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Question 4. Let o (u, v): K be a smooth function (not necessarily a surface patch). Let E Ou · Ou, F = Ouσ₂ and G = σ₂. Show that the following equalities hold: ||o₂ x 0₂||² = det ((Do)T (Do)) = EG – F². (Here D denotes total derivative.)

Question 4. Let o (u, v): K be a smooth function (not necessarily a surface patch). Let E Ou · Ou, F = Ouσ₂ and G = σ₂. Show that the following equalities hold: ||o₂ x 0₂||² = det ((Do)T (Do)) = EG – F². (Here D denotes total derivative.)

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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- Question 4. Let o(u, v) : R² → R³ be a smooth function (not necessarily a surface ou ou, F = 0₁ 0₂ and G = ₂₂. Show that the following patch). Let E equalities hold: = . ||o₁ x σ₂||² = det ((Do)T (Do)) = EG – F². (Here D denotes total derivative.)
Transcribed Image Text:- Question 4. Let o(u, v) : R² → R³ be a smooth function (not necessarily a surface ou ou, F = 0₁ 0₂ and G = ₂₂. Show that the following patch). Let E equalities hold: = . ||o₁ x σ₂||² = det ((Do)T (Do)) = EG – F². (Here D denotes total derivative.)
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