ʃdxdydzUδV + ʃdσU dV/dw - 4 πU’’ = ʃdxdydzVδU + ʃdσV dU/dw - 4 πV’ ….. (3’)
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I have no idea what it does, still less any idea how to calculate it if given the rest of the equations, purpose and values. I know only that it was quoted from the work of the English mathematician George Green, alongside a picture of a windmill commemorating his parents' milling business!
I'll hazard a guess...
I think it means the sum of a certain two three-dimensional integrals and a negative pi term, is identical to the sum of a sort of mirror image of each of those three terms.
So, if V = Volume, U might = area (but why not use A?); and Pi suggests revolution. I do not know what the two other Greek letters mean here.
So the work from which this is taken may describe the values and mutual relationships of surface-areas and volumes of solids generated by rotating complex but numerically defined curves. Just my guess!
Why "favourite"? Only because it intrigues me and is so far beyond any maths I could possibly learn!