Mathematics 317T2 Assignment#7(2) - Mathematics 317 T2 Assignment#7 due Wednesday 1 For any two twice differentiable functions f x y z and g x y z show

Mathematics 317T2 Assignment#7(2) - Mathematics 317 T2...

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Mathematics 317 T2 Assignment #7 due Wednesday, March 10, 2010 1. For any two twice differentiable functions ),,(zyxfand ),,,(zyxgshow that (a) .)(2gfgfgf+=(b) .)(22fggffggf-=-(c) ).()(2fgfggf=+(d) .)(gfgf×=×(e) .0)(=×fgg(f) .2)(gffggf×=-×2. For any two differentiable vector fields ),,(zyxFand ),,,(zyxGshow that ).()()(GFGFFG×=×-×3. A vector field Ffor which div F= 0 is said to be divergence-free or solenoidal. that the vector field given by
f Show
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