Modules in Mathematica allow you to treat the names of variables as local. Sometimes, however, you want the names to be global, but values to be local. You can do this in ...

Connecting to a subsidiary program via MathLink. This starts a subsidiary Mathematica process on the computer system used here. Here is a packet representing the first input ...

Converting to and from character codes. Mathematica assigns every character that can appear in a string a unique character code. This code is used internally as a way to ...

Constrained optimization problems are problems for which a function f(x) is to be minimized or maximized subject to constraints Φ(x). Here f:^n  is called the objective ...

The general principle that Mathematica follows in evaluating expressions is to go on applying transformation rules until the expressions no longer change. This means, for ...

Converting between strings, boxes, and expressions. Here is a simple expression. This gives the InputForm of the expression as a string.

Density and contour plots. This gives a density plot of sin(x) sin(y). Lighter regions show higher values of the function. Some options for DensityPlot.

Within a standard interactive session, you can create "subsessions" or dialogs using the Mathematica command Dialog. Dialogs are often useful if you want to interact with ...

The solutions to many second-order ODEs can be expressed in terms of special functions. Solutions to certain higher-order ODEs can also be expressed using AiryAi, BesselJ, ...

The hypergeometric functions play a unifying role in mathematical analysis since many important functions, such as the Bessel functions and Legendre functions, are special ...