  We show that the full symbol of the Dirichlet to Neumann map of the k-form
Laplace's equation on a Riemannian manifold (of dimension greater than 2) with
boundary determines the full Taylor series, at the boundary, of the metric.
This extends the result of Lee and Uhlmann for the case $k=0$. The proof avoids
the computation of the full symbol by using the calculus of pseudo-differential
operators parametrized by a boundary normal coordinate and recursively
calculating the principal symbol of the difference of boundary operators.
