Mean curvature of a surface

Hi everyone, new here and trying to calculate the mean curvature for the following surface:

__r__(u,v)=u__i__+f(u)cos(v)__j__+f(u)sin(v)__k__

I have been through the process of finding tangent vectors and a unit normal vector to the surface, so up to the point where I have had to substitute 6 scalars into:

h(p)=

__aG-2bF-cE __

2(EG-F^{2})

The only problem I seem to be having is not being able to simplify it... This is what I have:

h(p)=

±__ f''(u)f(u__)^{2}__-f'(u)__^{2}__-1 __

2f(u)(1+f'(u)^{2})√(cos^{2}(2v)f'(u)+1)

Maybe missing something really simple here or I have made a mistake in calculating the scalars.

Any help, much appreciated!

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Re: Mean curvature of a surface

Attachment 27245

I have worked through this again and shamefully the original post had some errors in. I have attached a correct answer, however still stuck with having to derive the differential equation!

1 Attachment(s)

Re: Mean curvature of a surface

From this link, because it would be a lot of typesetting:

Attachment 27465

Replace S(x,y) with your r(u,v). Respond with calculated partial derivatives as in the formula so we can see where you are going wrong.