Saturday, April 27, 2019

Someone says 'calculus' and you think ....


Someone says 'calculus' and you think ....
  • Yikes!
  • Get me out of here!
  • Calculus doesn't belong in the PMO
  • I took it in high school.... enough already!
Actually, some things are simpler than they appear:
  • Speedometers and direction
    You're driving. Got a smooth curve to go along (which could also be a straight line)?
    Want to find out which direction you're going at a particular point? Or, if you are changing direction? Or, how fast you're going

    "Derivative" is your answer!  (It's the most elementary calculus operation)

    The first derivative of distance with time (dx/T) is velocity (a small change in distance per a small change time); and  ...

    The first derivative distance with distance (dy/dx) is direction (a small change of distance vertically per a small change of distance horizontally.
    Zero means you a are going straight horizontally (dy = 0); infinity means you are going straight vertically (dx = 0); and any other number means you are going in a direction not either one of those)

  • Small stuff into a large thing
    Got bunch of small things -- or effects -- that need to be added, all of which are bounded by some curve (boundary)? Say, for example, the pixels in your camera or TV screen

    In effect, do you need to see the effect of a lot of small stuff co-existing, but from a distance so that each is not readily discernable? The so-called 10,000 ft view?

    "Integral" is your answer! And, taking an integral (meaning: calculate an integral) is what we call integrating or achieving integration. Integration melds all the little boundaries into something larger and more homogeneous
There you have it! Calculus 101. Not so difficult after all




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