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What is dx, dy and dz in spherical coordinates

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What is dx, dy and dz in spherical coordinates

- #2

fresh_42

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What are ##x,y,z## in polar coordinates? Now differentiate.

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Okay. Because there are many variables. x = r sinΘ cosΦ , y = r sinΘ sinΦ and z = r cos Θ, I differebtiate with respect to what variable?What are ##x,y,z## in polar coordinates? Now differentiate.

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fresh_42

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All. There is no 1:1 correspondence. E.g. the origin is artificial in polar coordinates, e.g. ##r=0##, and the angles? Then there has to be a restriction of valid intervals for the angles. We will have nine equations for (x,y,z) → (r,Θ,Φ).Okay. Because there are many variables. x = r sinΘ cosΦ , y = r sinΘ sinΦ and z = r cos Θ, I differebtiate with respect to what variable?

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Thanks, let me try

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jtbell

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Okay. Thanks

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fresh_42

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https://en.wikipedia.org/wiki/Polar_coordinate_system#Calculus

or here where the formulas are a bit easier to see quickly:

https://de.wikipedia.org/wiki/Polarkoordinaten#Funktionaldeterminante (Fläche = area, the rest is self explaining)

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