lecture notes 16.6-16.9 (1)

Examples 1 if s then upward unit normal vector 8 2

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Unformatted text preview: S: ( ) then 〈 〉 √ (upward unit normal vector) 8 (2) If S: , then S can be parameterized as . Then 〈 and | So, 〉 | 〈 〉 (outward unit normal vector). ( Definition ∬ ) is called the surface ∬ integral (or, flux) of F over S. Note: If | | ∬ ∬ 9 ( ) Examples {( , above ) (1) Let S: }. Let ( ) Evaluate ∬ . (n with upward orientation) 〈 〉. 10 (2) Let S be the upper semi-sphere: 〈 with upward orientation, and Evaluate ∬ . 11 , 〉. 16.8-16.9 Stokes’ theorem and the divergence theorem Stokes’ theorem Suppose S is an oriented surface that is bounded by a simple closed curve C with positive orientation. Th...
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This note was uploaded on 01/31/2014 for the course MAE 204 taught by Professor Errington during the Fall '08 term at SUNY Buffalo.

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