11.30 - Section 13.7 wrap-up Go through Stewart’s...

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 Stewart’s 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 π R 2 ) = 4 π . Check this with spherical coordinates: Imitating Example 4, we use r ( φ , θ ) = R sin φ cos θ i + R sin φ sin θ j + R cos φ k with 0 ≤ φ ≤ π and 0 ≤ θ ≤ 2 π ; note that the extra factor of R will multiply r φ and r θ by R, so that r φ × r θ = R 2 (sin 2 φ cos θ i + sin 2 φ sin θ j + sin φ cos φ k ) while F ( r ( φ ,...
View Full Document

This note was uploaded on 02/13/2012 for the course MATH 241 taught by Professor Staff during the Fall '11 term at UMass Lowell.

Page1 / 4

11.30 - Section 13.7 wrap-up Go through Stewart’s...

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