# Introduction {.unnumbered}

## Why an engineer needs calculus

Whenever a quantity changes — a temperature falling, a tank filling, a population growing, a voltage decaying — two questions recur. *How fast* is it changing at this instant? And *how much* has built up now, or in the future? Calculus is the mathematics that answers these questions.

The first question, *how fast*, is asking about a **rate of change**: an amount of change per unit of time or distance. The calculus tool that reports a rate at a single instant is the **derivative**.

The second question, *how much*, is asking about **accumulation**: given a rate, adding it up across an interval to get a total. The calculus tool for that total is the **integral**.

A third situation arises constantly in engineering: when does the rate of change equal zero. Locating where a rate equals zero — setting a derivative to zero — is how one finds a **steady state**.