Bump function

A bump function is a special kind of function that is shaped like a bump. It starts at zero, goes up to a certain height, and then comes back down to zero.

Now, imagine you have a function that is defined on all of space, but you only want it to be non-zero in a certain region. That's where the bump function comes in handy! You can use it to "bump up" the function only in that region, by multiplying the function by the bump function.

Here's how it works: if you multiply a function by a bump function, the result is a new function that is just like the original function, except it's zero outside of that certain region where you want it to be non-zero.

For example, let's say you have a function that describes the temperature in a room, and you only want the function to be non-zero near the window, where there's a draft. You can use a bump function to "bump up" the temperature function near the window, and make it zero everywhere else in the room.

So, think of a bump function as a tool that you can use to "shape" other functions, by making them non-zero in some regions and zero in others. It's like a way of highlighting certain parts of the function and saying "this is the important part!"