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 surfaceAttachment 23728

I dont even know where to start, please help me out

thanks

- Apr 28th 2012, 08:46 PMmath254Finding 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 surfaceAttachment 23728

I dont even know where to start, please help me out

thanks - May 1st 2012, 02:22 PMIvanator27Re: 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 http://latex.codecogs.com/gif.latex?\large z=\theta 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 http://latex.codecogs.com/gif.latex?\large r = 0, http://latex.codecogs.com/gif.latex?\large \theta =t and http://latex.codecogs.com/gif.latex?\large z = t on this grapher, the result is just a straight line.

surf_graph_cylin - May 2nd 2012, 01:11 AMBobPRe: Finding a parametric representation of the surface, (vector calculus) please help
Why $\displaystyle r=0$ ?

Try the plotter with $\displaystyle r=t$, $\displaystyle t=0$ to $\displaystyle 5, $ and $\displaystyle \theta = z = s,$ $\displaystyle s = 0$ to$\displaystyle 15.$ - May 2nd 2012, 09:41 AMIvanator27Re: 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 http://latex.codecogs.com/png.latex?r=0 or it's true for all values of r: http://latex.codecogs.com/gif.latex?...n%20\mathbb{R}, why would the equation http://latex.codecogs.com/gif.latex?\large%20z=\theta imply that http://latex.codecogs.com/gif.latex?...5%20\right%20]?

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

I think an appropriate parametric representation would be:

http://latex.codecogs.com/gif.latex?\large%20r%20=%20t

http://latex.codecogs.com/gif.latex?\large%20z%20=%20s

http://latex.codecogs.com/gif.latex?...\theta%20=%20s

where: http://latex.codecogs.com/gif.latex?...n%20\mathbb{R} and http://latex.codecogs.com/gif.latex?...n%20\mathbb{R}

That does seem a bit silly but it's all I've got at the moment. - May 3rd 2012, 12:43 AMBobPRe: Finding a parametric representation of the surface, (vector calculus) please help
I chose $\displaystyle r = 0\rightarrow 5,$ (and $\displaystyle \theta = z = 0\rightarrow 15),$ for no particular reason other than it gives a reasonable plot (and produces something like the surface shown in the original question) whereas $\displaystyle r = 0\rightarrow\infty$ does not. Just for example really.

If there are no limits specified then I think $\displaystyle \infty$ is correct, afterall if you were asked to plot, in [2D], $\displaystyle y=1$ for example, you would draw, or at least imply, a line of infinite length, not a single point at $\displaystyle (0,1).$ - May 3rd 2012, 08:16 AMIvanator27Re: 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

http://latex.codecogs.com/gif.latex?\large%20r%20=%20t

http://latex.codecogs.com/gif.latex?\large%20z%20=%20s

http://latex.codecogs.com/gif.latex?...\theta%20=%20s

where: http://latex.codecogs.com/gif.latex?...n%20\mathbb{R} and http://latex.codecogs.com/gif.latex?...n%20\mathbb{R}

...doesn't seem possible.