导数如何帮助我们精确描述运动

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Every discipline of science has its very own special language -- the way it communicates the ideas that it investigates.

For example, biology finds order in the world, by giving every living thing a name, in Latin.

Chemistry has a system of prefixes, suffixes, and numerals to tell you, in a word or two, the exact composition of an atom, or a compound.

But physics has to communicate its ideas differently. The language of physics, is mathematics.

Because, if you're trying to describe how the world works, you really have to know how things relate to each other in a mathematical way.

For example, we've been talking a lot about position, velocity, and acceleration, and how they're all connected.

Velocity is a measure of your change in position, and acceleration is a measure of your change in velocity.

They're connected -- one quality will describe how the other is changing. And the way we describe change in mathematics is through calculus.

Calculus explains how and why things change, using derivatives, which help you determine how an equation is changing, as well as with integrals, which you can use to calculate the area under a curve.

Derivatives and integrals themselves are closely connected. But let's start with derivatives.

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