241+formulas

# 241+formulas - Spherical and Cylindrical Coordinates 2 = x...

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Spherical and Cylindrical Coordinates ρ 2 = x 2 + y 2 + z 2 = r 2 + z 2 r = sin φ , z = cos x = r cos θ , y = r sin dV = 2 sin d d d Mass, Center of Mass, Centroid For a wire: M = δ ( x , y , z ) ds C where ds = r ( t ) dt Center of mass: x , y , z ( ) , x = 1 M x ( x , y , z ) ds C Centroid: x , y , z ( ) , x = 1 Length ( C ) x ds C For a surface: M = ( x , y , z ) d σ S ∫∫ d = r u × r v du dv or d = x 2 + z y 2 + 1 dx dy Center of mass x , y , z ( ) , x = 1 M x ( x , y , z ) d S ∫∫ Centroid: x , y , z ( ) , x = 1 Surface area ( S ) x d S ∫∫ Circulation and Flux The circulation of a vector field F around C is F d r C The flux of F = M , N across a closed plane curve is M dy
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## This note was uploaded on 09/23/2010 for the course MATH 216 taught by Professor Dickson during the Spring '10 term at UAA.

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