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
In regular algebra, we relate variables directly to each other. y=2x means that for every x there’s 2 y’s.
In physics, you often want to talk about how things change in relation to each other, or can only write down an equation talking about how things change. That’s where differential equations come in.
One way of writing something like this is to use a “d” with the variable, or a funny curly-looking “d”. So if you see “dx” it means a tiny little change in x. Mathematically speaking it’s an infinitesimally small change in x, but thinking about it as just “really really small” works for most purposes.
When we do this we can start writing equations like dy=2dx. This is a way of saying that if we change x by a teeny tiny amount, the amount that y changes by is twice as much. If we solve this we get the equation y=2x+C where C is some arbitrary constant, and as you can hopefully see (remember y=mx+b?), it’s a line with a slope of 2. It’s a line whose slope goes up twice as fast as it goes to the right, which is what we said when we started.
In physics this pops up *all the time*. We want to talk about how heat changes when we pump energy into a system, or how the speed of an object changes as we apply force, or how the resistance of a circuit changes as the current changes…the list is huge.
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