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Math Help - Finding a parametric representation of the surface, (vector calculus) please help me

  1. #1
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    Finding a parametric representation of the surface, (vector calculus) please help me

    Consider the surface z=thaita (sorry i dont know how to spell it) in cylindrical coordinates shown in figure 3. Find aparametric representation of this surfaceFinding a parametric representation of the surface, (vector calculus) please help me-mmm.png

    I dont even know where to start, please help me out
    thanks
    Attached Thumbnails Attached Thumbnails Finding a parametric representation of the surface, (vector calculus) please help me-mmm.png  
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  2. #2
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    Re: Finding a parametric representation of the surface, (vector calculus) please help

    I'll try and help you out, I've never really used cylindrical co-ordinates but I do know that they're defined by three properties; the radial distance from the z-axis, the azimuth (angle to) of the point and height z.
    Your equation would result in a straight line on the z-axis since the distance from the z-axis isn't mentioned. Are you sure the equation is correct as it clearly doesn't correspond with the diagram.

    Try it, let , and on this grapher, the result is just a straight line.
    surf_graph_cylin
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  3. #3
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    Re: Finding a parametric representation of the surface, (vector calculus) please help

    Why r=0 ?
    Try the plotter with r=t, t=0 to 5, and \theta = z = s, s = 0 to 15.
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    Re: Finding a parametric representation of the surface, (vector calculus) please help

    Hmmm, I understand what you're saying, but if r isn't explicitly defined surely that means it's either irrelevant hence or it's true for all values of r: , why would the equation imply that ?

    I'm not criticising you, just brainstorming. =)

    I think an appropriate parametric representation would be:







    where: and

    That does seem a bit silly but it's all I've got at the moment.
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  5. #5
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    Re: Finding a parametric representation of the surface, (vector calculus) please help

    I chose r = 0\rightarrow 5, (and \theta = z = 0\rightarrow 15), for no particular reason other than it gives a reasonable plot (and produces something like the surface shown in the original question) whereas r = 0\rightarrow\infty does not. Just for example really.
    If there are no limits specified then I think \infty is correct, afterall if you were asked to plot, in [2D], y=1 for example, you would draw, or at least imply, a line of infinite length, not a single point at (0,1).
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  6. #6
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    Re: Finding a parametric representation of the surface, (vector calculus) please help

    If the diagram weren't present I'd think the answer I gave was correct but I'm thinking that some information is missing. Given how the diagram looks







    where: and

    ...doesn't seem possible.
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