# Piecewise Functions

Turning conditions into numbers.

Boole[expr] is a basic function that turns True and False into and . It is sometimes known as the *characteristic function* or *indicator function*.

This gives the area of a unit disk.

Out[1]= | |

Piecewise[{{val_{1},cond_{1}},{val_{2},cond_{2}},...}] |

| give the first for which is True |

Piecewise[{{val_{1},cond_{1}},...},val] | give val if all are False |

Piecewise functions.

It is often convenient to have functions with different forms in different regions. You can do this using Piecewise.

This plots a piecewise function.

Out[2]= | |

Piecewise functions appear in systems where there is discrete switching between different domains. They are also at the core of many computational methods, including splines and finite elements. Special cases include such functions as Abs, UnitStep, Clip, Sign, Floor, and Max. *Mathematica* handles piecewise functions in both symbolic and numerical situations.

This generates a square wave.

Out[3]= | |

Here is the integral of the square wave.

Out[4]= | |