Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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only solute question c ， please

(a) For all differentiable vector fields v(r) and w(r), use index notation to show that x W) + w X Χυ) ▼ (v.w) (v. V ) w w. ·V)v. υχ = (b) In the (x, y)-plane, sketch the vector fields v = (y, 2y, 0) and w= (x- -y, x+y, 0), clearly labelling which sketch is for which field. (c) For the vector fields defined in part (b), evaluate separately each term in the iden- tity given in part (a) and hence verify the identity in this case.
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Transcribed Image Text:(a) For all differentiable vector fields v(r) and w(r), use index notation to show that x W) + w X Χυ) ▼ (v.w) (v. V ) w w. ·V)v. υχ = (b) In the (x, y)-plane, sketch the vector fields v = (y, 2y, 0) and w= (x- -y, x+y, 0), clearly labelling which sketch is for which field. (c) For the vector fields defined in part (b), evaluate separately each term in the iden- tity given in part (a) and hence verify the identity in this case.
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