ENAS 151 Useful Formulas Midterm 2

Y y0 fz x0 y0 z0 z z0 0 3 2 d fxx x0

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Unformatted text preview: (x0 , y0) · u Fx (x0 , y0, z0 )(x − x0 ) + Fy (x0 , y0, z0 )(y − y0 ) + Fz (x0 , y0, z0 )(z − z0 ) = 0 3 2 D = fxx (x0 , y0)fyy (x0 , y0 ) − fxy (x0 , y0 ) ∇f (x0 , y0) = λ∇g (x0, y0) g2 (x) b f (x, y )dA = R a h 2 (y ) d f (x, y )dA = R f (x, y ) dy dx g1 (x) f (x, y ) dx dy h 1 (y ) c 1 f (x, y ) dA A R where A is the area of the rectangular region R faverage = r 2 (θ ) β f (r, θ )dA = R ∂r ∂u ∂r ∂u n= R R ∂r ∂v ∂r ∂v × × ∂r ∂r × ∂u ∂v S= ∂z ∂x 2 b d c l G R θ2 θ1 k g2 (x,y ) f (x, y, z )dV = f (r, θ, z )dV = + 1 dA f (x, y, z )dz dy dx a G dA 2 ∂z + ∂y f (x, y, z )dV = G f (r, θ ) r dr dθ r 1 (θ ) α r 2 (θ ) r 1 (θ ) 4 f (x, y, z ) dz dA g1 (x,y ) g2 (r,θ ) g1 (r,θ ) f (r, θ, z ) r dz dr dθ x = r cos θ, y = r sin θ, z = z f (ρ, θ, φ)ρ2sin φ dρ dφ dθ f (ρ, θ, φ)dV = G x = ρ sin φ cos θ, y = ρ sin φ sin θ, z = ρ cos φ 5...
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This note was uploaded on 02/11/2014 for the course ENAS 151 taught by Professor Mitchellsmooke during the Fall '08 term at Yale.

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