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Question 4. Let o(u, v): R² →→→ R³ be a smooth function (not necessarily a surface patch). Let E = 0₂ - Ou F = O and G Show that the following equalities hold: . (Here D denotes total derivative.) = ||o₂ x 0₂||² = det ((Do)¹ (Do)) = EG —- F².

Question 4. Let o(u, v): R² →→→ R³ be a smooth function (not necessarily a surface patch). Let E = 0₂ - Ou F = O and G Show that the following equalities hold: . (Here D denotes total derivative.) = ||o₂ x 0₂||² = det ((Do)¹ (Do)) = EG —- F².

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. Our F = ₁0₂ and G = ₂₂. Show that the following patch). Let E equalities hold: = ||₁x0₂||²= det ((Do)T (Do)) (Here D denotes total derivative.) = EG - F².
Transcribed Image Text:Question 4. Let o(u, v) : R² → R³ be a smooth function (not necessarily a surface ou. Our F = ₁0₂ and G = ₂₂. Show that the following patch). Let E equalities hold: = ||₁x0₂||²= det ((Do)T (Do)) (Here D denotes total derivative.) = EG - F².
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