Quote:
Originally Posted by Botnst
Read what you wrote -- you described exactly why the calculus is a useful tool for rates of change.
let's say you want to model the atmosphere over time. the atmosphere is 3-d and curved parallel to the Earth's curvature. It is also dynamic -- density changes with temperature and chemistry and so forth. You have lots of ground data and you want to INTEGRATE in over time and through space.
let's ay you want to DERIVE a particular climatic condition from that data set at a particular time.
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The English language -- always full of nuance.
I was looking at some calculus on-line to refresh my memory. Oh mah God, half or more looks like Greek to me now.
I do remember getting a real kick out of that program I wrote, Newton's method for finding zero roots. Before the advent of computers, Good Lord, the application of that method to just one polynomial, let's say X to the fourth power on down, would take weeks of computation by hand.
Basically, you start with a number far to the left of the Y axis, plug it in, and reduce the number by regular increments until the sign of the result changes, meaning you just crossed the X axis. I would multiply the result of each trial and check to see if it was less than 0, meaning you had just entered a zone where the previous result was either positive or negative and the new result was the opposite sign, yielding a negative product. You then do a derivative of the graph at the point of the most recent result, the sign changing figure, and use that line as a pointer to take you back to the X axis at a point close to where the graph crossed, and repeat the process until you get as close to zero as you'd like. With my program, I could do equations starting with X to the tenth power in seconds. Oh man, what Newton or Copernicus would have given to be in my shoes.
Poor guys had to do lenghty cube root calculations and the like by hand.
