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 ...

When you execute a command like NotebookWrite[obj,data] the actual operation of inserting data into your notebook is performed in the front end. Normally, however, the kernel ...

This gives a result for the integral of x^n that is valid for almost all values of n. For the special case of x^-1, however, the correct result is different. The overall goal ...

The way modules work in Mathematica is basically very simple. Every time any module is used, a new symbol is created to represent each of its local variables. The new symbol ...

Mathematica's unique symbolic architecture makes it easy to add toolbars with any possible appearance and action to a Mathematica notebook. The ruler is a toolbar used to set ...

LayeredGraphPlot attempts to draw the vertices of a graph in a series of layers, placing dominant vertices at the top, and vertices lower in the hierarchy progressively ...

Numerical integration functions. This finds a numerical approximation to the integral ∫_(0)^∞ e^-x^3 x. Here is the numerical value of the double integral ∫_(-1)^1 dx ...

Testing for numeric quantities. Pi is a symbol, so Pi+3 is not explicitly a number. It does however have a numerical value.

Specifying patterns that involve alternatives. This defines h to give p when its argument is either a or b. The first two cases give p.

In using Mathematica, you sometimes need to repeat an operation many times. There are many ways to do this. Often the most natural is in fact to set up a structure such as a ...