# Defining Functions

There are many functions that are built into *Mathematica*. This tutorial discusses how you can add your own simple functions to *Mathematica*.

As a first example, consider adding a function called which squares its argument. The *Mathematica* command to define this function is . The (referred to as "blank") on the left-hand side is very important; what it means will be discussed below. For now, just remember to put a on the left-hand side, but not on the right-hand side, of your definition.

This defines the function

. Notice the

on the left-hand side.

squares its argument.

Out[2]= | |

The argument can be a number.

Out[3]= | |

Or it can be a more complicated expression.

Out[4]= | |

You can use

in a calculation.

Out[5]= | |

This shows the definition you made for

.

f[x_]:=x^2 | define the function |

?f | show the definition of |

Clear[f] | clear all definitions for |

Defining a function in *Mathematica*.

The names like that you use for functions in *Mathematica* are just symbols. Because of this, you should make sure to avoid using names that begin with capital letters, to prevent confusion with built-in *Mathematica* functions. You should also make sure that you have not used the names for anything else earlier in your session.

*Mathematica* functions can have any number of arguments.

You can use the

function just as you would any of the built-in functions.

Out[8]= | |

This gives a new definition for

, which overwrites the previous one.

The new definition is displayed.

This clears all definitions for

.

When you have finished with a particular function, it is always a good idea to clear definitions you have made for it. If you do not do this, then you will run into trouble if you try to use the same function for a different purpose later in your *Mathematica* session. You can clear all definitions you have made for a function or symbol f by using Clear[f].