This concept is used in many equations engineers love – it is the rate of change. The rate of change, the change in a value y per change in a value x. That almost makes me giddy just writing that.

dy/dx is used so frequently and is so powerful in engineering applications, from falling objects, to increasing pressure with depth in a liquid, to electrical applications, flow, strength of materials, and the list goes on.

To make things even more fantabulous, engineers will frequently evaluate rate of change of rate of change. Woah! What-what?

Think about measuring an object moving – falling or rolling – in one direction. We can measure that rate of change of position in terms of dy/dx, or change in distance over change in time. This is velocity, speed if it is in one direction. But what if the velocity changes? Then we measure the change in velocity over time, or in other words, the change in distance over time over time, or something like that. It makes more sense in an equation. This is acceleration. What happens if we measure the change in acceleration? Well, we may just be going back in time. No. I am kidding.

But rate of change is powerful, and engineers use it frequently. An engineer could even use it to measure non-engineering things, like the rate of change in time for, say, his wife to get ready to leave for the evening, with change in the years of marriage. We may save that one for another day. But it can be done.

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