Infinitesimal calculus

Infinitesimal calculus is like magic that helps us understand how things change. Imagine you have a rollercoaster and you want to know how fast it's going at any point. Infinitesimal calculus can help you figure this out.

It's like breaking the rollercoaster ride down into tiny little bits, like breaking a cookie into crumbs. Each of these crumbs is called an infinitesimal. And we can use the crumbs to figure out how fast the rollercoaster is going at any point.

To do this, we use two main things - derivatives and integrals. A derivative tells us how fast something is changing at a specific point. So in our rollercoaster example, we can find the derivative at any point to figure out how fast the rollercoaster is going at that point.

An integral is like the opposite of a derivative. It helps us add up all the little pieces to figure out the whole thing. So if we wanted to find out how far the rollercoaster went during the ride, we could use an integral to add up all the little infinitesimal pieces along the way.

Infinitesimal calculus is really helpful in lots of fields, like engineering, physics, and economics. It's like having a superpower that lets you understand how the world works in a really cool and precise way.