11.30 - Section 13.7 wrap-up: Go through Stewarts...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Section 13.7 wrap-up: Go through Stewarts derivation of the formula S F d S = S F n dS = D F ( r u r v ) dA on page 781. Discuss Group Work 2: 1. G / x , G / y , G / z = 2 x ,2 y ,2 z 2. Outward 3. n = (1/ R ) x , y , z (check: | n | 2 = (1/ R 2 ) ( x 2 + y 2 + z 2 ) = 1) 4. Everywhere but (0,0,0) 5. On the surface x 2 + y 2 + z 2 = R 2 , we have F = ( x i + y j + z k )/ R 3 = (1/ R 3 ) x , y , z so F n = (1/ R 4 ) ( x 2 + y 2 + z 2 ) = 1/ R 2 and S F n dS = S 1/ R 2 dS = (1/ R 2 ) Area( S ) = (1/ R 2 ) (4 R 2 ) = 4 . Check this with spherical coordinates: Imitating Example 4, we use r ( , ) = R sin cos i + R sin sin j + R cos k with 0 and 0 2 ; note that the extra factor of R will multiply r and r by R, so that r r = R 2 (sin 2 cos i + sin 2 sin j + sin cos k ) while F ( r ( ,...
View Full Document

Page1 / 4

11.30 - Section 13.7 wrap-up: Go through Stewarts...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online