Lab6A_Ex4 - Exercise 4 f theta phi Sin phi Cos theta Sin...

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Unformatted text preview: Exercise 4 f theta , phi Sin phi Cos theta , Sin phi Sin theta , 1 ; ParametricPlot3D f theta, phi , theta, 0, 2 Pi , phi, 0, Pi 4 0.5 0.5 x 0.0 0.5 y 0.0 0.5 2.0 1.5 z 1.0 0.5 0.0 2 Lab6A_Ex4.nb g t ,p Cos p Sin p ^ 2; graph t , p Sin p Cos t , Sin p Sin t , Cos p 1 ParametricPlot3D graph t, p , p, 0, Pi 4 , t, 0, 2 Pi ColorFunction Function x, y, z, p , GrayLevel g 0, p Cos 3 t .4 4 ; 1.2 1.0 0.8 0.6 0.0 0.5 0.0 x 0.5 0.5 y 0.5 z g 0, p ColorFunction Function x, y, z, p , GrayLevel 0.4 dt dp D f t, p , t D f t, p , p Sin p Sin t , Cos t Sin p , 0 Cos p Cos t , Cos p Sin t , 0 v Cross dp, dt ; Norm v Cos p Cos t , Cos p Sin t , 0 Cos p Cos t 2 Sin p y^2 Cos p Sin p Sin t 22 g x ,y ,z x^2 Apply g, f t, p 2 Cos p Cos t x2 y2 Sin p Cos p Sin p Sin t 22 Lab6A_Ex4.nb 3 Cos t 2 Sin p 2 Sin p 2 Sin t 2 integrand Simplify Apply g, f t, p Norm Cross dp, dt ans NIntegrate integrand , p, 0, Pi 4 , t, 0, 2 Pi Simplify ans Cos t Sin p 2 Sin p 2 Sin p 2 2 Sin t 2 2 Cos p Sin p 2 0.392699 0.392699 ...
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This note was uploaded on 03/07/2011 for the course MATH 2374 taught by Professor Mosher during the Spring '07 term at Minnesota.

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