Originally Posted by
Roobo
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While that 11 page document is relevant, it's a hard read for most. I like to help people by building on concepts they will be familiar with, something like a car moving over a certain distance is displacement (miles - s), this happens over a certain amount of time (hours - t). Plot these on a graph and show using some trigonometry that you can calculate the rate of change (d), specifically in this example the rate of displacement with respect to time (ds/dt) or the miles per hour and that this is the velocity. The time it takes to reach a given velocity is the rate of change of velocity with respect to time (dv/dt or ds^2/dt^2) and this is the acceleration. With a simple example of a car moving someone can understand the basic concepts of calculus that can be built on very quickly...
And we may be protesting too much about Shiva's reference. It was meant to illuminate a point, which it did. But it's fun to spool it out.
Richard Hamming writes well on the subject of, say, intuition behind math. From his "The Art of Probability for Scientists and Engineers", section 8.5 starts with:
"Idealists believe that the postulates determine the subject;
realists believe that the subject determines the postulates."
and continues with:
... I have long said, "If whether an airplane will fly or not depends on some function that arose in the design being Lebesgue integrable but not Riemann integrable, then I would not fly in that plane."
All of section 8.5 is worth reading.
If I recall correctly, he was known to be a bit of a crab. I find him refreshing.