Chapter 1. Functions
A function tells us how one quantity depends on other quantities. You've no doubt already seen plenty examples of functions, and you'll encounter many more as you continue your studies.
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The area of a circle depends on its radius.
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The height of a projectile depends on the time since its launch.
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The pressure of an ideal gas depends on its volume, its temperature, and the number of molecules.
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etc.
Our approach to functions will emphasize the ways in which we can combine simple functions to get more complicated examples. In particular we'll borrow the idea of a schematic from engineering to depict how functions fit together.
Schematics are indispensable for explaining subtle issues of dependence, but they are cumbersome for day-to-day calculations. Most of the time we'll stick to using a concise algebraic notation. But schematics will always be nearby: there is no Calculus without dependence!