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The two main areas of
Calculus have scary sounding names. |
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Differential
Calculus - finding derivatives
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Integral
Calculus - finding integrals |
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This is such a
bunch of hype. |
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If
you have ever driven or even ridden in a car, |
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you understand both of
these things completely. |
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These pages will just fill in
the funny Calculus vocabulary |
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and funny Calculus notation. |
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Here
we go...
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Say you drive in a straight
line at 50 miles per hour for three hours.
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What
can you say about the trip other than you were probably bored silly.
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You can say how
far you went. |
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You can say how fast you were
going. |
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You probably also know where
you started and where you ended up. |
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Almost all of Integral
and Differential calculus |
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involves starting with one of these and
calculating another one. |
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If you know how fast
you were going |
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and how much time you were going that fast, |
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you can
figure out how far you went. |
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In the world up to now, |
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we have called that multiplying your velocity (a fancy name for speed) |
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by
the time you were traveling. |
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In the fancy
schmancy calculus world, |
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they call it integrating the velocity
function with respect to time. |
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Guess What? |
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They both mean
the same thing! |
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It's kind of
like calling a janitor a sanitation engineer. |
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The other half
of calculus is just as simple. |
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We know we
started in one place |
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and three hours later were in another place 150
miles away. |
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What was our
average speed? |
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In the world up
to now, |
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we called that dividing the distance traveled by the elapsed
time |
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to get the velocity (that fancy name for speed again). |
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In the fancy
schmancy calculus world, |
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they call it differentiating the distance
traveled function with respect to time |
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to get velocity. |
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And guess what
again? |
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They both mean
the same thing again! |
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More sanitation
engineers! |
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So we've got
two little secrets math types don't want you to catch on to, |
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at
least not right away |
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1 -
Differential calculus is just dividing |
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2 - Integral
Calculus is just multiplying |
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OK, Right about
now you're probably saying something like: |
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HOLD ON!
TIME OUT! STOP RIGHT THERE! |
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What's the
catch? There's got to be WAAAAY more to it than that. |
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Most colleges
have 12 to 15 credits of general calculus classes. |
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Here's the
catch. |
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In our example,
we were going exactly 50 miles per hour |
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for the entire three hours. |
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What if we were
speeding up and slowing down during the 3 hours?. |
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What if we
wanted to be able to calculate how fast we were going |
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at any point
in that 3 hours? |
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What if we
wanted to know haw far we went in any part of those 3 hours? |
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What if our
speed, er that is, velocity function was some kind of equation |
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with
"exponents and logarithms and trig functions oh my." |
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That's where
the 12 credits comes in. |
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There are a
whole basket of tricks you need to learn |
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so you can deal with the
messy algebra and trig equations |
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your teacher might throw at you. |
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That brings us
to the last secret about calculus. |
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Calculus is
easy, it's just multiplying and dividing. |
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The hard part
is the goofy algebra and trig equations you have to do it on. |
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copyright 2005 Bruce
Kirkpatrick |
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