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
Sometimes it is very hard to look at a scenario and come up with a math equation that can tell you what that scenario is going to do. However, a lot of times it’s very easy to look at a scenario and come up with a math equation that describes what it is doing at that exact moment.
Lets use rabbits as an example. Imagine I tell you that I have five pairs of rabbits. Every month each pair of rabbits will produce five more pairs of rabbits.
This is a pretty simple scenario. If you’ve taken some algebra classes you might be able to recognize this as an exponential growth function, but lets just assume you have no idea how to come up with a math equation to describe how many rabbits there are at any given time. Just reading the scenario and coming up with an equation would be pretty difficult. Instead try and come up with an equation that explains how fast the rabbits are growing. That’s actually pretty easy.
r’ = 5*r
Where r’ is how fast the rabbits are growing per month, and r is the number of pairs of rabbits. This function has both rabbits (r) and the growth rate of rabbits (r’). We call an equation that contains the rate of a variable and that variable a differential equation.
Once we have a differential equation we can do a bunch of mathy things to it to turn it into a normal equation. The rabbit scenario was pretty simple, but there can be scenario’s where it can be almost impossible to come up with an equation without starting at a differential equation.
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