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What is calculus?

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Quick answer

Calculus is the mathematics of continuous change. It has two halves: differential calculus (rates of change, slopes) and integral calculus (accumulation, areas). It powers physics, engineering, economics, and more. Derivatives measure how fast something changes (e.g., speed = change in position).

Key things to understand

  1. Derivatives measure how fast something changes (e.g., speed = change in position).
  2. Integrals add up tiny pieces to find totals (e.g., area, or distance from speed).
  3. The two are linked by the Fundamental Theorem of Calculus.
  4. It was developed independently by Newton and Leibniz.

People also ask

What is a derivative?
A measure of an instantaneous rate of change — the slope of a curve at a point.
What is an integral?
A way to add up infinitely many tiny pieces to get a total, like the area under a curve.
Why is calculus useful?
It describes motion, growth, and change, underpinning physics, engineering, economics, and machine learning.