Unformatted text preview: v x and v y , as well as the cylindrical components v r (radial component) and v θ (tangential coordinate). Assign numerical values to all components. 4. Show that ∇ 2 ψ = 0, where the function ψ ( r, θ, φ ) (i.e., a function of the spherical coordinates) is given by ψ ( r, θ, φ ) = ψ cos θ r 2 , where ψ is a constant. 5. Consider the function y ( x ) = x sinh x . Perform a Taylor series expansion about x = 0, keeping the Frst two nonzero terms. 6. Solve the di±erential equation d 2 v x dy 2 = C, where C is a constant, subject to the boundary conditions v x = 0 at y = 0 v x = 0 at y = h to determine the function v x ( y ). 1...
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 Fall '08
 Staff
 Derivative, Taylor Series, Coordinate system, Polar coordinate system

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