For each of the parametric surfaces o given below and every pair of param- eters (u, v) in the domain of o, compute the following: (i) d₁o(u, v) and 0₂0(u, v). (ii) d₁o(u, v) × d₂o(u, v). (iii) |d₁o(u, v) × d₂0(u, v)|. (a) Sphere: o: R² → R³, where o(u, v) = (cos u sin v, sin u sin v, cos v). (b) Torus: o: R² → R³, where o(u, v) = ((2 + cos u) cos v, (2 + cos u) sin v, sin u).
For each of the parametric surfaces o given below and every pair of param- eters (u, v) in the domain of o, compute the following: (i) d₁o(u, v) and 0₂0(u, v). (ii) d₁o(u, v) × d₂o(u, v). (iii) |d₁o(u, v) × d₂0(u, v)|. (a) Sphere: o: R² → R³, where o(u, v) = (cos u sin v, sin u sin v, cos v). (b) Torus: o: R² → R³, where o(u, v) = ((2 + cos u) cos v, (2 + cos u) sin v, sin u).
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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Transcribed Image Text:For each of the parametric surfaces σ given below and every pair of param-
eters (u, v) in the domain of o, compute the following:
(i) d₁o(u, v) and λ₂0(u, v).
(ii) d₁σ(u, v) × d₂σ(u, v).
(iii) 0₁σ(u, v) × d₂0(u, v)|.
(a) Sphere: o: R² → R³, where σ(u, v) :
=
(b) Torus: o: R² → R³, where σ(u, v)
=
(cos u sin v, sin u sin v, cos v).
((2 + cos u) cos v, (2 + cos u) sin v, sin u).
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