What is the Derivative of Memory?

[spykitten]

Over burgers last night, Scotty asked me about my first-semester classes at business school next year. When I mentioned that Calculus is required, and used a great deal in Economics, he said, "What do you need to know about Calculus

Comments

[juuro]

This is a beautiful example of how learning, while well taken, doesn't really get internalised. It seems to me that the one key property of derivatives is taboo in high school, and often in universities, even. Moreover, it is the same property that is represented by "the slope of a line at a single point."

Derivative is the rate of change.

Derivative of place over time is the rate of change of location -- speed.
Derivative of speed over time is the rate of change of velocity -- acceleration.
Derivative of value over time is the rate of change of value -- inflation.

Or the converse operation, the integral. We are taught that the determined integral represents an area under a curve, or the volume within a surface, or so on. But what does it mean?

Integral is accumulation.

Integral of salary over time is total income over the period.
Integral of speed over time is distance traveled.
Integral of food over time is energy to be expended lest one wish to avoid accumulation of storage lipids around the waist.

[spykitten]

It's true - these (and all other) mathematical concepts are around us constantly, yet we never notice any of them.

And then students in math class complain, "Why do I need to learn this stuff? I'll never use it in the real world!" A pity that more teachers don't give examples like yours.