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

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