(v) div(ƒÃ) = f div Ã+ grad(f).Ã

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please solve only  (v) and (vi).

(a)
Show that the following identities are correct.
(i) div rot A = 0
(ii) rot grad f = 0
(iii) div grad f = V²ƒ = Aƒ, (A: Laplace Operatörü)
(iv) grad(fg) = g grad(f) + f grad(g)
(v) div(ƒÃ) = f div Ã+ grad(f).Ã
(vi) rot(fÃ) = f rot Ã+ grad(f) × rot Ã
(vii) div(Ã × B) = B. rot à – Ã. rot B
(viii) rot rot A = grad div à – AÃ
Transcribed Image Text:(a) Show that the following identities are correct. (i) div rot A = 0 (ii) rot grad f = 0 (iii) div grad f = V²ƒ = Aƒ, (A: Laplace Operatörü) (iv) grad(fg) = g grad(f) + f grad(g) (v) div(ƒÃ) = f div Ã+ grad(f).à (vi) rot(fÃ) = f rot Ã+ grad(f) × rot à (vii) div(Ã × B) = B. rot à – Ã. rot B (viii) rot rot A = grad div à – AÃ
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