Ken Kundert

If you approximate a sine wave at a point with a polynomial (think Taylor series expansion), there will be terms at all orders, but they generally get smaller as the order increases. A piecewise linear approximation represents the sine wave at that point with a straight line. That is a first order approximation. However, the piecewise linear approximation does not include any of the higher order terms, the largest is assumed to be second order. Thus it is said to have secondorder errors. Of course it also has third, fourth, fifth, ... order errors, but they are assumed to be smaller. If a piecewise quadratic interpolation was used, then it would accurately model the zero, first and second order terms but would have thirdorder error.
In otherwords, if you were to subtract a pure sine wave from a piecewise linear approximation of the sine wave, and looked at the terms of the Taylor series expansion of the difference at an interpolation point, then the difference would only include secondorder terms and above. These are the error terms for the piecewiselinear approximation.
Ken
