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Exterior derivative with Excel

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The exterior derivative in dimensions 1 and 2 can be computed with Excel.

Dimension 1

The only difference form the algebra we have seen is that here we have to produce results in terms of the coordinates with respect to the basis of cells. They are listed at the top.

The computation is shown on the right and explained on the left:

Exterior derivative in dimension 1 Excel.png

The Excel formulas are hidden but only two need to be explained.

First, "B=∂a, 0-chain numbers B_i assigned to 0-cells, differences of adjacent values of a" is computed by $$=R[-4]C-R[-4]C[-1];$$ Second, "df_i=df(a_i), 1-cochain, differences of adjacent values of f -- the output" is computed by $$=R[-16]C-R[-16]C[1].$$

The exterior derivative is computed Stokes Theorem as well as directly. The results match.

Dimension 2