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Spherical coordinates prob

  1. Oct 5, 2009 #1
    I need to brush up my math. I am trying to solve a spherical coordinates problem.
    compute the divergence of the function
    v=r cos[tex]\theta[/tex] r^ + r sin [tex]\theta[/tex] [tex]\theta[/tex]^+ r sin [tex]\theta[/tex] cos [tex]\varphi[/tex] [tex]\varphi[/tex]^
    (r^ is r hat ...)
    check the divergence theorem for this function, using as your volume the inverted hemisphere of radius R, resting on xy plane and centered at origin.

    I couldn't find the surface area :
    r is R
    theta is from 0 to pi/2
    phi is from 0 to 2pi

    with constant R, surface area da = R^2 sin [tex]\theta[/tex] d[tex]\theta[/tex] d[tex]\varphi[/tex]
    How do I calculate the surface area of the hemisphere and the circle in the xy plane.
    thanks.
     
  2. jcsd
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