Proof of Gauss divergence theorem?

In the cartesian coordinates we proved the divergence theorem in the class by taking the divergence of any vector and then finding the volume integral

and then finding the flux throught six faces of the cube and then adding all. which gives LHS=RHS

Now in cylindrical coordinates i dont know what to take for the flux, i mean which surfaces??? i dont know for which surfaces of the cylinder i have to calculate flux and then add all of them. Please guide me?

we have been given limits for row, phi and z and S IS THE SURFACE OF A WEDGE!

Re: Proof of Gauss divergence theorem?

Hey szak1592.

If you want to go from Cartesian to Cylindrical co-ordinates, you need to use the multi-variable integration by substitution to go from (x,y,z) to (row,phi,z).

The first thing you need are the formulae to go from one space to another and then you can use this to get the Jacobian and finally to get the integral.

I'm guessing you have formulas for this but if not here is the Wiki:

List of common coordinate transformations - Wikipedia, the free encyclopedia

Re: Proof of Gauss divergence theorem?

Buy a cheese wheel. Cut out a wedge. Look at it, and the answer should be apparent.

Re: Proof of Gauss divergence theorem?

no I have a vector in cylindrical coordinates. First i will take the divergence and then evaluate volume integral. That is the RHS.

Now i have to take surface integral for all surfaces of the cylinder, which surfaces do I have to consider???