MIT
18 02 -
Lecture 31
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Lecture 31 Stoke s Theorem Green s theorem is a special case of Stoke s Theorem F r curl F n s Example n 0 0 1 and F P Q 0 F r P x Q y Q P x y Curl F 0 0 Q P Curve C equator unit circle S Northern hemisphere F x x y zx Line integral c cos sin 0 0 2 and r sin cos 0 F r cos cos sin 0 sin cos 0 2sin cos cos Surface line integral sin cos sin sin cos 0 2 and 0 2 curl F 0 cos 1 and n s sin cos sin sin cos sin curl F n s 0 cos 1 sin cos sin sin cos sin cos sin sin cos sin 2 cos sin Let u sin and u cos 2 u u How to nd N s sin sin sin cos u 0 x cos cos cos sin sin sin cos sin sin sin cos sin cos cos General fact s t x st y s t z s t so n s x y z x x y z s t
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