The gradient of a scalar can be expressed in terms of the new coordinate system ∇g = a∂r...

The gradient of a scalar can be expressed in terms of the new coordinate system ∇g = a∂r/∂u+b ∂r/∂v+c ∂r/∂w, where you will determine the scalars a, b, c. Using dg = ∇g · dr, derive that the gradient in an orthogonal curvilinear coordinate system is given by

An expression for the divergence is more difficult to derive, and we will just state that if a vector p is expressed in terms of this new coordinate system

then the divergence satisfies