Wednesday, March 17, 2010

AP Calculus BC Pep Talk!

OK, we finished a 2 week unit on convergence tests for sequences and series of all positive terms last week. We focused on the Integral Test, Comparison Test, Ratio Test and Root Test theorems. We also stressed the Divergence Test (Cauchy's Minimal Criterion for Convergence of Series of Constants with All Positive Terms - a necessary but insufficient condition for convergence). We did a little with alternating series and absolute vs. conditional convergence too.
This week we started a 2 week unit on MacLaurin/Taylor/LaGrange plus radius of convergence based on the ratio test for absolute convergence of power series using last week's work to test endpoints. We do the Alternating Series Test here too.

Then we have Easter break. After that, 4/6 - 4/16, we will do a 2 week unit on vector/polar. In the past I've rushed this unit as we've touched on it a bit here and there through out the year. I think we have a little extra time to do this topic justice this year. This will reduce our AP Review time, but every unit this year has had a Free Response Friday and a Multiple Choice Monday test, so that's a lot of AP Review right there!

Anyway, what I stress in this last BC unit is
Part I:
r(t) = position vectors
v(t) = velocity vectors
a(t) = acceleration vectors
arc length in parametric mode

Part II:
slope along a polar graph
area bound by a polar curve
arc length along a polar trajectory
we use parametrics/vectors to derive formulas for part II 

So, as you can see, we are nearing the home stretch - we are nearly done!  Here's to a great showing on the AP exam!! Good luck to us all!!!

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