Plotting

Expressions defining functions in one variable can be plotted:

The syntax {x,0,1} defines a list (similar to an array in Julia).
Lists can contain anything, and can be arbitrarily nested

We will see later how to access and manipulate lists. For now we will just use simple lists to define the axes.

More plotting

The plotting and visualization functionality of Mathematica is very advanced
You can read the built-in documentation to learn more
Some examples:

Interactivity

One of Mathematica’s most powerful features is its interactivity

Consider plotting a set of parabolas

parameterized by the value a

We begin by choosing a “representative” set

Plotting these functions gives us some insight

More useful is manipulating the parameter interactively

We can use manipulate to understand e.g. frequency and amplitude of waves