Partial Differential Equations Let w be a scalar eld and a

Partial Differential Equations:

Let w be a scalar ?eld and ? a vector ?eld. Verify the vector identity div (w?)=?·grad w + w div ?. Integrate this equation over ? and take ? = gradu, where u is a scalar ?eld, to prove Green’s identity....

1.7 Heat Conduction in Higher Dimensions 65 4. Let w be a scalar field and a vector field. Verify the vector identity div (wO) = . grad to + u, div . Integrate this equation over and take field, to prove Green\'s identity grad u, where u is a scalar u ndA.

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