  Here we follow the basic analysis that is common for real and complex
variables and find how it can be applied to a quaternionic variable.
Non-commutativity of the quaternion algebra poses obstacles for the usual
manipulations; but we show how many of those obstacles can be overcome. After a
tiny bit of linear algebra we look at the beginnings of differential calculus.
The surprising result is that the first order term in the expansion of
F(x+delta) is a compact formula involving both F'(x) and [F(x) - F(x*)]/(x-x*).
