My boyfriend is a huge nerd and likes to talk about physics. Most of the things he tells me I can understand but I still can’t grasp differential equations. I love talking about physics and programming with him and I just wanna understand. Thanks!
In: Physics
Regular equations talk about how some value changes as something else changes. If you’re driving a car, your speed will vary depending on your acceleration, and your distance will vary depending on your speed.
But lots of things are more complicated than that. Many things will change depending on a difference between things. For example, how quickly a mug of coffee cools depends on the difference between the temperature of the coffee and the temperature of the room. At first, this difference is big, meaning the coffee cools very quickly. But as it gets cooler, the difference gets smaller. This means it will cool more slowly. So maybe in the first 10mins it drops by 20 degrees, but in the next 10mins it only goes down by 5 degrees. This is what differential equations do. Instead of something being related to the value of something else, it’s related to how something else changes (over time or over space).
The one I’ve described is called the heat equation. Another common differential equation is the wave equation. Think of a spring. The force it pulls with is directly related to how stretched it is. If you pull it twice as far, it pulls back twice as hard. Force is related to acceleration. This means the acceleration is directly related to the distance you pull it. This results in something called sinusoidal motion, the classic boing motion of a spring. But it comes up everywhere!
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