1. Suppose that f(x, y, z) is a smooth function. (a) Show that where the Laplacian (b) Show that curl Vf = 0 and div Vf = Af, 2² 2² + 2² A + მ2 მ2 მ/2 div (fVg) = Vf. Vg+fAg.
1. Suppose that f(x, y, z) is a smooth function. (a) Show that where the Laplacian (b) Show that curl Vf = 0 and div Vf = Af, 2² 2² + 2² A + მ2 მ2 მ/2 div (fVg) = Vf. Vg+fAg.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Suppose that f(x, y, z) is a smooth function.
(a) Show that
where the Laplacian
(b) Show that
curl Vf= 0 and div Vf = Af,
2²
2²
2²
Δ=
+
+
Əx² dy² dz²
div (fVg) = Vf. Vg+fAg.
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