class="fl">1.7.0</span> (<span class="fl">2021</span><span class="op">-</span><span class="fl">11</span><span class="op">-</span><span class="fl">30</span>)</span>
|
||||
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a> _<span class="op">/</span> <span class="op">|\</span>__<span class="ch">'_|_|_|\__'</span>_<span class="op">|</span> <span class="op">|</span> Official https<span class="op">://</span>julialang.org<span class="op">/</span> release</span>
|
||||
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a><span class="op">|</span>__<span class="op">/</span> <span class="op">|</span></span>
|
||||
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a></span>
|
||||
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a>julia<span class="op">></span> <span class="fl">2</span> <span class="op">+</span> <span class="fl">2</span></span>
|
||||
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a><span class="fl">4</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||||
<p>Above, <code>julia></code> is the prompt. These notes will not include the prompt, so that copying-and-pasting can be more easily used. Input and output cells display similarly, though with differences in coloring. For example:</p>
|
||||
<div class="cell" data-execution_count="4">
|
||||
<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="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="4">
|
||||
<pre><code>4</code></pre>
|
||||
</div>
|
||||
</div>
|
||||
<p>While many prefer a command line for interacting with <code>Julia</code>, when learning a notebook interfaces is suggested. (An IDE like <a href="https://www.julia-vscode.org/">Julia for Visual Studio Code</a> might be preferred for experienced programmers). In <a href="./julia_interfaces.html">Julia interfaces</a>, we describe two different notebook interfaces that are available through add-on packages.</p>
|
||||
</section>
|
||||
<section id="add-on-packages" class="level2" data-number="66.4">
|
||||
<h2 data-number="66.4" class="anchored" data-anchor-id="add-on-packages"><span class="header-section-number">66.4</span> Add-on packages</h2>
|
||||
<p><code>Julia</code> is well on its way towards 10,000 external add-on packages that enhance the offerings of base <code>Julia</code>. We refer to one, <code>CalculusWithJulia</code>, that is designed to accompany these notes. <a href="./calculus_with_julia.html">Installation notes</a> are available.</p>
|
||||
<p>In <code>Julia</code> graphics are provided only by add-on packages – there is no built-in graphing. This is the case under <code>Pluto</code> or <code>Jupyter</code> or the command line.</p>
|
||||
<p>In these notes, we use the <code>Plots</code> package and its default backend. The <code>Plots</code> package provides a common interface to several different backends; this choice is easily changed. The <code>gr</code> backend is used in these notes, though for interactive use the <code>Plotly</code> backend has advantages; for more complicated graphics, <code>pyplot</code> has some advantages; for publication <code>PGFPlotsX</code> has advantages.</p>
|
||||
<p>The package, if installed, is loaded as any other package:</p>
|
||||
<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><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>
|
||||
<p>With that in hand, to make a graph of a function over a range, we follow this pattern:</p>
|
||||
<div class="cell" 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><span class="fu">plot</span>(sin, <span class="fl">0</span>, <span class="fl">2</span>pi)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<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"><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>
|
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|
||||
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|
||||
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|
||||
<div class="sidebar-item-container">
|
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<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>
|
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<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>
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<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>
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<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>
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<a href="../misc/julia_interfaces.html" class="sidebar-item-text sidebar-link active"><span class="chapter-number">67</span> <span class="chapter-title">Julia interfaces</span></a>
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<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>
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<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>
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<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>
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<a href="../references.html" class="sidebar-item-text sidebar-link">References</a>
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<h2 id="toc-title">Table of contents</h2>
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<ul>
|
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<li><a href="#the-repl" id="toc-the-repl" class="nav-link active" data-scroll-target="#the-repl"> <span class="header-section-number">67.1</span> The <code>REPL</code></a></li>
|
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<li><a href="#pluto" id="toc-pluto" class="nav-link" data-scroll-target="#pluto"> <span class="header-section-number">67.2</span> <code>Pluto</code></a></li>
|
||||
<li><a href="#ijulia" id="toc-ijulia" class="nav-link" data-scroll-target="#ijulia"> <span class="header-section-number">67.3</span> <code>IJulia</code></a></li>
|
||||
<li><a href="#vscode" id="toc-vscode" class="nav-link" data-scroll-target="#vscode"> <span class="header-section-number">67.4</span> VSCode</a></li>
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</ul>
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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/misc/julia_interfaces.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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<div class="quarto-title">
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<h1 class="title d-none d-lg-block"><span class="chapter-number">67</span> <span class="chapter-title">Julia interfaces</span></h1>
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
<div class="quarto-title-meta">
|
||||
|
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|
||||
|
||||
</div>
|
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|
||||
|
||||
</header>
|
||||
|
||||
<p><code>Julia</code> can be used in many different manners. This page describes a few.</p>
|
||||
<section id="the-repl" class="level2" data-number="67.1">
|
||||
<h2 data-number="67.1" class="anchored" data-anchor-id="the-repl"><span class="header-section-number">67.1</span> The <code>REPL</code></h2>
|
||||
<p>Base <code>Julia</code> comes with a <code>REPL</code> package, which provides a means to interact with <code>Julia</code> at the command line.</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>
|
||||
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a> _ _ <span class="fu">_</span>(_)_ <span class="op">|</span> Documentation<span class="op">:</span> https<span class="op">://</span>docs.julialang.org</span>
|
||||
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a> (_) <span class="op">|</span> (_) (_) <span class="op">|</span></span>
|
||||
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a> _ _ _<span class="op">|</span> <span class="op">|</span>_ __ _ <span class="op">|</span> <span class="dt">Type</span> <span class="st">"?"</span> <span class="cf">for</span> help, <span class="st">"]?"</span> <span class="cf">for</span> <span class="bu">Pkg</span> help.</span>
|
||||
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a> <span class="op">|</span> <span class="op">|</span> <span class="op">|</span> <span class="op">|</span> <span class="op">|</span> <span class="op">|</span> <span class="op">|/</span> _<span class="ss">` | |</span></span>
|
||||
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a> <span class="op">|</span> <span class="op">|</span> <span class="op">|</span>_<span class="op">|</span> <span class="op">|</span> <span class="op">|</span> <span class="op">|</span> (_<span class="op">|</span> <span class="op">|</span> <span class="op">|</span> Version <span class="fl">1.7.0</span> (<span class="fl">2021</span><span class="op">-</span><span class="fl">11</span><span class="op">-</span><span class="fl">30</span>)</span>
|
||||
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a> _<span class="op">/</span> <span class="op">|\</span>__<span class="ch">'_|_|_|\__'</span>_<span class="op">|</span> <span class="op">|</span> Official https<span class="op">://</span>julialang.org<span class="op">/</span> release</span>
|
||||
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a><span class="op">|</span>__<span class="op">/</span> <span class="op">|</span></span>
|
||||
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a></span>
|
||||
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a>julia<span class="op">></span> <span class="fl">2</span> <span class="op">+</span> <span class="fl">2</span></span>
|
||||
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a><span class="fl">4</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||||
<p>The <code>julia></code> prompt is where commands are typed. The <code>return</code> key will send a command to the interpreter and the results are displayed in the REPL terminal.</p>
|
||||
<p>The REPL has many features for editing, for interacting with the package manager, or interaction with the shell. However it is command-line based, which no support for mouse interaction. For that, other options are available.</p>
|
||||
</section>
|
||||
<section id="pluto" class="level2" data-number="67.2">
|
||||
<h2 data-number="67.2" class="anchored" data-anchor-id="pluto"><span class="header-section-number">67.2</span> <code>Pluto</code></h2>
|
||||
<p>The <code>Pluto</code> package provides a notebook interface for interacting with <code>Julia</code>, which has a few idiosyncrasies, as compared to other interfaces.</p>
|
||||
<p>Pluto is started from the REPL terminal with these two commands:</p>
|
||||
<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="im">using</span> <span class="bu">Pluto</span></span>
|
||||
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>Pluto.<span class="fu">run</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||||
<p>Primarily, the variables in the notebook are <strong>reactive</strong>, meaning if a variable’s value is modified, all references to that variables are also modified. This reactive nature makes it very easy to see the results of slight modifications and when coupled with HTML controls, allows easy user interfaces to be developed.</p>
|
||||
<p>As a result, a variable name may only be used once in the top-level scope. (Names can be reused inside functions, which create their own scope and in “<code>let</code>” blocks, a trick used within these notes.) In the notes, subscripting and unicode variants are used for symbols which are typically repurposed (e.g., <code>x</code> or <code>f</code>).</p>
|
||||
<p>Pluto cells may only contain one command, the result of which is displayed <em>above</em> the cell. This one command can be a <code>begin</code> or <code>let</code> block to join multiple statements.</p>
|
||||
<p>Pluto has a built-in package management system that manages the installation of packages on demand.</p>
|
||||
<p><code>Pluto</code> notebooks can be easily run locally using <code>Pluto</code>.</p>
|
||||
<p><code>Pluto</code> notebooks are just <code>.jl</code> scripts, so can easily be shared.</p>
|
||||
</section>
|
||||
<section id="ijulia" class="level2" data-number="67.3">
|
||||
<h2 data-number="67.3" class="anchored" data-anchor-id="ijulia"><span class="header-section-number">67.3</span> <code>IJulia</code></h2>
|
||||
<p>“Project <a href="https://jupyter.org/">Jupyter</a> exists to develop open-source software, open-standards, and services for interactive computing across dozens of programming languages.” The <code>IJulia</code> package allows <code>Julia</code> to be one of these programming languages. This package must be installed prior to use.</p>
|
||||
<p>The Jupyter Project provides two web-based interfaces to <code>Julia</code>: the Jupyter notebook and the newer JupyterLab. The the <a href="https://mybinder.org/">binder</a> project use Juptyer notebooks for their primary interface to <code>Julia</code>. To use a binder notebook, follow this link:</p>
|
||||
<p><a href="https://mybinder.org/v2/gh/CalculusWithJulia/CwJScratchPad.git/master">lauch binder</a></p>
|
||||
<p>To run locally, these interfaces are available once <code>IJulia</code> is installed. Since version 1.7, the following commands should do this:</p>
|
||||
<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><span class="im">using</span> <span class="bu">IJulia</span></span>
|
||||
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a><span class="fu">notebook</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||||
<p>Should that not work, then this should as well:</p>
|
||||
<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><span class="im">using</span> <span class="bu">Pkg</span></span>
|
||||
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="bu">Pkg</span>.<span class="fu">add</span>(<span class="st">"PyCall"</span>)</span>
|
||||
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a><span class="bu">Pkg</span>.<span class="fu">add</span>(<span class="st">"IJulia"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||||
<hr>
|
||||
<p>The notebook interface has “cells” where one or more commands can be entered.</p>
|
||||
<p>In <code>IJulia</code>, a block of commands is sent to the kernel (the <code>Julia</code> interpreter) by typing “shift+return” or clicking on a “run” button. The output is printed below a cell, including graphics.</p>
|
||||
<p>When a cell is evaluating, the leading <code>[]</code> has an asterick (<code>[*]</code>) showing the notebook is awaiting the results of the calculation.</p>
|
||||
<p>Once a cell is evaluated, the leading <code>[]</code> has a number inserted (e.g., <code>[1]</code>, as in the figure). This number indicates the order of cell evaluation. Once a notebook is interacted with, the state of the namespace need not reflect the top-to-bottom order of the notebook, but rather reflects the order of cell evaluations.</p>
|
||||
<p>To be specific, a variable like <code>x</code> may be redefined in a cell above where the variable is intially defined and this redefinition will hold the current value known to the interpreter. As well, a notebook, when reloaded, may have unevaluated cells with output showing. These will not influence the state of the kernel until they are evaluated.</p>
|
||||
<p>When a cell’s commands are evaluated, the last command executed is displayed. If it is desirable that multiple values be displayed, they can be packed into a tuple. This is done by using commas to separate values. <code>IJulia</code> will also display other means to print output (e.g., <code>@show</code>, <code>display</code>, <code>print</code>, …).</p>
|
||||
<p>To run all cells in a notebook from top to bottom, the “run all” command under the “Cell” menu is available.</p>
|
||||
<p>If a calculation takes much longer than anticipated, the “kernel” can be interrupted through a menu item of “Kernel”.</p>
|
||||
<p>If the kernal appears unresponsive, it can be restarted through a menu item of “Kernel”.</p>
|
||||
<p>Notebooks can be saved (as <code>*.ipynb</code> files) for sharing or for reuse. Notebooks can be printed at HTML pages, and if the proper underlying software is available, as formatted pages.</p>
|
||||
<p>JupyterLab, a variant, has more features, commonly associated with an integrated development environment (IDE).</p>
|
||||
</section>
|
||||
<section id="vscode" class="level2" data-number="67.4">
|
||||
<h2 data-number="67.4" class="anchored" data-anchor-id="vscode"><span class="header-section-number">67.4</span> VSCode</h2>
|
||||
<p><a href="https://www.julia-vscode.org/">Julia for Visual Studio Code</a> provides support for the julia programming language for <a href="https://code.visualstudio.com/">VS Code</a>. VS Code is an open-sourced code editor supported by Microsoft. VS Code provides a cross-platform interface to <code>Julia</code> geared towards programming within the language.</p>
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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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|
||||
</li>
|
||||
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|
||||
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|
||||
<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>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<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>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<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>
|
||||
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|
||||
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|
||||
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<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>
|
||||
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|
||||
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||||
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|
||||
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|
||||
<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>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<a href="../integrals/substitution.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">38</span> <span class="chapter-title">Substitution</span></a>
|
||||
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||||
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||||
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||||
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|
||||
<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>
|
||||
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|
||||
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||||
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|
||||
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||||
<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>
|
||||
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|
||||
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||||
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|
||||
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|
||||
<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>
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
<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>
|
||||
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|
||||
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|
||||
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||||
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|
||||
<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>
|
||||
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|
||||
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||||
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|
||||
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||||
<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>
|
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||||
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||||
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||||
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||||
<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>
|
||||
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||||
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||||
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|
||||
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||||
<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>
|
||||
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|
||||
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||||
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||||
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<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>
|
||||
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||||
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||||
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||||
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<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>
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<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-5" aria-expanded="false">
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<a href="../ODEs/odes.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">48</span> <span class="chapter-title">ODEs</span></a>
|
||||
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||||
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||||
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||||
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<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>
|
||||
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||||
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||||
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||||
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||||
<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>
|
||||
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||||
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||||
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||||
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|
||||
<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>
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||||
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||||
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|
||||
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||||
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|
||||
<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>
|
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<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>
|
||||
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||||
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||||
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||||
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||||
<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>
|
||||
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|
||||
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||||
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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.html" class="sidebar-item-text sidebar-link"><span class="chapter-number">55</span> <span class="chapter-title">Scalar functions</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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<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>
|
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<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>
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<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>
|
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<a href="../misc/unicode.html" class="sidebar-item-text sidebar-link active"><span class="chapter-number">69</span> <span class="chapter-title">Usages of Unicode symbols</span></a>
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<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>
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<h1 class="title d-none d-lg-block"><span class="chapter-number">69</span> <span class="chapter-title">Usages of Unicode symbols</span></h1>
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<p><code>Julia</code> allows the use of <em>Unicode</em> symbols to replace variable names and for function calls. Unicode operations are entered in this pattern <code>\name[tab]</code>. That is a slash, <code>\</code>, the name (e.g., <code>alpha</code>), and then a press of the <code>tab</code> key.</p>
|
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<p>In these notes, the following may appear as variable or function names</p>
|
||||
<table class="table">
|
||||
<thead>
|
||||
<tr class="header">
|
||||
<th style="text-align: left;"><code>\Name</code></th>
|
||||
<th style="text-align: left;">Symbol</th>
|
||||
<th style="text-align: left;">Usage notes</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr class="odd">
|
||||
<td style="text-align: left;"><code>\euler</code></td>
|
||||
<td style="text-align: left;"><code>ℯ</code></td>
|
||||
<td style="text-align: left;">The variable <code>e</code></td>
|
||||
</tr>
|
||||
<tr class="even">
|
||||
<td style="text-align: left;"><code>\pi</code></td>
|
||||
<td style="text-align: left;"><code>π</code></td>
|
||||
<td style="text-align: left;"></td>
|
||||
</tr>
|
||||
<tr class="odd">
|
||||
<td style="text-align: left;"><code>\alpha</code></td>
|
||||
<td style="text-align: left;"><code>α</code></td>
|
||||
<td style="text-align: left;"></td>
|
||||
</tr>
|
||||
<tr class="even">
|
||||
<td style="text-align: left;"><code>\beta</code></td>
|
||||
<td style="text-align: left;"><code>β</code></td>
|
||||
<td style="text-align: left;"></td>
|
||||
</tr>
|
||||
<tr class="odd">
|
||||
<td style="text-align: left;"><code>\delta</code></td>
|
||||
<td style="text-align: left;"><code>δ</code></td>
|
||||
<td style="text-align: left;"></td>
|
||||
</tr>
|
||||
<tr class="even">
|
||||
<td style="text-align: left;"><code>\Delta</code></td>
|
||||
<td style="text-align: left;"><code>Δ</code></td>
|
||||
<td style="text-align: left;">Change, as in <code>Δx</code></td>
|
||||
</tr>
|
||||
<tr class="odd">
|
||||
<td style="text-align: left;"><code>\gamma</code></td>
|
||||
<td style="text-align: left;"><code>γ</code></td>
|
||||
<td style="text-align: left;"></td>
|
||||
</tr>
|
||||
<tr class="even">
|
||||
<td style="text-align: left;"><code>\phi</code></td>
|
||||
<td style="text-align: left;"><code>ϕ</code></td>
|
||||
<td style="text-align: left;"></td>
|
||||
</tr>
|
||||
<tr class="odd">
|
||||
<td style="text-align: left;"><code>\Phi</code></td>
|
||||
<td style="text-align: left;"><code>Φ</code></td>
|
||||
<td style="text-align: left;">Used for parameterized surfaces</td>
|
||||
</tr>
|
||||
<tr class="even">
|
||||
<td style="text-align: left;"><code>x\_1</code></td>
|
||||
<td style="text-align: left;"><code>x₁</code></td>
|
||||
<td style="text-align: left;">Subscripts</td>
|
||||
</tr>
|
||||
<tr class="odd">
|
||||
<td style="text-align: left;"><code>r\vec</code></td>
|
||||
<td style="text-align: left;"><code>r⃗</code></td>
|
||||
<td style="text-align: left;">Vector annotation</td>
|
||||
</tr>
|
||||
<tr class="even">
|
||||
<td style="text-align: left;"><code>T\hat</code></td>
|
||||
<td style="text-align: left;"><code>T̂</code></td>
|
||||
<td style="text-align: left;">Unit vector annotation</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<p>The following are associated with derivatives</p>
|
||||
<table class="table">
|
||||
<thead>
|
||||
<tr class="header">
|
||||
<th style="text-align: left;"><code>\Name</code></th>
|
||||
<th style="text-align: left;">Symbol</th>
|
||||
<th style="text-align: left;">Usage notes</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr class="odd">
|
||||
<td style="text-align: left;"><code>\partial</code></td>
|
||||
<td style="text-align: left;"><code>∂</code></td>
|
||||
<td style="text-align: left;"></td>
|
||||
</tr>
|
||||
<tr class="even">
|
||||
<td style="text-align: left;"><code>\nabla</code></td>
|
||||
<td style="text-align: left;"><code>∇</code></td>
|
||||
<td style="text-align: left;">del operator in CwJ package</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<p>The following are <em>infix</em> operators</p>
|
||||
<table class="table">
|
||||
<thead>
|
||||
<tr class="header">
|
||||
<th style="text-align: left;"><code>\Name</code></th>
|
||||
<th style="text-align: left;">Symbol</th>
|
||||
<th style="text-align: left;">Usage notes</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr class="odd">
|
||||
<td style="text-align: left;"><code>\circ</code></td>
|
||||
<td style="text-align: left;"><code>∘</code></td>
|
||||
<td style="text-align: left;">composition</td>
|
||||
</tr>
|
||||
<tr class="even">
|
||||
<td style="text-align: left;"><code>\cdot</code></td>
|
||||
<td style="text-align: left;"><code>⋅</code></td>
|
||||
<td style="text-align: left;">dot product</td>
|
||||
</tr>
|
||||
<tr class="odd">
|
||||
<td style="text-align: left;"><code>\times</code></td>
|
||||
<td style="text-align: left;"><code>×</code></td>
|
||||
<td style="text-align: left;">cross product</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<p>Infix operators may need parentheses due to precedence rules. For example, to call a composition, one needs <code>(f ∘ g)(x)</code> so that composition happens before function evaluation (<code>g(x)</code>).</p>
|
||||
|
||||
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<i class="bi bi-arrow-left-short"></i> <span class="nav-page-text"><span class="chapter-number">68</span> <span class="chapter-title">The <code>CalculusWithJulia</code> package</span></span>
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<span class="nav-page-text"><span class="chapter-number">70</span> <span class="chapter-title">Quick introduction to Calculus with Julia</span></span> <i class="bi bi-arrow-right-short"></i>
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