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Topic: Applications of the definite integral - what to teach?
Replies: 3   Last Post: Feb 28, 1998 1:48 PM

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Alvar J. Garcia

Posts: 304
Registered: 12/6/04
Re: Applications of the definite integral - what to teach?
Posted: Feb 26, 1998 3:48 PM
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Greetings David:

I started including the 'work' topic last year as I was burned the year
before last with the the work questions on both the AB and BC exams! Mea
culpa, mea maxima culpa! I had't seen work questions on the free response
section for decades, so I thought I could skip that topic to make more
time for others. I know, that's no excuse....

My first year teaching BC, I had a lot of time trouble. As I recall, 2nd
year I did the Calculus of inverse trig functions for the first time and
the 3rd year I did trig substitution integrals for the first time. Now I
do every single thing I have ever done, and can think of doing plus the
new differential equations (slope fields, Euler's Method, etc.) unit
(additional two weeks). The ODEs dove-tial great into the topic of
applications of integration and I love partial fractions anyway
(Logistic Growth). My students love the Shroud of Tourin (exponential
decay/carbon dating), Columbo (Newton's Law of Cooling), US Census 1790-1950
(Logistic Growth), Predator-Prey (Phase Planes) modeling problems. In
fact, tommorow's test has the Skydiver (ala Newton's Law of Heating)
problem (with a prgmSLOPEF and prgmEULERG part added on) from the 97BC
free response section and another question (with phase planes and
simultaneous diffequs) using the Lanchaster Model to analyse the Battle at
Trafalgar or Iwo Jima (don't tell anyone, ;-{)).

I guess this will be my 5th year teaching BC Calculus (7th for AB
and 1st for PreCalulus). My kids must think that I've gone mad! We do it
all with time to spare for review!

BTW, I use DWFT plus H-H and go over lots of old AP free response
questions as part of teaching, reviewing and testing all year
long. If you would like free response materials, please check-out
'The Calculus Page' website listed below. I sell all the materials I've
developed for my students over the years through this website.

Good Luck,
A. Jorge Garcia Teacher/Professor Mathematics/CompSci BaldwinSHS/NassauCC
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