I'm getting ready to write up new teaching notes for Calc II. I am
wondering about the best way to teach sequences and series. We use the TI-85.
I have taught sequences and series the "traditional" way incorporating the 85.
I am considering two things. I'd appreciate comments (pro and con) on both
ideas. I really haven't made up my mind on either idea.
1. I may choose to teach Taylor polynomials before I teach any intervals of
convergence. I can motivate them by saying we are looking for the best
linear approximation, then the best parabolic approx, then the best cubic
approx, etc.
I think I can get them to intuitively understand an "infinite polynomial"
and hence and infinite series this way. then I can go back and more
rigorously develop the concept. Anybody out there ever done this? Good
idea or bad?
2. Whether or not I use the above idea I am wondering how much depth I
should go into on tests of convergence. I teach primarily (90% or greater)
engineering majors. I continually struggle with the fact that calculus
curriculum has changed drastically since I was in school. I have adjusted
to less Theorem and Proof and more real-world applications. But I also
believe that we must proceed slowly with doing away with background
information. We can't let technology substitute for understanding; it
should enhance it. (Am I making any sense at all?)
What I'm probably looking for is the answer to the question, "How important,
in light of the technology available, to teach all the traditional
'mathematical manipulations' associated with comparison, ratio,and root
tests? And how important is it to distinguish between intervals of
convergence and radius of convergence?" (What I may be looking for is for
someone who uses "reform calculus" to assure me that all of the above are
still imprtant and should be taught.)
Thanks for taking time to read and respond.
I hop all of you ahve a merry and blessed Christmas.
Bret Taylor Lake-Sumter Community College Leesburg FL
"It matters not the subject taught, nor all the books on all the shelves.
What matters more, yes most of all, is what the teachers are themselves."
John Wooden
John 3: 3 3