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<h1 class="title d-none d-lg-block">Calculus with Julia</h1>
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<div class="quarto-title-meta-heading">Author</div>
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<p>John Verzani </p>
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<div class="quarto-title-meta-heading">Published</div>
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<p class="date">August 11, 2022</p>
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<section id="preface" class="level1 unnumbered">
<h1 class="unnumbered">Preface</h1>
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<p>This is a set of notes for learning <a href="http://en.wikipedia.org/wiki/Calculus">calculus</a> using the <a href="https://julialang.org"><code>Julia</code></a> language. <code>Julia</code> is an open-source programming language with an easy to learn syntax that is well suited for this task.</p>
<p>Read “<a href="./misc/getting_started_with_julia.html">Getting started with Julia</a>” to learn how to install and customize <code>Julia</code> for following along with these notes. Read “<a href=".misc/julia_interfaces.html">Julia interfaces</a> to review different ways to interact with a <code>Julia</code> installation.</p>
<p>Since the mid 90s there has been a push to teach calculus using many different points of view. The <a href="http://www.math.harvard.edu/~knill/pedagogy/harvardcalculus/">Harvard</a> style rule of four says that as much as possible the conversation should include a graphical, numerical, algebraic, and verbal component. These notes use the programming language <a href="http://julialang.org">Julia</a> to illustrate the graphical, numerical, and, at times, the algebraic aspects of calculus.</p>
<p>There are many examples of integrating a computer algebra system (such as <code>Mathematica</code>, <code>Maple</code>, or <code>Sage</code>) into the calculus conversation. Computer algebra systems can be magical. The popular <a href="http://www.wolframalpha.com/">WolframAlpha</a> website calls the full power of <code>Mathematica</code> while allowing an informal syntax that is flexible enough to be used as a backend for Apple’s Siri feature. (“Siri what is the graph of x squared minus 4?”) For learning purposes, computer algebra systems model very well the algebraic/symbolic treatment of the material while providing means to illustrate the numeric aspects. Theses notes are a bit different in that <code>Julia</code> is primarily used for the numeric style of computing and the algebraic/symbolic treatment is added on. Doing the symbolic treatment by hand can be very beneficial while learning, and computer algebra systems make those exercises seem kind of redundant, as the finished product can be produced much easier.</p>
<p>Our real goal is to get at the concepts using technology as much as possible without getting bogged down in the mechanics of the computer language. We feel <code>Julia</code> has a very natural syntax that makes the initial start up not so much more difficult than using a calculator, but with a language that has a tremendous upside. The notes restrict themselves to a reduced set of computational concepts. This set is sufficient for working many of the problems in calculus, but do not cover thoroughly many aspects of programming. (Those who are interested can go off on their own and <code>Julia</code> provides a rich opportunity to do so.) Within this restricted set, are operators that make many of the computations of calculus reduce to a function call of the form <code>action(function, arguments...)</code>. With a small collection of actions that can be composed, many of the problems associated with introductory calculus can be attacked.</p>
<p>These notes are presented in pages covering a fairly focused concept, in a spirit similar to a section of a book. Just like a book, there are try-it-yourself questions at the end of each page. All have a limited number of self-graded answers. These notes borrow ideas from many sources, for example <span class="citation" data-cites="Strang">Strang (<a href="references.html#ref-Strang" role="doc-biblioref">n.d.</a>)</span>, <span class="citation" data-cites="Knill">Knill (<a href="references.html#ref-Knill" role="doc-biblioref">n.d.</a>)</span>, <span class="citation" data-cites="Schey">Schey (<a href="references.html#ref-Schey" role="doc-biblioref">1997</a>)</span>, <span class="citation" data-cites="Thomas">Hass, Heil, and Weir (<a href="references.html#ref-Thomas" role="doc-biblioref">2018</a>)</span>, <span class="citation" data-cites="RogawskiAdams">Rogawski, Adams, and Franzosa (<a href="references.html#ref-RogawskiAdams" role="doc-biblioref">2019</a>)</span>, several Wikipedia pages, and other sources..</p>
<p>These notes are accompanied by a <code>Julia</code> package <code>CalculusWithJulia</code> that provides some simple functions to streamline some common tasks and loads some useful packages that will be used repeatedly.</p>
<p>These notes are presented as a Quarto book. To learn more about Quarto books visit <a href="https://quarto.org/docs/books" class="uri">https://quarto.org/docs/books</a>.</p>
<p>These notes may also be compiled into <code>Pluto</code> notebooks. As such, to accommodate <code>Pluto</code>’s design of only one global variable definition being allowed per notebook, there is frequent use of <a href="./misc/unicode.html">Unicode</a> symbols for variable names.</p>
<p>To contribute – say by suggesting addition topics, correcting a mistake, or fixing a typo – click the “Edit this page” link.</p>
<hr>
<p>Calculus with Julia version {{&lt; meta version }}, produced on {{&lt; meta</p>
<div id="refs" class="references csl-bib-body hanging-indent" role="doc-bibliography" style="display: none">
<div id="ref-Thomas" class="csl-entry" role="doc-biblioentry">
Hass, Joel R., Christopher E. Heil, and Maurice D. Weir. 2018. <em>Thomas’ Calculus</em>. Pearson.
</div>
<div id="ref-Knill" class="csl-entry" role="doc-biblioentry">
Knill, Oliver. n.d. <span>“Some Teaching Notes.”</span> <a href="https://people.math.harvard.edu/~knill/teach/index.html">https://people.math.harvard.edu/~knill/teach/index.html</a>.
</div>
<div id="ref-RogawskiAdams" class="csl-entry" role="doc-biblioentry">
Rogawski, Jon, Colin Adams, and Robert Franzosa. 2019. <em>Calculus</em>. Macmillan.
</div>
<div id="ref-Schey" class="csl-entry" role="doc-biblioentry">
Schey, H. M. 1997. <em>Div, Grad, Curl, and All That</em>. W.W. Norton.
</div>
<div id="ref-Strang" class="csl-entry" role="doc-biblioentry">
Strang, Gilbert. n.d. <span>“<span>MS Windows NT</span> Kernel Description.”</span> <a href="https://ocw.mit.edu/courses/res-18-001-calculus-online-textbook-spring-2005/">https://ocw.mit.edu/courses/res-18-001-calculus-online-textbook-spring-2005/</a>.
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