Non-standard calculus

Okay kiddo, do you remember what calculus is? It’s a type of math where we learn how to find slopes, areas, and volumes of shapes. But there’s something called non-standard calculus which combines calculus with a bit of magic.

Imagine you want to figure out how fast a car is going by measuring how far it goes in a certain amount of time. But what if the car isn’t moving at a constant speed? That can make things tricky. Non-standard calculus helps us solve these types of problems by using something called infinitesimals.

Infinitesimals are really, really small numbers that are so tiny, they’re almost zero. But they’re not exactly zero. They’re like magic numbers that help us figure out how things change over time even when they don't change at a constant rate.

With non-standard calculus, we use these infinitesimals to help us find out more about curves and shapes. It’s like we’re zooming in really, really close and seeing how things change at every single point. This can help us make really accurate predictions and see things that we might not be able to see otherwise.

So, non-standard calculus is a really cool way to use math and magic to understand how things change and move over time, even when they’re not moving at a steady pace. It’s like having superpowers for math!