Pseudodifferential operator

Okay kiddo, imagine you are sitting in front of a board with some numbers on it. Now, let's say you have an imaginary friend who can write equations and solve them quickly. This imaginary friend is like a special type of operator.

A pseudodifferential operator is also like your imaginary friend in that it works with equations, but it's a bit different. It's a type of operator that can turn one equation into another one with different numbers in it. It's like magic!

But there's a catch, just like how some numbers might be too hard for you to solve without the help of your imaginary friend, some equations are too hard for regular operators to solve. Instead, pseudodifferential operators come in and save the day! They're like superheroes of the math world.

So, in summary, a pseudodifferential operator is like an imaginary friend that can change equations into other equations with different numbers in them, and they're really good at solving really hard equations that other types of operators can't handle. Cool, right?