Today’s soundtrack is Extol: The Blueprint Dives, a metal album with alternating singing and growls, fascinating polyrhythms, and layered song structures.
This evening, I’m reading Martin Gardner’s third (and final) preliminary chapter of Thompson’s Calculus Made Easy, titled “What is a Derivative?”
Algebraically speaking, Gardner (1998) says that a derivative is a function that tells us at what rate our dependent variable changes in relation to the independent variable’s rate of change. We can also describe a derivative geometrically: A derivative “determines the exact slope of the tangent to a function’s curve at any specified point along the curve” (Thompson, 1998, p. 34).
An example given is the well-known function y=x², the graph of which I’ve added on the right. Its derivative is 2x, because the dependent variable (y) is growing at 2x the rate of the independent variable (x).
That’s it for today! Next time, we’ll start in on the book proper!