So I'm fiddling about with formulae...trying things out...consolidating...as you do...and something didn't work - why?(adsbygoogle = window.adsbygoogle || []).push({});

The infinitesimal area element in polar coordinates dA = r*d(theta)*dr . Agreed? Now in the same coordinate system [tex] x = r \cos{\theta} ; y = r \sin{\theta} [/tex]. Taking differentials, we have:

[tex]

dx = dr \cos{\theta} - r \sin{\theta} d\theta ;

dy = dr \sin{ \theta} + r \cos{\theta} d\theta [/tex].

Multiplying together we get dx dy, the area element in cartesian coordinates, and hopefully equal to r*d(theta)*dr, but

[tex] dx dy = {dr}^2 \cos{\theta} \sin{\theta} - d\theta^2 r^2 \sin{\theta} \cos{\theta} + \cos^2{\theta} r d\theta dr - \sin^2{\theta} r d\theta dr [/tex].

Neglecting squares of differential forms, we have that:

[tex] dx dy = \cos{2\theta} r d\theta \dr [/tex]

Not what I was hoping, you see. So could someone explain? It's probably down to some assumption I'm making, but I don't know what it is. All I can think of is that either the area elements are different in the different coordinates, or that since we are considering the product of differentials the squared forms cannot be ignored.

P.S. can someone refer me to somewhere that'll show me where I can type Greek letters without reverting to Latex? Thanks.

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# Area element in polar co's/trouble with diff. forms

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