21-356 Lecture 38

Monday april 25 2011 b remark 176 in physics u f x x

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Unformatted text preview: B Remark 176 In physics " U f (x)·$ (x) dHN #1 (x) represents the outward flux of a vector field f across the boundary of a region U . If E ) RN and f : E * RN is di"erentiable, then f is called a divergence-free field or solenoidal field if div f = 0. Thus for a smooth solenoidal field, the outward flux across the boundary of a regular set U is zero. 104 Corollary 177 The theorem continues to hold if U ) RN is open, bounded, and its boundary consists of two sets E1 and E2 , where E1 is a closed set contained in the finite union of compact surfaces of class C 1 and dimension less than N ' 1, while for ever...
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