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Let G denote the sphere of radius 1, which can be parameterized by 0 < 0 < 2π, 0 < Σπ r(0,0) = (sin cos 0, sin o sin 0, cos d), The Jacobian of this map is dS = sin ododo. Note that the normal vector on the sphere is n(x, y, z) = (x, y, z) = n(0, 6) = (sin cos 0, sin o sin 0, cos 6) Fc he following problems, let F(x, y, z) = (2y, —2x, 3z). Compute SF-nds directly using the parameterization. . Now compute SF · ndS using the Divergence Theorem.

Let G denote the sphere of radius 1, which can be parameterized by 0 < 0 < 2π, 0 < Σπ r(0,0) = (sin cos 0, sin o sin 0, cos d), The Jacobian of this map is dS = sin ododo. Note that the normal vector on the sphere is n(x, y, z) = (x, y, z) = n(0, 6) = (sin cos 0, sin o sin 0, cos 6) Fc he following problems, let F(x, y, z) = (2y, —2x, 3z). Compute SF-nds directly using the parameterization. . Now compute SF · ndS using the Divergence Theorem.

Advanced Engineering Mathematics
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 G denote the sphere of radius 1, which can be parameterized by 0 < 0 < 2π, 0 < Σπ r(0,0) = (sin cos 0, sin o sin 0, cos d), The Jacobian of this map is dS = sin ododo. Note that the normal vector on the sphere is n(x, y, z) = (x, y, z) = n(0, 6) = (sin cos 0, sin o sin 0, cos 6) Fc he following problems, let F(x, y, z) = (2y, —2x, 3z). Compute SF-nds directly using the parameterization. . Now compute SF-nds using the Divergence Theorem.
Transcribed Image Text:Let G denote the sphere of radius 1, which can be parameterized by 0 < 0 < 2π, 0 < Σπ r(0,0) = (sin cos 0, sin o sin 0, cos d), The Jacobian of this map is dS = sin ododo. Note that the normal vector on the sphere is n(x, y, z) = (x, y, z) = n(0, 6) = (sin cos 0, sin o sin 0, cos 6) Fc he following problems, let F(x, y, z) = (2y, —2x, 3z). Compute SF-nds directly using the parameterization. . Now compute SF-nds using the Divergence Theorem.
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