more maple not from bob:
non-bob resources for a different point of view:
At the end of this course, possible follow up books (naahh!):
There are a lot of "computer geek" materials that involve differential geometry but usually it is very difficult to penetrate their jargon. Here is a full book that has some useful resources, in particular an almost clear discussion of geodesics on implicitly defined surfaces that at least enables you to translate where their equations come from even though they are simply presented and not explained
Popular articles:
GR stuff:
Sean Carroll's
Lecture Notes on General Relativity: preliminary version of his longer
published book
Robert Geroch, General Relativity: 1972 Lecture
Notes (Minkowski Institute Press, Montreal 2013)
http://www.minkowskiinstitute.org/mip/books/geroch-gr.html
Robert Geroch's lecture notes on general relativity are unique in three main
respects. First, the physics of general relativity and the mathematics,
which describes it, are masterfully intertwined in such a way that both
reinforce each other to facilitate the understanding of the most abstract
and subtle issues. Second, the physical phenomena are first properly
explained in terms of spacetime and then it is shown how they can be
“decomposed” into familiar quantities, expressed in terms of space and time,
which are measured by an observer. Third, Geroch's successful pedagogical
approach to teaching theoretical physics through visualization of even the
most abstract concepts is fully applied in his lectures on general
relativity by the use of around a hundred figures.
Although the book contains lecture notes written in 1972, it is (and will
remain) an excellent introduction to general relativity, which covers its
physical foundations, its mathematical formalism, the classical tests of its
predictions, its application to cosmology, a number of specific and
important issues (such as the initial value formulation of general
relativity, signal propagation, time orientation, causality violation,
singularity theorems, conformal transformations, and asymptotic structure of
spacetime), and the early approaches to quantization of the gravitational
field.