Infinite difference method

The infinite difference method is a way of understanding how things change over time or space by looking at the differences between neighboring points. Imagine you are playing a game of hopscotch and you're jumping from one number to the next. If you want to know how much you moved, you can subtract the second number from the first number. This is like finding the difference between two neighboring points.

Now, let's say you want to know how things are changing over time or space. You can use the same idea of finding the difference between two neighboring points, but instead of just looking at two points you can look at an infinite number of neighboring points. This means you can see how things are changing very precisely.

For example, let's say you're studying the temperature of a room over time. You can take measurements every hour and use the infinite difference method to calculate how the temperature is changing from one hour to the next. By doing this, you can see if the temperature is increasing, decreasing or staying the same.

Another example could be studying the change in elevation over distance while hiking. You can take multiple measurements of elevation along your path, and use the infinite difference method to see how much elevation changes over a short distance. This can help you understand how steep the terrain is and whether you need to prepare extra for a steep climb.

Overall, the infinite difference method is a powerful tool that helps us understand how things change over time or space. By looking at an infinite number of neighboring points, we can get very precise information about how things are changing.