Divergence Theorem to prove the identity

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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Let E be a closed region in R³ and let the boundary of E be
given by the surface S. Given scalar functions, a = a(x,y, z) and
b = b(x, y, z), and the unit normal vector n
Divergence Theorem to prove the identity
= n(x, y, z), use the
// (V . Va)bdV =
Va · Vb dV +
bVa ·n dS.
E
E
S
Transcribed Image Text:Let E be a closed region in R³ and let the boundary of E be given by the surface S. Given scalar functions, a = a(x,y, z) and b = b(x, y, z), and the unit normal vector n Divergence Theorem to prove the identity = n(x, y, z), use the // (V . Va)bdV = Va · Vb dV + bVa ·n dS. E E S
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