Scalar factors of parabolic cylindrical coords

[lazyluke]

Homework Statement

I have a question to find Scalar factors of parabolic cylindrical coords and element dV with provided tranformation equations. I know the values for both of them and that the product of the scalar factors is the dV, but how do i derive those scalar factors? I don't even know where to start, i know i can use them to find Laplacian, curl and divergence but how do i find those values? how do i show my work? Please help Thank You Luke

Homework Equations

The Attempt at a Solution

 

[lazyluke]

Ok, so i came up with this using the Jacobian, but how do i get the scalar factors?, i assumed from Jacobian that hz=1 i donno if that is a legit assumption, please help.
ThatYou Luke

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