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20. Let S be an oriented surface parametrized by r(u,v). Define the notation do = r, du × r, dv so that do is a vector normal to the surface. Also, the magnitude do = face area (by Equation 5 in Section 16.5). Derive the identity do is the element of sur- do = (EG – F²)'/² du dv where E = r?, F = r„ • r,, and G = |r,|?.

20. Let S be an oriented surface parametrized by r(u,v). Define the notation do = r, du × r, dv so that do is a vector normal to the surface. Also, the magnitude do = face area (by Equation 5 in Section 16.5). Derive the identity do is the element of sur- do = (EG – F²)'/² du dv where E = r?, F = r„ • r,, and G = |r,|?.

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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20. Let S be an oriented surface parametrized by r(u,v). Define the notation do = r, du × r, dv so that do is a vector normal to the surface. Also, the magnitude do = face area (by Equation 5 in Section 16.5). Derive the identity do is the element of sur- do = (EG – F²)'/² du dv where E = r?, F = r„ • r,, and G = |r,|?.
Transcribed Image Text:20. Let S be an oriented surface parametrized by r(u,v). Define the notation do = r, du × r, dv so that do is a vector normal to the surface. Also, the magnitude do = face area (by Equation 5 in Section 16.5). Derive the identity do is the element of sur- do = (EG – F²)'/² du dv where E = r?, F = r„ • r,, and G = |r,|?.
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