93 lines
4.4 KiB
Plaintext
93 lines
4.4 KiB
Plaintext
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---
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title: Calculus with Julia
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date: today
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jupyter: julia-1.11
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execute:
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daemon: false
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format:
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typst:
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toc: false
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section-numbering: "1."
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keep-typ: false
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include-before-body:
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- text: |
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#set figure(placement: auto)
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---
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[{}](https://calculuswithjulia.github.io/)
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This is a set of notes for learning
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[calculus](http://en.wikipedia.org/wiki/Calculus) using the
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[`Julia`](https://julialang.org) language. `Julia` is an open-source
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programming language with an easy to learn syntax that is well suited
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for this task.
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Read "[Getting started with Julia](./misc/getting_started_with_julia.html)" to learn how to install and customize `Julia` for following along with these notes. Read "[Julia interfaces](./misc/julia_interfaces.html)" to review different ways to interact with a `Julia` installation.
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Since the mid 90s there has been a push to teach calculus using many
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different points of view. The
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[Harvard](http://www.math.harvard.edu/~knill/pedagogy/harvardcalculus/)
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style rule of four says that as much as possible the conversation
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should include a graphical, numerical, algebraic, and verbal
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component. These notes use the programming language
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[Julia](http://julialang.org) to illustrate the graphical, numerical,
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and, at times, the algebraic aspects of calculus.
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There are many examples of integrating a computer algebra system (such
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as `Mathematica`, `Maple`, or `Sage`) into the calculus
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conversation. Computer algebra systems can be magical. The popular
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[WolframAlpha](http://www.wolframalpha.com/) website calls the full
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power of `Mathematica` while allowing an informal syntax that is
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flexible enough to be used as a backend for Apple's Siri
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feature. ("Siri what is the graph of x squared minus 4?") For
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learning purposes, computer algebra systems model very well the
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algebraic/symbolic treatment of the material while providing means to
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illustrate the numeric aspects. These notes are a bit different in
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that `Julia` is primarily used for the numeric style of computing and
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the algebraic/symbolic treatment is added on. Doing the symbolic
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treatment by hand can be very beneficial while learning, and computer
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algebra systems make those exercises seem kind of redundant, as the
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finished product can be produced much more easily.
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Our real goal is to get at the concepts using technology as much as
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possible without getting bogged down in the mechanics of the computer
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language. We feel `Julia` has a very natural syntax that makes the
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initial start up not so much more difficult than using a calculator,
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but with a language that has a tremendous upside. The notes restrict
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themselves to a reduced set of computational concepts. This set is
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sufficient for working many of the problems in calculus, but do not
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cover thoroughly many aspects of programming. (Those who are
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interested can go off on their own and `Julia` provides a rich
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opportunity to do so.) Within this restricted set, are operators that
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make many of the computations of calculus reduce to a function call of
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the form `action(function, arguments...)`. With a small collection of
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actions that can be composed, many of the problems associated with
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introductory calculus can be attacked.
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These notes are accompanied by a `Julia` package [`CalculusWithJulia`](https://github.com/jverzani/CalculusWithJulia.jl)
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that provides some simple functions to streamline some common tasks
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and loads some useful packages that will be used repeatedly.
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----
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The [online book](https://calculuswithjulia.github.io/) is compiled using the excellent [Quarto](https://quarto.org/) publishing system. Quarto does not support both [typst](https://typst.app/) and the book format, so this pdf file is pieced together section by section. This is useful, but less than optimal:
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* there is no table of contents
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* there is no index of sections, rather search must be utilized to navigate
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* in HTML, the questions are interactive and self-grading; with the pdf they are rendered in plain text, with some residual formatting. Also the questions in the pdf have *really* long section numbers.
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* there is little attention paid to page layout, as HTML is the preferred presentation format.
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----
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```{julia}
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#| echo: false
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using YAML, Dates, Markdown
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cfg = YAML.load_file("_quarto.yml")
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version = VersionNumber(cfg["version"])
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yr=Dates.year(now())
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Markdown.parse("[CalculusWithJulia](https://calculuswithjulia.github.io/) version $version; Copyright 2022-$yr, John Verzani")
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```
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