Let F be a C¹ vector field and let W be a symmetric elementary region in R³ with boundary OW = S. Then the Gauss Divergence theorem states that ° ] [₁ F · ds = [ ] [₁, ² (V.F) dV 01/α-1²-1/[@xn-s = /₁² S (V.F) dS = (V x F). dS S F. ds 0 [[ (V x F) · ds = [ F ° / [(V x F) · ds = // ₁ (v dS S °/-BS-[[[ (V.F) ds = (V.F) dV (V.F) dV
Let F be a C¹ vector field and let W be a symmetric elementary region in R³ with boundary OW = S. Then the Gauss Divergence theorem states that ° ] [₁ F · ds = [ ] [₁, ² (V.F) dV 01/α-1²-1/[@xn-s = /₁² S (V.F) dS = (V x F). dS S F. ds 0 [[ (V x F) · ds = [ F ° / [(V x F) · ds = // ₁ (v dS S °/-BS-[[[ (V.F) ds = (V.F) dV (V.F) dV
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 F be a C¹ vector field and let W be a symmetric elementary region in R³ with boundary oW = S. Then the Gauss
Divergence theorem states that
· ] [ F · ds = [ ] [ ₁ (v
//
W
(V.F) ds =
(V.F) dV
= [] [₁₂²²
W
Off-Bas
(V x F). dS
of [xx-48= /v-d
(V x F). dS = F. ds
მა
0 [[XF)-8=// /_ FAV
(V x F). dS
.F) dV
W
(V · F) ds = / / / w ( (V.F) dV](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccceb61d-0b39-4729-973d-5eeee6d6d189%2F0d218e50-9a89-4ccd-99c5-d795d2f81b89%2Fx9of045_processed.png&w=3840&q=75)
Transcribed Image Text:Let F be a C¹ vector field and let W be a symmetric elementary region in R³ with boundary oW = S. Then the Gauss
Divergence theorem states that
· ] [ F · ds = [ ] [ ₁ (v
//
W
(V.F) ds =
(V.F) dV
= [] [₁₂²²
W
Off-Bas
(V x F). dS
of [xx-48= /v-d
(V x F). dS = F. ds
მა
0 [[XF)-8=// /_ FAV
(V x F). dS
.F) dV
W
(V · F) ds = / / / w ( (V.F) dV
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