The notion of expressions is a crucial unifying principle in Mathematica. It is the fact that every object in Mathematica has the same underlying structure that makes it ...

"Sound" describes how you can take functions and lists of data and produce sounds from them. Here we discuss how sounds are represented in Mathematica. Mathematica treats ...

Mathematica can be used to make plots of functions. You give Mathematica a function, and it builds up a curve or surface by evaluating the function at many different points. ...

Derivatives in Mathematica work essentially the same as in standard mathematics. The usual mathematical notation, however, often hides many details. To understand how ...

"Graphics and Sound" discusses how to use functions like Plot and ListPlot to plot graphs of functions and data. This tutorial discusses how Mathematica represents such ...

Particularly when you use transformation rules, you often need to name pieces of patterns. An object like x_ stands for any expression, but gives the expression the name x. ...

When you make a sequence of definitions in Mathematica, some may be more general than others. Mathematica follows the principle of trying to put more general definitions ...

In doing calculations, it is often convenient to collect together several objects, and treat them as a single entity. Lists give you a way to make collections of objects in ...

NDSolve is broken up into several basic steps. For advanced usage, it can sometimes be advantageous to access components to carry out each of these steps separately. NDSolve ...

The Mathematica side of a MathLink connection is set up to work exactly the same on all computer systems. But inevitably there are differences between external programs on ...