



The two main areas of
Calculus have scary sounding names. 





Differential
Calculus  finding derivatives



Integral
Calculus  finding integrals 





This is such a
bunch of hype. 





If
you have ever driven or even ridden in a car, 


you understand both of
these things completely. 





These pages will just fill in
the funny Calculus vocabulary 


and funny Calculus notation. 





Here
we go...






Say you drive in a straight
line at 50 miles per hour for three hours.






What
can you say about the trip other than you were probably bored silly.






You can say how
far you went. 





You can say how fast you were
going. 





You probably also know where
you started and where you ended up. 





Almost all of Integral
and Differential calculus 


involves starting with one of these and
calculating another one. 





If you know how fast
you were going 


and how much time you were going that fast, 


you can
figure out how far you went. 





In the world up to now, 


we have called that multiplying your velocity (a fancy name for speed) 


by
the time you were traveling. 





In the fancy
schmancy calculus world, 


they call it integrating the velocity
function with respect to time. 





Guess What? 





They both mean
the same thing! 





It's kind of
like calling a janitor a sanitation engineer. 





The other half
of calculus is just as simple. 





We know we
started in one place 


and three hours later were in another place 150
miles away. 





What was our
average speed? 





In the world up
to now, 


we called that dividing the distance traveled by the elapsed
time 


to get the velocity (that fancy name for speed again). 





In the fancy
schmancy calculus world, 


they call it differentiating the distance
traveled function with respect to time 


to get velocity. 





And guess what
again? 





They both mean
the same thing again! 





More sanitation
engineers! 





So we've got
two little secrets math types don't want you to catch on to, 


at
least not right away 





1 
Differential calculus is just dividing 





2  Integral
Calculus is just multiplying 





OK, Right about
now you're probably saying something like: 





HOLD ON!
TIME OUT! STOP RIGHT THERE! 





What's the
catch? There's got to be WAAAAY more to it than that. 


Most colleges
have 12 to 15 credits of general calculus classes. 





Here's the
catch. 


In our example,
we were going exactly 50 miles per hour 


for the entire three hours. 


What if we were
speeding up and slowing down during the 3 hours?. 


What if we
wanted to be able to calculate how fast we were going 


at any point
in that 3 hours? 


What if we
wanted to know haw far we went in any part of those 3 hours? 


What if our
speed, er that is, velocity function was some kind of equation 


with
"exponents and logarithms and trig functions oh my." 





That's where
the 12 credits comes in. 


There are a
whole basket of tricks you need to learn 


so you can deal with the
messy algebra and trig equations 


your teacher might throw at you. 





That brings us
to the last secret about calculus. 


Calculus is
easy, it's just multiplying and dividing. 


The hard part
is the goofy algebra and trig equations you have to do it on. 





copyright 2005 Bruce
Kirkpatrick 
