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A TA has got me very and utterly confused. He won't be avaible for a few days, so I'm asking you guys.

Consider the transformation to cilindrical coord.

x-->r.con[the]

y-->r.sin[the]

z-->z

I have the Jabobian (no problems here).

He then asks the differential d

**a**, where

**a**is a vector.

Enter the first confusion. I know the differential of the transformation (the linear function given by the Jacobian matrix), but what the hell is the differential of a vector?

My guess is: d

**a**=dx

**x**+dy

**y**+dz

**z**.

I have the unity vectors of the new system.

The trick is now what is d

**r**in fuction of the new unity vectors?

Then answer : d

**a**=dr

**r**+rd[the]

**[the]**+dz

**z**

How the hell is this determined?