Math Playground
Calculus

Introduction

What is calculus? Tiny changes, instant rates and infinite sums — a tour.

Calculus is the math of change. Two big ideas: differentiation (instantaneous rate of change) and integration (accumulation of change).

Quick check

Calculus has two big ideas. Which pair is right?

Where you'll meet this

Calculus models anything that changes: speed and acceleration, population growth, electrical current, the area of an irregular shape, the path of a rocket. If a quantity moves, calculus describes how.

physicsengineeringeconomicsmodelling

What you'll meet

  • Limits — what a function approaches.
  • Derivatives — the slope / instantaneous rate of change.
  • Integrals — accumulated area under a curve.
  • The Fundamental Theorem — derivatives and integrals are inverses.
Recap
  • Calculus is the mathematics of change.
  • Differentiation = rate of change; integration = accumulation.
  • It all rests on the idea of a limit.

Newton and Leibniz invented it independently in the late 1600s — and have been arguing about who got there first ever since.