$MaxExtraPrecision gives the maximum number of extra digits of precision to be used in functions such as N.

$PerformanceGoal gives the default setting for the option PerformanceGoal for graphics and other algorithmic functions.

$ProcessorType is a string giving the architecture of the processor on which Mathematica is being run.

$SystemCharacterEncoding gives the default raw character encoding for the computer system on which Mathematica is being run.

Structural Operations on Polynomials Finding the Structure of a Polynomial Polynomial Orderings

In an expression like f[{a,b,c}] you are giving a list as the argument to a function. Often you need instead to apply a function directly to the elements of a list, rather ...

The general solution to a differential equation contains undetermined coefficients that are labeled C[1], C[2], and so on. This example has one undetermined parameter, C[1]. ...

This equation is solved by simply integrating the right-hand side with respect to x. Here is a plot of the integral curves for different values of the arbitrary constant C[1].

In many kinds of calculations, you may find yourself typing the same input to Mathematica over and over again. You can save yourself a lot of typing by defining a function ...

Importing and Exporting Data Importing and Exporting Files Exporting Graphics and Sounds