Suppose I have a deformed unit sphere whose shape is given by $ r(r, \theta, \phi) = 1 + \epsilon x_iA_{ij}x_j$ for $\epsilon << 1$ and $A_{ij}$ is a symmetric traceless second order tensor.
How can I Taylor expand any scalar or vector function near sphere? That is, I want to find $\psi_{1+\delta r}$ and $\delta r = \epsilon x_iA_{ij}x_j$. I assume it would involve the higher order derivatives of tensor $A$?
Is there a general way to do it?