Finite difference coefficient is like a magic number that helps us figure out how to turn values in a table into a math equation.
Imagine you have a table of values representing something, like how many balloons you have at a party over time. Each row in the table represents a certain amount of time, and each column represents how many balloons you have at that time.
Now, let's say you want to use math to figure out how many balloons you'll have at a certain time in the future. You could use a fancy equation called a polynomial, but in order to do that you need some special numbers called finite difference coefficients.
These coefficients help us turn the values in our table into a polynomial equation that we can use to predict future values. They're kind of like puzzle pieces that fit together to make a complete picture.
So, to sum it up: finite difference coefficients are special numbers that help us turn a table of values into a math equation, which we can then use to predict future values. Pretty cool, huh?