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To calculate the divergence of a vectorfield in cartesian coordinates, you can think of it as a dot product, and to calculate the curl, you can think of it as a cross product. But how can you calculate the div and curl when you have spherical or cylindrical coordinates, without explicitely converting them to the cartesian system?

For example the radial unity vector e_r = (sin a * cos b, sin a * sin b, cos a)

(standard: a = Theta, b = phi) should affect the curl and div by more than the scaling factor (h)

P.S Is it possible to use tex when writing a post?

For example the radial unity vector e_r = (sin a * cos b, sin a * sin b, cos a)

(standard: a = Theta, b = phi) should affect the curl and div by more than the scaling factor (h)

P.S Is it possible to use tex when writing a post?

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