I'm going through Introduction_to_Tensor_Calculus by Wiskundige_Ingenieurstechnieken. I want to find the covariant and contravariant components of the cylindrical cooridnates. Ingerniurstechnieken sets tangent vectors as basis (E1, E2, E3). He also sets the normal vectors as another basis (E1, E2, E3) The coorindates relationships are: x=r*cosθ y=r*sinθ z=z r=sqrt(x2+y2) θ=arctan(y/x) z=z I'm setting R= vector r R=[r*cosθ, r*sinθ, 1] I found: E1 = [cosθ, sinθ, 0] E2 = [-r*sinθ, r*cosθ, 0] E3 = [0, 0, 1] He says to take gradient of r, θ, and z for normal basis (E1, E2, E3). What do I take the gradient of to get this basis? Is it ∇r=(1, 0, 0) ∇θ=(0, 1, 0) ∇z=(0, 0, 1)?