79 lines
4.4 KiB
Plaintext
79 lines
4.4 KiB
Plaintext
# Preface {.unnumbered}
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----
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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 easier.
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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 presented in pages covering a fairly focused concept,
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in a spirit similar to a section of a book. Just like a book, there
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are try-it-yourself questions at the end of each page. All have a
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limited number of self-graded answers. These notes borrow ideas from
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many sources, for example @Strang, @Knill, @Schey, @Thomas,
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@RogawskiAdams, several Wikipedia pages, and other sources..
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These notes are accompanied by a `Julia` package `CalculusWithJulia`
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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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These notes are presented as a Quarto book. To learn more about Quarto
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books visit <https://quarto.org/docs/books>.
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These notes may be compiled into a `pdf` file through Quarto. As the result is rather large, we do not provide that file for download. For the interested reader, downloading the repository, instantiating the environment, and running `quarto` to render to `pdf` in the `quarto` subdirectory should produce that file (after some time).
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To *contribute* -- say by suggesting addition topics, correcting a
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mistake, or fixing a typo -- click the "Edit this page" link and join the list of [contributors](https://github.com/jverzani/CalculusWithJuliaNotes.jl/graphs/contributors). Thanks to all contributors and a *very* special thanks to `@fangliu-tju` for their careful and most-appreciated proofreading.
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----
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Calculus with Julia version {{< meta version >}}, produced on {{< meta date >}}.
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