Given two vectors Y (parameter Par1) and X (parameter Par2), and an integration constant C1 (input as CON1), Y* (parameter ParR) is replaced by the accumulated integral of Y over X as follows:

(16–1)

Then for each remaining point in the vector, set:

(16–2)

where:

= integrated value of Y up to point n in the vector

L = length of the vectors

Figure 16.1:  Integration Procedure

Given two vectors Y (parameter Par1) and X (parameter Par2), integration constants C₁ and C₂, (input as CON1 and CON2) set:

(16–3)

(16–4)

Then, for each remaining point in the vector,

(16–5)

(16–6)

Given two vectors Y (parameter Par1) and X (parameter Par2), the derivative is found by averaging the slopes of two adjacent intervals (central difference procedure):

(16–7)

A constant second derivative is assumed for the starting and ending intervals.

(16–8)

(16–9)

For DERIV calculation, the first and last terms may differ slightly from that calculated with *VOPER because DERIV linearly extrapolates these terms from adjacent values.

This is performed by simply repeating the differentiation procedure reported above.