3	Ghosts of departed quantities Calculus

What does it say?

To find the instantaneous rate of change of a quantity that varies with (say) time, calculate how its value changes over a short time interval and divide by the time concerned. Then let that interval become arbitrarily small.

Why is that important?

It provides a rigorous basis for calculus, the main way scientists model the natural world.

What did it lead to?

Calculation of tangents and areas. Formulas for volumes of solids and lengths of curves. Newton’s laws of motion, differential equations. The laws of conservation of energy and momentum. Most of mathematical physics.