Euler integration

Imagine you have a toy car that you want to move from point A to point B along a road. But the road is bumpy and the car can't move too fast or it might tip over. So you decide to move the car in small steps, like taking baby steps. This way, you can make sure the car stays steady and you don't miss any details along the road.

Euler integration is just like taking those baby steps. It's a way for computers to move from one point to another in small steps when they're trying to solve a problem with a lot of complicated math.

For example, let's say you want to figure out how a ball will move when you throw it. The ball might go up, down, left, right, and all around, but you want to figure out exactly where it will be at a certain time. That's where Euler integration comes in.

It's like you divide up the ball's movement into tiny steps, each step representing a very short amount of time. Then you use math to figure out how much the ball moves in each step, and where it will be at the end of that step. Then you use that new position as a starting point for the next step, and so on.

It's kind of like drawing the ball's path, but instead of drawing a smooth curve, you draw a bunch of tiny straight lines. Each line represents the ball moving just a little bit more, until you've drawn a whole bunch of lines that connect and form a picture of where the ball went.

Euler integration is just one way to do this kind of math, but it's a simple and effective one that a lot of people use. Basically, it's just taking baby steps to make sure you get to where you want to go without tripping along the way.