If you have a list of elements, it is often important to be able to apply a function separately to each of the elements. You can do this in Mathematica using Map. This ...

Applying transformation rules. The replacement operator /. (pronounced "slash-dot") applies rules to expressions. You can give a list of rules to apply. Each rule will be ...

In many kinds of numerical computations, it is convenient to introduce approximate functions. Approximate functions can be thought of as generalizations of ordinary ...

When you use //N to get a numerical result, Mathematica does what a standard calculator would do: it gives you a result to a fixed number of significant figures. You can also ...

When you do calculations with arbitrary-precision numbers, Mathematica keeps track of precision at all points. In general, Mathematica tries to give you results which have ...

You can do arithmetic with Mathematica just as you would on an electronic calculator. This is the sum of two numbers. Here the / stands for division, and the ^ stands for ...

When you make a definition in the form f[args]=rhs or f[args]:=rhs, Mathematica associates your definition with the object f. This means, for example, that such definitions ...

Definitions such as f[x_]=x^2 specify values for functions. Sometimes, however, you need to specify general properties of functions, without necessarily giving explicit ...

In addition to the interfaces of Import and Export, Mathematica 8 comes with an autoloading mechanism that simplifies the registration of formats used by the Import and ...

Other tutorials have discussed explicit loading of Mathematica packages using <<package and Needs[package]. Sometimes, however, you may want to set Mathematica up so that it ...