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Calc 3 Coordinate questions

  1. Oct 23, 2005 #1
    1) Rewrite the following expression in polar coordinates:
    (second derivative of z with respect to x) + (second derivative of z with respect to y)

    where x=rcos(theta)
    y = rsin(theta)

    i had first derivative of z with respect to x = (dz/dx)(dx/dr) + (dz/dx)(dx/d(theta))

    same concept for y

    and then i just took the derivative of my dz/dz and dz/dy variables again

    2) describe this surface in cylindrical coordinates
    z = rcos3(phi)

    express in cartesian coordinates

    i really do not get cartesian coordinates

    can anyone show me the generic method?

    3) x = psin(phi)cos(theta)
    y = psin(phi)sin(theta)
    z = pcos(phi)

    near which points of R^3 can we solve for: p phi and theta in terms of x, y and z, describe the geometry behind your answer.

    again, i am really really weak in coordinate systems.

    any help is appreciated, thanks guys
     
  2. jcsd
  3. Oct 24, 2005 #2
    what does z = in #1

    x = p sin phi cos theta

    y =p sin phi sin theta

    z = p cos phi
     
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