Changing x From x y u x y to x x y u x x y x 0 u x x y u x y 1 0 u x Changing y 0 1 u y Lecture 28 These vectors tell us n S i e area and the normal Vector connecting points x u x x u x x u x x i u x n S 1 0 u x 0 1 u x y u u 1 x y S Example F 0 0 z and z x y 1 Flux F n S n S 2x 2y 1 x y Flux 0 0 x y 2x 2y 1 x x y x y r r 2 Divergence theorem F n S div F V Example Given that F 0 0 z and S Unit sphere nd the ux Method 1 parameterize the sphere sin cos sin sin cos 0 2 and 0 n sin cos sin sin cos and S sin Flux 0 0 cos blah blah cos sin Flux cos sin and let u cos and u sin Flux u u u u 4 3 Method 2 Flux div F V Vol Ball 4 3 Three pieces of boundary S1 the paraboloid itself S2 the side of the can S3 the bottom Flux S1 Flux S2 Flux S3 div F V Volume of the inside n S u v r u v r u u v r u v r u r u v v r u v r v
View Full Document
Unlocking...