Machine Do the Work

I calculated all of the yps using the current values of y. These are the elements in the last column of sleq. Then I incremented the first dependent variable y(i) by a small amount, yinc, and recalculated all of the yps. I subtracted the new values from the original values and divided the difference by yinc. These are the elements for the first column of the sleq array. I restored y(l) to its original value and repeated the procedure with y(2) to get the elements for the second column. I did this until all the columns had been evaluated. Finally, I added IIdelx to the diagonal elements. These procedures yielded values of the elements of the sleq array that are identical to those calculated with the linearized algebraic expressions. 

I found it convenient to use y(i) times a parameter dlny for yinc, with a 

DIM sleq(nrow, ncol), unk(nrow), y(nrow), dely(nrow) 

EQUATIONS Subroutine to calculate the coefficient matrix prod prodz (x delx) / 2000 

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The central idea of our industrialized society is to have machines do the work formerly done by humans or animals. The technical problem that kicked off the industrial revolution was flooding in the tin mines of Cornwall, a region in southern Britain. To work the mines and extract the valuable tin ore, steam-driven reciprocating pumps had been constructed. These plunger-type pumps were moved up and down by the famous beam engines, and these reciprocating engines were powered by steam, thanks to the efforts of Thomas Newcomen, in 1712. 

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