Dear Jack:
I see you are getting ready for a great stat! Here goes some
brief additional advice.
A) I share your feelings of Anton and all its "clones". Trying
not to put down the book too much in front of students, I used to tell
them:"Everything the book says is good. But here, in class, we will
emphasize the REALLY important things - the rest you can read by
yourselves."
B) To start with a review of functions is a good idea. But I
strongly recommend concentrating on those functions which will be used
later, and those properties applying to calculus.
The exponential function (2^x, 10^x or e^x) can be mentioned, and
state clearly the properties which you assume the students to know.
Emphasize the logarithm as INVERSE of the exponential.
The same applies to the trig functions. Keep in mind that this
review can be made now or sometimes later.
Polynomials and quotients of polynomials are crucial, and students
know much less about them than you may expect. You will of course do graphs,
but use it to discuss the important features of calculus: where f(x) is
increasing, decreasing, maximum, minimum, zero, positive ...
In such discussions you will have an opportunity to tell them
about 80% of what you have to explain when discussing the derivative,
hence it will be time well spent! The quotients of polynomials gives
you the opportunity to set their minds straight about the domain of
a function, continuity, infinity as a limit, limits from right and left
and so on. They should discover the NEED and convenience of these
concepts BEFORE attempting their FORMAL definition.
But don't forget: time flies! And particularly when you do a GOOD
job getting them interested, it is hard to stay on schedule!
Good luck! Emilio