When doing surface integrals of surfaces described parametrically, we use the area element dA = ndS = (rv x rw )dvdw
Where dS is the surface area element and v and w are the parameters.
I'm fine with the derivation of this (I think) but I don't understand why it's necessary to have n and dS together, as in not just make an expression for n and dS seperately.
I think I'm misunderstanding something because I thought n = rv x rw because this is a vector perpendicular to rv and rw therefore perpendicular to the surface. But then if this were true, according to the equation for dA at the top that would make dS = dvdw, which isn't necessarily true e.g. if v and w are polars.
Thanks
Where dS is the surface area element and v and w are the parameters.
I'm fine with the derivation of this (I think) but I don't understand why it's necessary to have n and dS together, as in not just make an expression for n and dS seperately.
I think I'm misunderstanding something because I thought n = rv x rw because this is a vector perpendicular to rv and rw therefore perpendicular to the surface. But then if this were true, according to the equation for dA at the top that would make dS = dvdw, which isn't necessarily true e.g. if v and w are polars.
Thanks
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