Pseudodifferential operators

Okay kiddo, so think of numbers that you can add, subtract, multiply, and divide with. But sometimes we need to do more complex math like taking derivatives or integrals. That's where pseudodifferential operators come in!

Pseudodifferential operators are like special tools that help us do more complicated math with functions. They're special because they're not just normal operations like addition or multiplication. Instead, they use something called Fourier Transformations to do their job.

You know how when you mix all the colors together you get white? Well, the Fourier Transform is kind of like that, but for math! It takes a function and turns it into a bunch of different waves that are added together. And then we can use these waves to do fancy things like take derivatives or integrals.

Pseudodifferential operators use these waves to do things like find the rate of change of a function, or how it's changing over time. They're super useful in areas like physics or engineering where we need to solve complicated problems.

So that's what pseudodifferential operators are, kiddo. They're like special tools that let us do more advanced math with functions, using a special kind of math called Fourier Transformations.