Getting started with Julia

Julia is a freely available, open-source programming language aimed at technical computing.

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).

lauch binder

We recommend taking advantage of Binder, which provides a web-based interface to Julia built around Jupyter, a wildly succesful platform for interacting with different open-source software programs. Clicking the launch button above will open a web page which provides a blank notebook, save for a package used by these notes.

COCALC offers free access to Julia through the web. The free version can be slow due to limits on the resources used, but the monthly price for paid version is modest and the performance is quite reasonable.

Installing Julia locally

Binder is great and convenient, but it may not be the best option. Fortunately, installing Julia is a not-so-difficult option.

Binaries of Julia are provided at 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.

The base Julia provides a command-line interface, or REPL (read-evaluate-parse).

Basic interactive usage

Once installed, Julia can be started by clicking on an icon or typing julia at the command line. Either will open a command line interface for a user to interact with a Julia process. The basic workflow is easy: commands are typed then sent to a Julia process when the "return" key is pressed for a complete expression. Then the output is displayed.

A command is typed following the prompt. An example might be 2 + 2. To send the command to the Julia interpreter the "return" key is pressed. A complete expression or expressions will then be parsed and evaluated (executed). If the expression is not complete, julia's prompt will still accept input to complete the expression. Type 2 + to see. (The expression 2 + is not complete, as the infix operator + expects two arguments, one on its left and one on its right.)

   _       _ _(_)_     |  Documentation:
  (_)     | (_) (_)    |
   _ _   _| |_  __ _   |  Type "?" for help, "]?" for Pkg help.
  | | | | | | |/ _` |  |
  | | |_| | | | (_| |  |  Version 1.0.0 (2018-08-08)
 _/ |\__'_|_|_|\__'_|  |  Official release
|__/                   |

julia> 2 + 2

Above, julia> 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:

2 + 2

Other interfaces to Julia are described briefly in Julia interfaces. The notebook interface provided through IJulia most closely matches the style of the notes.

Add-on packages

Julia has well over a 1000 external, add-on packages that enhance the offerings of base Julia. We refer to one, CalculusWithJulia, that is designed to accompany these notes. This package installs several other packages that provide the needed functionality. The package (and its dependencies) can be installed through:

using Pkg

(Or the one liner ] add CalculusWithJulia. Some additional details on packages is provided here.)

Installation only needs to be done once, but to use a package it must be loaded into each new session. This can be done with this command:

using CalculusWithJulia

The basics of working with IJulia

The very basics of the Jupyter notebook interface provided by IJulia are covered here.

An IJulia notebook is made up of cells. Within a cell a collection of commands may be typed (one or more).

When a cell is executed (by the triangle icon or under the Cell menu) the contents of the cell are evaluated by the Julia kernel and any output is displayed below the cell. Typically this is just the output of the last command.

2 + 2
3 + 3

If the last commands are separated by commas, then a "tuple" will be formed and each output will be displayed, separated by commas.

2 + 2, 3 + 3
(4, 6)

Comments can be made in a cell. Anything after a # will be ignored.

2 + 2  # this is a comment, you can ignore me...

Graphics are provided by external packages. There is no built-in graphing. We use the Plots package and its default backend. The Plots package provides a common interface to several different backends, so this choice is easily changed. The GR and plotly backends are used in these notes, when possible; the PyPlot backend is used for some surface plots.

using CalculusWithJulia
using Plots

With that in hand, to make a graph of a function over a range, we follow this pattern:

plot(sin, 0, 2pi)

A few things: