Surface interal

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Unformatted text preview: llows. Let U = (0, 2π ) × (0, 2π ), and W = R3 \ { (x, y, z ) | x ≥ 0 and y = 0, or x2 + y 2 ≥ a2 and z = 0 }. Let � : U −→ M ∩ W, g be the function � (s, t) = ((a + b cos t) cos s, (a + b cos t) sin s, b sin t). g Let’s calculate the tangent vectors, ∂� g � Ts = = (−(a + b cos t) sin s, (a + b cos t) cos s, 0), ∂s ∂� g � Tt = = (−b sin t cos s, −b sin t sin s, b cos t). ∂t So � � � ˆ ˆ ı j ˆ k � � � � � Ts × Tt = �−(a + b cos t) sin s (a + b cos t) cos s 0� � � � −b sin t cos s � −b sin t sin s b cos t ˆ =...
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This note was uploaded on 01/27/2014 for the course MATH 324 taught by Professor Kopp during the Winter '08 term at University of Washington.

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