82 lines
4.0 KiB
Plaintext
82 lines
4.0 KiB
Plaintext
|
# Preface {.unnumbered}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
----
|
||
|
|
|
||
|
|
This is a set of notes for learning
|
||
|
|
[calculus](http://en.wikipedia.org/wiki/Calculus) using the
|
||
|
|
[`Julia`](https://julialang.org) language. `Julia` is an open-source
|
||
|
|
programming language with an easy to learn syntax that is well suited
|
||
|
|
for this task.
|
||
|
|
|
||
|
|
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.
|
||
|
|
|
||
|
|
Since the mid 90s there has been a push to teach calculus using many
|
||
|
|
different points of view. The
|
||
|
|
[Harvard](http://www.math.harvard.edu/~knill/pedagogy/harvardcalculus/)
|
||
|
|
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
|
||
|
|
[Julia](http://julialang.org) to illustrate the graphical, numerical,
|
||
|
|
and, at times, the algebraic aspects of calculus.
|
||
|
|
|
||
|
|
There are many examples of integrating a computer algebra system (such
|
||
|
|
as `Mathematica`, `Maple`, or `Sage`) into the calculus
|
||
|
|
conversation. Computer algebra systems can be magical. The popular
|
||
|
|
[WolframAlpha](http://www.wolframalpha.com/) website calls the full
|
||
|
|
power of `Mathematica` 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 `Julia` 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.
|
||
|
|
|
||
|
|
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 `Julia` 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 `Julia` 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 `action(function, arguments...)`. With a small collection of
|
||
|
|
actions that can be composed, many of the problems associated with
|
||
|
|
introductory calculus can be attacked.
|
||
|
|
|
||
|
|
|
||
|
|
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 @Strang, @Knill, @Schey, @Thomas,
|
||
|
|
@RogawskiAdams, several Wikipedia pages, and other sources..
|
||
|
|
|
||
|
|
These notes are accompanied by a `Julia` package `CalculusWithJulia`
|
||
|
|
that provides some simple functions to streamline some common tasks
|
||
|
|
and loads some useful packages that will be used repeatedly.
|
||
|
|
|
||
|
|
These notes are presented as a Quarto book. To learn more about Quarto
|
||
|
|
books visit <https://quarto.org/docs/books>.
|
||
|
|
|
||
|
|
These notes may also be compiled into `Pluto` notebooks. As such, to
|
||
|
|
accommodate `Pluto`'s design of only one global variable definition
|
||
|
|
being allowed per notebook, there is frequent use of
|
||
|
|
[Unicode](./misc/unicode.html) symbols for variable names.
|
||
|
|
|
||
|
|
To contribute -- say by suggesting addition topics, correcting a
|
||
|
|
mistake, or fixing a typo -- click the "Edit this page" link.
|
||
|
|
|
||
|
|
----
|
||
|
|
|
||
|
|
Calculus with Julia version {{< meta version }}, produced on {{< meta
|