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. ...

The following is the sequence of steps that Mathematica follows in evaluating an expression like h[e_1,e_2…]. Every time the expression changes, Mathematica effectively ...

On most computer systems, you can execute external programs or commands from within Mathematica. Often you will want to take expressions you have generated in Mathematica, ...

As discussed in "Exact and Approximate Results", Mathematica can handle approximate real numbers with any number of digits. In general, the precision of an approximate real ...

Mathematica uses various syntactic rules to interpret input that you give, and to convert strings and boxes into expressions. The version of these rules that is used for ...

Basic 3D plotting function. This makes a three-dimensional plot of the function sin(xy). Three-dimensional graphics can be rotated in place by dragging the mouse inside of ...

The functions FindMinimum, FindMaximum, and FindRoot have the HoldAll attribute and so have special semantics for evaluation of their arguments. First, the variables are ...

The general symbolic string patterns in Mathematica allow you to perform powerful string manipulation efficiently. What follows discusses the details of string patterns, ...

Transparency is useful in plots when you need an unobstructed view of multiple components of one plot, or simply want to lighten a single plot component against a white ...

For most differential equations, the results given by NDSolve are quite accurate. However, because its results are based on numerical sampling and error estimates, there can ...