The application of several point loads at different locations will lead to being a piecewise function.

The lemma is implicit in the use of piecewise functions.

A piecewise function is continuous on a given interval if the following conditions are met:

With no external forces, the piecewise functions should attach and show no discontinuity.

Its frequency-domain description is a piecewise function, given by:

In mathematics, a piecewise function is a function that can give different outputs based on its input.

Consider the piecewise function f(x) evaluated at certain values of x:

Natural number level hyperoperations can be defined recursively as a piecewise function:

In convex analysis, the notion of a derivative may be replaced by that of the subderivative for piecewise functions.

Piecewise functions are defined using the common functional notation, where the body of the function is an array of functions and associated subdomains.

Further, piecewise functions such as splines and polygonal chains are common in mathematics, and PDIFF provides a category for discussing them.

Sin, arctan, polynomial functions, or piecewise functions (such as the hard clipping function) are commonly used as waveshaping transfer functions.

Thus, in order to evaluate a piecewise function at a given input value, the appropriate subdomain needs to be chosen in order to select the correct function and produce the correct output value.

The Placzek transient can be derived analytically by solving for the neutron flux using a piecewise function solution to a differential equation involving a Heaviside step function in energy intervals of width .

In mathematics, a piecewise-defined function (also called a piecewise function) is a function which is defined by multiple subfunctions, each subfunction applying to a certain interval of the main function's domain (a subdomain).

The general scoring modifiers apply (see above), with the point translation function being a piecewise function: a constant amount is given for scoreless hands and the score is doubled for each point (that is, an exponential function).