Math

Math#

Integral Volume Element in Different Dimensions#

2-Dimensional (2D)#

In 2D polar coordinates: \(d\Omega' = r \, dr \, d\theta\)

  • \(\theta\): Ranges from \(0\) to \(2\pi\).

3-Dimensional (3D)#

In 3D spherical coordinates: \(d\Omega' = r^2 \sin\theta \, dr \, d\theta \, d\phi\)

  • \(\theta\): Polar angle, ranges from \(0\) to \(\pi\).

  • \(\phi\): Azimuthal angle, ranges from \(0\) to \(2\pi\).

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