Gradient in Spherical Coordinates: Computing w/ {em} & {wm}

[autobot.d]

So I am working in spherical coordinates and to find the gradient I have the eqn

G^-1d\phi
where \phi is a scalar function

Then I am supposed to compute in terms of {e_m} and {w^m}.

I am just confused what it means to compute in terms of? Do i have to convert the
co and contra vectors into scalars? Any help is appreciated.

 

[autobot.d]

Just confused on what the gradient of phi in terms of the vector and covector in spherical coordinates are. Maybe that is a little easier to help with?

 

[Bacle]

You need to use charts to define the gradient --seen as a vector field--on the sphere.

Use the charts to pull it back from R^n.