What Calculus Measures

Calculus answers two questions about changing quantities. Differential calculus asks: how fast is something changing right now? Integral calculus asks: how much has accumulated over an interval?

Two big questions

Calculus answers two questions about changing quantities. Differential calculus asks: how fast is something changing right now? Integral calculus asks: how much has accumulated over an interval?

If algebra describes static relationships, calculus describes motion, growth, area, and accumulation — the language of physics, economics, machine learning, and engineering.

You do not need to be a genius to learn calculus. You need comfort with functions, algebra, and the idea of "getting arbitrarily close."

Functions as machines

A function f assigns to each allowed input x exactly one output f(x). Graphs, tables, and formulas are three views of the same machine.

Domain: allowed inputs. Range: possible outputs.
Linear: constant rate. Quadratic: changing rate. Exponential: rate proportional to size.
Composition f(g(x)) feeds the output of g into f — central for the chain rule later.