Calculus Why Calculus is Easy
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The 3 Secrets
Why Calculus is Easy

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:
 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

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