Expressions are the main type of data in Mathematica. Expressions can be written in the form h[e_1,e_2,…]. The object h is known generically as the head of the expression. ...

We first encountered lists in "Making Lists of Objects" as a way of collecting numbers together. Here, we shall see many different ways to use lists. You will find that lists ...

If you make a definition such as f[x_]:=value, Mathematica will use the value you give for any f function it encounters. In some cases, however, you may want to define a ...

Here is an example of an exact ODE. This verifies the solution. Here is a contour plot of the solution.

Here is a homogeneous equation in which the total degree of both the numerator and the denominator of the right-hand side is 2. The two parts of the solution list give ...

Around 1870, Marius Sophus Lie realized that many of the methods for solving differential equations could be unified using group theory. Lie symmetry methods are central to ...

The general solution to this equation is found by separation of variables. Even when variables can be separated, the final solution might be accompanied by a warning message ...

You may have noticed that there are two different ways to make assignments in Mathematica: lhs=rhs and lhs:=rhs. The basic difference between these forms is when the ...

Mathematica allows you not only to export graphics and sounds, but also to import them. With Import you can read graphics and sounds in a wide variety of formats, and bring ...

To run Mathematica using a network license, both the client machine and the license server must be on the network and MathLM must be running. If you do not have a MathLM ...