This week's episode of Steven Strogatz's series -- Math: From Basic To Baffling -- is on calculus: Change We Can Believe In:
Calculus is the mathematics of change. It describes everything from the spread of epidemics to the zigs and zags of a well-thrown curveball. The subject is gargantuan — and so are its textbooks. Many exceed 1,000 pages and work nicely as doorstops.
But within that bulk you’ll find two ideas shining through. All the rest, as Rabbi Hillel said of the Golden Rule, is just commentary. Those two ideas are the “derivative” and the “integral.” Each dominates its own half of the subject, named in their honor as differential and integral calculus.
Roughly speaking, the derivative tells you how fast something is changing; the integral tells you how much it’s accumulating. They were born in separate times and places: integrals, in Greece around 250 B.C.; derivatives, in England and Germany in the mid-1600s. Yet in a twist straight out of a Dickens novel, they’ve turned out to be blood relatives — though it took almost two millennia to see the family resemblance.