Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adv. In terms or by means of pieces; a piece at a time.
 adv. Throughout separate parts, but not necessarily throughout the whole
Etymologies
Examples

We formulate a mathematical model for daily activities of a cow (eating, lying down, and stand  ing) in terms of a piecewise affine dynamical system.

We modeled the eating, lying, and standing dynamics of a cow using a piecewise affine dynamical system.

In essence, they consist of piecewise polynomials with local supports.

Since Version 5.1, Mathematica has offered general support for piecewise functions, both numerically and symbolically.

In the above examples, each piecewise polynomial is defined on an interval with the same length and thus forms a uniform basis.

Even though their algebraic forms look different, one can verify that the antiderivatives differ by a piecewise constant:
Wolfram Blog : Mathematica and the Fundamental Theorem of Calculus

These companies were then broken up and sold piecewise, their pension obligations replaced with 401 (k)  type individual retirement accounts, many of which were entrusted to investment companies created specifically for this purpose  thereby supplying a secondary source of investment capital for more leveraged buyouts.

The vertically filtered station data from each section are interpolated onto an evenly spaced latitudinal or longitudinal grid depending on section orientation at 0.033° spacing using a shapepreserving piecewise cubic Hermite interpolant at each pressure level.

The variance inflation in multiple dimensions is a type of piecewise PLS.

I had suggested this piecewise comparision 19101940; 19501975; 19752000
USHCN Survey Results based on 33% of the network « Climate Audit
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